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Title: The Modern Clock

Author: Ward L. Goodrich

Release date: February 24, 2020 [eBook #61494]

Language: English

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Transcriber's Note:

Midi music recordings have been provided containing the Westminster chimes shown
in Fig. 122. Click on the links below the figure to listen to the chimes if this is supported
by your browser or device.

The Modern Clock

A Study of Time Keeping Mechanism;
Its Construction, Regulation
and Repair.

BY WARD L. GOODRICH
Author of the Watchmaker’s Lathe, Its Use and Abuse.

WITH NUMEROUS ILLUSTRATIONS
AND DIAGRAMS

CHICAGO
Hazlitt & Walker, Publishers
1905

Copyrighted
1905
BY HAZLITT & WALKER.

TABLE OF CONTENTS
CHAP. PAGE
THE NECESSITY FOR BETTER SKILL AMONG
I. 3
CLOCKMAKERS.
II. THE NATURAL LAWS GOVERNING PENDULUMS. 10
III. COMPENSATING PENDULUMS. 23
THE CONSTRUCTION OF MERCURIAL
IV. 53
PENDULUMS.
REGULATIONS, SUSPENSIONS, CRUTCHES AND
V. 79
MINOR POINTS.
TORSION PENDULUMS FOR FOUR-HUNDRED DAY
VI. 91
CLOCKS.
VII. PECULIARITIES OF ANGULAR MEASUREMENT—
HOW TO READ
98
DRAWINGS.
VIII. THE GRAHAM OR DEAD BEAT ESCAPEMENT. 109
IX. LE PAUTE’S PIN WHEEL ESCAPEMENT. 135
X. THE RECOIL OR ANCHOR ESCAPEMENT. 141
XI. THE DENNISON OR GRAVITY ESCAPEMENT. 150
THE CYLINDER ESCAPEMENT AS APPLIED TO
XII. 163
CLOCKS.
THE DETACHED LEVER ESCAPEMENT AS APPLIED
XIII. 184
TO CLOCKS.
XIV. PLATES, PIVOTS AND TIME TRAINS. 198
XV. SPRINGS, WEIGHTS AND POWER. 264
XVI. MOTION WORK AND STRIKING TRAINS. 293
XVII. CLEANING AND REPAIRING CUCKOO CLOCKS. 319
SNAIL STRIKING WORK, ENGLISH, FRENCH AND
XVIII. 330
AMERICAN.

THE CONSTRUCTION OF SIMPLE AND PERPETUAL
XIX. 347
CALENDARS.
XX. HAMMERS, GONGS AND BELLS. 367
XXI. ELECTRIC CLOCKS AND BATTERIES. 376
XXII. THE CONSTRUCTION AND REPAIR OF DIALS. 426
XXIII. CLOCK CASING AND CASE REPAIRS. 446
XXIV. SOME HINTS ON MAKING A REGULATOR. 463
LIST OF ILLUSTRATIONS 495
INDEX 497

CHAPTER I.
THE NECESSITY FOR BETTER SKILL AMONG CLOCKMAKERS.

The need for information of an exact and reliable character in regard to
the hard worked and much abused clock has, we presume, been felt by
every one who entered the trade. This information exists, of course, but it is
scattered through such a wide range of publications and is found in them in
such a fragmentary form that by the time a workman is sufficiently
acquainted with the literature of the trade to know where to look for such
information he no longer feels the necessity of acquiring it.
The continuous decrease in the prices of watches and the consequent
rapid increase in their use has caused the neglect of the pendulum
timekeepers to such an extent that good clock men are very scarce, while
botches are universal. When we reflect that the average ‘life’ of a worker at
the bench is rarely more than twenty years, we can readily see that
information by verbal instruction is rapidly being lost, as each apprentice
rushes through clock work as hastily as possible in order to do watch work
and consequently each “watchmaker” knows less of clocks than his
predecessor and is therefore less fitted to instruct apprentices in his turn.
The striking clock will always continue to be the timekeeper of the
household and we are still dependent upon the compensating pendulum, in
conjunction with the fixed stars, for the basis of our timekeeping system,
upon which our commercial and legal calendars and the movements of our
ships and railroad trains depend, so that an accurate knowledge of its
construction and behavior forms the essential basis of the largest part of our
business and social systems, while the watches for which it is slighted are
themselves regulated and adjusted at the factories by the compensated
pendulum.
The rapid increase in the dissemination of “standard time” and the
compulsory use of watches having a maximum variation of five seconds a
week by railway employees has so increased the standard of accuracy
demanded by the general public that it is no longer possible to make
careless work “go” with them, and, if they accept it at all, they are apt to

make serious deductions from their estimate of the watchmaker’s skill and
immediately transfer their custom to some one who is more thorough.
The apprentice, when he first gets an opportunity to examine a clock
movement, usually considers it a very mysterious machine. Later on, if he
handles many clocks of the simple order, he becomes tolerably familiar
with the time train; but he seldom becomes confident of his ability
regarding the striking part, the alarm and the escapement, chiefly because
the employer and the older workmen get tired of telling him the same things
repeatedly, or because they were similarly treated in their youth, and
consider clocks a nuisance, any how, never having learned clock work
thoroughly, and therefore being unable to appreciate it. In consequence of
such treatment the boy makes a few spasmodic efforts to learn the portions
of the business that puzzle him, and then gives it up, and thereafter does as
little as possible to clocks, but begs continually to be put on watch work.
We know of a shop where two and sometimes three workmen (the best
in the shop, too) are constantly employed upon clocks which country
jewelers have failed to repair. If clock work is dull they will go upon watch
work (and they do good work, too), but they enjoy the clocks and will do
them in preference to watches, claiming that there is greater variety and
more interest in the work than can be found in fitting factory made material
into watches, which consist of a time train only. Two of these men have
become famous, and are frequently sent for to take care of complicated
clocks, with musical and mechanical figure attachments, tower, chimes, etc.
The third is much younger, but is rapidly perfecting himself, and is already
competent to rebuild minute repeaters and other sorts of the finer kinds of
French clocks. He now totally neglects watch work, saying that the clocks
give him more money and more fun.
We are confident that this would be also the case with many another
American youth if he could find some one to patiently instruct him in the
few indispensable facts which lie at the bottom of so much that is
mysterious and from which he now turns in disgust. The object of these
articles is to explain to the apprentice the mysteries of pendulums,
escapements, gearing of trains, and the whole technical scheme of these
measurers of time, in such a way that hereafter he may be able to answer his
own questions, because he will be familiar with the facts on which they
depend.

Many workmen in the trade are already incompetent to teach clockwork
to anybody, owing to the slighting process above referred to; and the
frequent demands for a book on clocks have therefore induced the writer to
undertake its compilation. Works on the subject—nominally so, at least—
are in existence, but it will generally be found on examination that they are
written by outsiders, not by workmen, and that they treat the subject
historically, or from the standpoint of the artistic or the curious. Any
information regarding the mechanical movements is fragmentary, if found
in them at all, and they are better fitted for the amusement of the general
public than for the youth or man who wants to know “how and why.” These
facts have impelled the writer to ignore history and art in considering the
subject; to treat the clock as an existing mechanism which must be
understood and made to perform its functions correctly; and to consider
cases merely as housings of mechanism, regardless of how beautiful,
strange or commonplace those housings may be.
We have used the word “compile” advisedly. The writer has no new
ideas or theories to put forth, for the reason that the mechanism we are
considering has during the last six hundred years had its mathematics
reduced to an exact science; its variable factors of material and mechanical
movements developed according to the laws of geometry and trigonometry;
its defects observed and pointed out; its performances checked and
recorded. To gather these facts, illustrate and explain them, arrange them in
their proper order, and point out their relative importance in the whole sum
of what we call a clock, is therefore all that will be attempted. In doing this
free use has been made of the observations of Saunier, Reid, Glasgow,
Ferguson, Britten, Riefler and others in Europe and of Jerome, Playtner,
Finn, Learned, Ferson, Howard and various other Americans. The work is
therefore presented as a compilation, which it is hoped will be of service in
the trade.
In thus studying the modern American clocks, we use the word
American in the sense of ownership rather than origin, the clocks which
come to the American workmen to-day have been made in Germany,
France, England and America.
The German clocks are generally those of the Schwartzwald (or Black
Forest) district, and differ from others in their structure, chiefly in the
following particulars: The movement is supported by a horizontal seatboard

in the upper portion of the case. The wooden trains of many of the older
type instead of being supported by plates are held in position by pillars, and
these pillars are held in position by top and bottom boards. In the better
class of wooden clocks the pivot holes in the pillars are bushed with brass
tubing, while the movement has a brass ’scape wheel, steel wire pivots and
lantern pinions of wood, with steel trundles. In all these clocks the front
pillars are friction-tight, and are the ones to be removed when taking down
the trains. Both these and the modern Swartzwald brass movements use a
sprocket wheel and chain for the weights and have exposed pendulums and
weights.
The French clocks are of two classes, pendules and carriage clocks, and
both are liable to develop more hidden crankiness and apparently causeless
refusals to go than ever occurred to all the English, German and American
clocks ever put together. There are many causes for this, and unless a man is
very new at the business he can tell stories of perversity, that would make a
timid apprentice want to quit. Yet the French clocks, when they do go, are
excellent timekeepers, finely finished, and so artistically designed that they
make their neighbors seem very clumsy by comparison. They are found in
great variety, time, half-hour and quarter-hour strike, musical and repeating
clocks being a few of the general varieties. The pendulums are very short,
to accommodate themselves to the artistic needs of the cases, and nearly all
have the snail strike instead of the count wheel. The carriage clocks have
watch escapements of cylinder or lever form, and the escapement is
frequently turned at right angle by means of bevel gears, or contrate wheel
and pinion, and placed on top of the movement.
The English clocks found in America are generally of the “Hall” variety,
having heavy, well finished movements, with seconds pendulum and
frequently with calendar and chime movements. They, like the German, are
generally fitted with weights instead of springs. There are a few English
carriage clocks, fitted with springs and fuzees, though most of them, like
the French, have springs fitted in going barrels.
The American clocks, with which the apprentice will naturally have
most to do, may be roughly divided into time, time alarm, time strike, time
strike alarm, time calendar and electric winding. The American factories
generally each make about forty sizes and styles of movements, and case
them in many hundreds of different ways, so that the workman will

frequently find the same movement in a large number of clocks, and he will
soon be able to determine from the characteristics of the movement what
factory made the clock, and thus be able to at once turn to the proper
catalogue if the name of the maker be erased, as frequently happens.
This comparative study of the practice of different factories will prove
very interesting, as the movement comes to the student after a period of
prolonged and generally severe use, which is calculated to bring out any
existing defects in construction or workmanship; and having all makes of
clocks constantly passing through his hands, each exhibiting a characteristic
defect more frequently than any other, he is in a much better position to
ascertain the merits and defects of each maker than he would be in any
factory.
Having thus briefly outlined the kinds of machinery used in measuring
time, we will now turn our attention to the examination of the theoretical
and mechanical construction of the various parts.
The man who starts out to design and build a clock will find himself
limited in three particulars: It must run a specified time; the arbor carrying
the minute hand must turn once in each hour; the pendulum must be short
enough to go in the case. Two of these particulars are changeable according
to circumstances; the length of time run may be thirty hours, eight, thirty,
sixty or ninety days. The pendulum may be anywhere from four inches to
fourteen feet, and the shorter it is the faster it will go. The one definite point
in the time train is that the minute hand must turn once in each hour. We
build or alter our train from this point both ways, back through changeable
intermediate wheels and pinions to the spring or weight forming the source
of power, and forward from it through another changeable series of wheels
and pinions to the pendulum. Now as the pendulum governs the rate of the
clock we will commence with that and consider it independently.

CHAPTER II.
THE NATURAL LAWS GOVERNING PENDULUMS.

Length of Pendulum.—A pendulum is a falling body and as such is
subject to the laws which govern falling bodies. This statement may not be
clear at first, as the pendulum generally moves through such a small arc that
it does not appear to be falling. Yet if we take a pendulum and raise the ball
by swinging it up until the ball is level with the point of suspension, as in
Fig. 1, and then let it go, we shall see it fall rapidly until it reaches its
lowest point, and then rise until it exhausts the momentum it acquired in
falling, when it will again fall and rise again on the other side; this process
will be repeated through constantly smaller arcs until the resistance of the
air and that of the pendulum spring shall overcome the other forces which
operate to keep it in motion and it finally assumes a position of rest at the
lowest point (nearest the earth) which the pendulum rod will allow it to
assume. When it stops, it will be in line between the center of the earth
(center of gravity) and the fixed point from which it is suspended. True, the
pendulum bob, when it falls, falls under control of the pendulum rod and
has its actions modified by the rod; but it falls just the same, no matter how
small its arc of motion may be, and it is this influence of gravity—that force
which makes any free body move toward the earth’s center—which keeps
the pendulum constantly returning to its lowest point and which governs
very largely the time taken in moving. Hence, in estimating the length of a
pendulum, we must consider gravity as being the prime mover of our
pendulum.

Fig. 1. Dotted lines show path of pendulum.
The next forces to consider are mass and weight, which, when put in
motion, tend to continue that motion indefinitely unless brought to rest by
other forces opposing it. This is known as momentum. A heavy bob will
swing longer than a light one, because the momentum stored up during its
fall will be greater in proportion to the resistance which it encounters from
the air and the suspension spring.
As the length of the rod governs the distance through which our bob is
allowed to fall, and also controls the direction of its motion, we must
consider this motion. Referring again to Fig. 1, we see that the bob moves
along the circumference of a circle, with the rod acting as the radius of that
circle; this opens up another series of facts. The circumference of a circle
equals 3.1416 times its diameter, and the radius is half the diameter (the
radius in this case being the pendulum rod). The areas of circles are
proportional to the squares of their diameters and the circumferences are
also proportional to their areas. Hence, the lengths of the paths of bobs
moving along these circumferences are in proportion to the squares of the
lengths of the pendulum rods. This is why a pendulum of half the length
will oscillate four times as fast.
Now we will apply these figures to our pendulum. A body falling in
vacuo, in London, moves 32.2 feet in one second. This distance has by

common consent among mathematicians been designated as g. The
circumference of a circle equals 3.1416 times its diameter. This is
represented as π. Now, if we call the time t, we shall have the formula:
t = π √ (1/g)
Substituting the time, one second, for t, and doing the same with the
others, we shall have:
(32.2 ft.)
1 = ————— = 3.2616 feet.
(3.1416)²
Turning this into its equivalent in inches by multiplying by 12, we shall
have 39.1393 inches as the length of a one-second pendulum at London.
Now, as the force of gravity varies somewhat with its distance from the
center of the earth, we shall find the value of g in the above formula varying
slightly, and this will give us slightly different lengths of pendulum at
different places. These values have been found to be as follows:
Inches.
The Equator is 39
Rio de Janeiro 39.01
Madras 39.02
New York 39.1012
Paris 39.13
London 39.14
Edinburgh 39.15
Greenland 39.20
North and South Pole 39.206

Now, taking another look at our formula, we shall see that we may get
the length of any pendulum by multiplying π (which is 3.1416) by the
square of the time required: To find the length of a pendulum to beat three
seconds:
3² = 9.
39.1393 × 9 = 352.2537 inches = 29.3544 feet.

A pendulum beating two-thirds of a second, or 90 beats:
(⅔)² = ⁴⁄₉
39.1393 × 4
————— = 17.3952 inches.
9
A pendulum beating half-seconds or 120 beats:
(½)² = ¼
39.1393 × 1
—————— = 9.7848 inches.
4
Center of Oscillation.—Having now briefly considered the basic facts
governing the time of oscillation of the pendulum, let us examine it still
further. The pendulum shown in Fig. 1 has all its weight in a mass at its end,
but we cannot make a pendulum that way to run a clock, because of
physical limitations. We shall have to use a rod stiff enough to transmit
power from the clock movement to the pendulum bob and that rod will
weigh something. If we use a compensated rod, so as to keep it the same
length in varying temperature, it may weigh a good deal in proportion to the
bob. How will this affect the pendulum?
If we suspend a rod from its upper end and place along-side of it our
ideal pendulum, as in Fig. 2, we shall find that they will not vibrate in equal
times if they are of equal lengths. Why not? Because when the rod is
swinging (being stiff) a part of its weight rests upon the fixed point of
suspension and that part of the rod is consequently not entirely subject to
the force of gravity. Now, as the time in which our pendulum will swing
depends upon the distance of the effective center of its mass from the point
of suspension, and as, owing to the difference in construction, the center of
mass of one of our pendulums is at the center of its ball, while that of the
other is somewhere along the rod, they will naturally swing in different
times.

Fig. 2. Two pendulums of equal length but unequal vibration.
B, center of oscillation for both pendulums.

Fig. 3.
Our other pendulum (the rod) is of the same size all the way up and the
center of its effective mass would be the center of its weight (gravity) if it
were not for the fact which we stated a moment ago that part of the weight
is upheld and rendered ineffective by the fixed support of the pendulum rod,
all the while the pendulum is not in a vertical position. If we support the rod
in a horizontal position, as in Fig. 3, by holding up the lower end, the point
of suspension, A, will support half the weight of the rod; if we hold it at 45
degrees the point of suspension will hold less than half the weight of the rod
and more of the rod will be affected by gravity; and so on down until we
reach the vertical or up and down position. Thus we see that the force of
gravity pulling on our pendulum varies in its effects according to the
position of the rod and consequently the effective center of its mass also
varies with its position and we can only calculate what this mean (or
average) position is by a long series of calculations and then taking an
average of these results.

We shall find it simpler to measure the time of swing of the rod which
we will do by shortening our ball and cord until it will swing in the same
time as the rod. This will be at about two-thirds of the length of the rod, so
that the effective length of our rod is about two-thirds of its real length. This
effective length, which governs the time of vibration, is called the
theoretical length of the pendulum and the point at which it is located is
called its center of oscillation. The distance from the center of oscillation to
the point of suspension is called the theoretical length of the pendulum and
is always the distance which is given in all tables of lengths of pendulums.
This length is the one given for two reasons: First, because, it is the
timekeeping length, which is what we are after, and second, because, as we
have just seen in Fig. 3, the real length of the pendulum increases as more
of the weight of the instrument is put into the rod. This explains why the
heavy gridiron compensation pendulum beating seconds so common in
regulators and which measures from 56 to 60 inches over all, beats in the
same time as the wood rod and lead bob measuring 45 inches over all, while
one is apparently a third longer than the other.
Table Showing the Length of a Simple Pendulum
That performs in one hour any given number
of oscillations, from 1 to 20,000, and the
variation in this length that will occasion a
difference of 1 minute in 24 hours.

Calculated by E. Gourdin.

Number of Variation in Length for
Length in
Oscillations One Minute in 24 Hours
Millimeters.
per Hour. in Millimeters.
20,000 32.2 0.04
19,000 35.7 0.05
18,000 39.8 0.05
17,900 40.2 0.06
17,800 40.7 0.06
17,700 41.1 0.06

Number of Variation in Length for
Length in
Oscillations One Minute in 24 Hours
Millimeters.
per Hour. in Millimeters.
17,600 41.6 0.06
17,500 42.1 0.06
17,400 42.4 0.06
17,300 43.0 0.06
17,200 43.5 0.06
17,100 44.0 0.06
17,000 44.6 0.06
16,900 45.1 0.06
16,800 45.7 0.06
16,700 46.3 0.06
16,600 46.7 0.07
16,500 47.3 0.07
16,400 47.9 0.07
16,300 48.5 0.07
16,200 49.1 0.07
16,100 49.7 0.07
16,000 50.0 0.07
15,900 51.0 0.07
15,800 51.6 0.07
15,700 52.3 0.07
15,600 52.9 0.07
15,500 53.6 0.07
15,400 54.3 0.08
15,300 55.0 0.08
15,200 55.7 0.08
15,100 56.5 0.08
15,000 57.3 0.08
14,900 58.0 0.08
14,800 58.8 0.08
14,700 59.6 0.08

Number of Variation in Length for
Length in
Oscillations One Minute in 24 Hours
Millimeters.
per Hour. in Millimeters.
14,600 60.4 0.08
14,500 61.3 0.08
14,400 62.1 0.09
14,300 63.0 0.09
14,200 63.9 0.09
14,100 64.8 0.09
14,000 65.7 0.09
13,900 66.7 0.09
13,800 67.6 0.09
13,700 68.6 0.09
13,600 69.6 0.09
13,500 70.7 0.09
13,400 71.7 0.10
13,300 72.8 0.10
13,200 73.9 0.10
13,100 75.1 0.10
13,000 76.2 0.10
12,900 77.4 0.11
12,800 78.6 0.11
12,700 79.9 0.11
12,600 81.1 0.11
12,500 82.4 0.11
12,400 83.8 0.11
12,300 85.1 0.12
12,200 86.5 0.12
12,100 88.0 0.12
12,000 89.5 0.12
11,900 91.0 0.12
11,800 92.5 0.13
11,700 94.1 0.13

Number of Variation in Length for
Length in
Oscillations One Minute in 24 Hours
Millimeters.
per Hour. in Millimeters.
11,600 95.7 0.13
11,500 97.4 0.13
11,400 99.1 0.13
11,300 100.9 0.14
11,200 102.7 0.14
11,100 104.5 0.14
11,000 106.5 0.14
10,900 108.4 0.15
10,800 110.5 0.15
10,700 112.5 0.15
10,600 114.6 0.16
10,500 116.8 0.16
10,400 119.1 0.16
10,300 121.4 0.17
10,200 123.8 0.17
10,100 126.3 0.17
10,000 128.8 0.18
9,900 131.4 0.18
9,800 134.1 0.18
9,700 136.9 0.19
9,600 139.8 0.19
9,500 142.7 0.19
9,400 145.8 0.20
9,300 148.9 0.20
9,200 152.2 0.21
9,100 155.5 0.21
9,000 159.0 0.22
8,900 162.6 0.22
8,800 166.3 0.23
8,700 170.2 0.23

Number of Variation in Length for
Length in
Oscillations One Minute in 24 Hours
Millimeters.
per Hour. in Millimeters.
8,600 173.7 0.24
8,500 178.3 0.24
8,400 182.5 0.25
8,300 187.0 0.25
8,200 191.5 0.26
8,100 196.3 0.27
8,000 201.3 0.27
7,900 206.4 0.28
7,800 211.7 0.29
7,700 217.2 0.30
7,600 223.0 0.30
7,500 229.0 0.31
7,400 235.2 0.32
7,300 241.7 0.33
7,200 248.5 0.34
7,100 255.7 0.35
7,000 262.9 0.36
6,900 270.5 0.37
6,800 278.6 0.38
6,700 286.9 0.39
6,600 295.7 0.40
6,500 304.9 0.41
6,400 314.5 0.43
6,300 324.5 0.44
6,200 335.1 0.46
6,100 346.2 0.47
6,000 357.8 0.48
5,900 370.0 0.50
5,800 382.9 0.52
5,700 396.4 0.54

Number of Variation in Length for
Length in
Oscillations One Minute in 24 Hours
Millimeters.
per Hour. in Millimeters.
5,600 410.7 0.56
5,500 425.8 0.58
5,400 440.1 0.60
5,300 458.5 0.62
5,200 476.3 0.65
5,100 495.2 0.67
5,000 515.2 0.70
4,900 536.5 0.73
4,800 559.1 0.76
4,700 583.1 0.79
4,600 608.7 0.83
4,500 636.1 0.86
4,400 665.3 0.90
4,300 696.7 0.95
4,200 730.2 0.99
4,100 766.3 1.04
4,000 805.0 1.09
3,950 825.5 1.12
3,900 846.8 1.15
3,850 869.0 1.16
3,800 892.0 1.21
3,750 915.9 1.25
3,700 940.1 1.28
3,650 966.8 1.31

Table of the Length of a Simple Pendulum,
(CONTINUED.)

To Produce in 24 Hours
Number of 1 Minute.
Length in
Oscillations Loss, Gain,
Meters.
per Hour. Lengthen by Shorten by
Millimeters. Millimeters.
3,600 0.9939 1.38 1.32
3,550 1.0221 1.42 1.36
3,500 1.0515 1.46 1.40
3,450 1.0822 1.50 1.44
3,400 1.1143 1.55 1.48
3,350 1.1477 1.60 1.53
3,300 1.1828 1.64 1.57
3,250 1.2194 1.69 1.62
3,200 1.2578 1.75 1.67
3,150 1.2981 1.80 1.73
3,100 1.3403 1.86 1.78
3,050 1.3846 1.93 1.84
3,000 1.4312 1.99 1.90
2,900 1.5316 2.13 2.04
2,800 1.6429 2.28 2.18
2,700 1.7669 2.46 2.35
2,600 1.9054 2.65 2.53
2,500 2.0609 2.87 2.74
2,400 2.2362 3.11 2.97
2,300 2.4349 3.38 3.24
2,200 2.6612 3.70 3.54
2,100 2.9207 4.06 3.88
2,000 3.2201 4.48 4.28
by Meters. by Meters.
1,900 3.568 0.0050 0.0048
1,800 3.975 0.0055 0.0053
1,700 4.457 0.0062 0.0059
1,600 5.031 0.0070 0.0067

To Produce in 24 Hours
Number of 1 Minute.
Length in
Oscillations Loss, Gain,
Meters.
per Hour. Lengthen by Shorten by
Millimeters. Millimeters.
1,500 5.725 0.0080 0.0076
1,400 6.572 0.0091 0.0087
1,300 7.622 0.0106 0.0101
1,200 8.945 0.0124 0.0119
1,100 10.645 0.0148 0.0142
1,000 12.880 0.0179 0.0171
900 15.902 0.0221 0.0211
800 20.126 0.0280 0.0268
700 26.287 0.0365 0.0350
600 35.779 0.0497 0.0476
500 51.521 0.0716 0.0685
400 80.502 0.1119 0.1071
300 143.115 0.1989 0.1903
200 322.008 0.4476 0.4282
100 1,288.034 1.7904 1.7131
60 3,577.871 4.9732 4.7586
50 5,152.135 7.1613 6.8521
1 12,880,337.930 17,903.6700 17,130.8500

In the foregoing tables all dimensions are given in meters and
millimeters. If it is desirable to express them in feet and inches, the
necessary conversion can be at once effected in any given case by
employing the following conversion table, which will prove of considerable
value to the watchmaker for various purposes:
Conversion Table of Inches, Millimeters and French Lines.

Inches expressed in
Millimeters and French Lines.
Equal to
Inches.
Millimeters. French Lines.
1 25.39954 11.25951
2 50.79908 22.51903
3 76.19862 33.77854
4 101.59816 45.03806
5 126.99771 56.29757
6 152.39725 67.55709
7 177.79679 78.81660
8 203.19633 90.07612
9 228.59587 101.33563
10 253.99541 112.59516
Millimeters expressed in
Inches and French Lines.
Equal to
Millimeters.
Inches. French Lines.
1 0.0393708 0.44329
2 0.0787416 0.88659
3 0.1181124 1.32989
4 0.1574832 1.77318
5 0.1968539 2.21648
6 0.2362247 2.65978
7 0.2755955 3.10307
8 0.3149664 3.54637
9 0.3543371 3.98966
10 0.3937079 4.43296
French Lines expressed in
Inches and Millimeters.
Equal to
French Lines.
Inches. Millimeters.

Inches expressed in
Millimeters and French Lines.
Equal to
Inches.
Millimeters. French Lines.
1 0.088414 2.25583
2 0.177628 4.51166
3 0.266441 6.76749
4 0.355255 9.02332
5 0.444069 11.27915
6 0.532883 13.53497
7 0.621697 15.79080
8 0.710510 18.04663
9 0.799324 20.30246
10 0.888138 22.55829
11 0.976952 24.81412
12 1.065766 27.06995

Center of Gravity.—The watchmaker is concerned only with the
theoretical or timekeeping lengths of pendulums, as his pendulum comes to
him ready for use; but the clock maker who has to build the pendulum to fit
not only the movement, but also the case, needs to know more about it, as
he must so distribute the weight along its length that it may be given a
length of 60 inches or of 44 inches, or anything between them, and still beat
seconds, in the case of a regulator. He must also do the same thing in other
clocks having pendulums which beat other numbers than 60. Therefore he
must know the center of his weights; this is called the center of gravity. This
center of gravity is often confused by many with the center of oscillation as
its real purpose is not understood. It is simply used as a starting point in
building pendulums, because there must be a starting point, and this point is
chosen because it is always present in every pendulum and it is convenient
to work both ways from the center of weight or gravity. In Fig. 2 we have
two pendulums, in one of which (the ball and string) the center of gravity is
the center of the ball and the center of oscillation is also at the center

(practically) of the ball. Such a pendulum is about as short as it can be
constructed for any given number of oscillations. The other (the rod) has its
center of gravity manifestly at the center of the rod, as the rod is of the same
size throughout; yet we found by comparison with the other that its center
of oscillation was at two-thirds the length of the rod, measured from the
point of suspension, and the real length of the pendulum was consequently
one-half longer than its timekeeping length, which is at the center of
oscillation. This is farther apart than the center of gravity and oscillation
will ever get in actual practice, the most extreme distance in practice being
that of the gridiron pendulum previously mentioned. The center of gravity
of a pendulum is found at that point at which the pendulum can be balanced
horizontally on a knife edge and is marked to measure from when cutting
off the rod.
The center of oscillation of a compound pendulum must always be
below its center of gravity an amount depending upon the proportions of
weight between the rod and the bob. Where the rod is kept as light as it
should be in proportion to the bob this difference should come well within
the limits of the adjusting screw. In an ordinary plain seconds pendulum,
without compensation, with a bob of eighteen or twenty pounds and a rod
of six ounces, the difference in the two points is of no practical account, and
adjustments for seconds are within the screw of any ordinary pendulum, if
the screw is the right length for safety, and the adjusting nut is placed in the
middle of the length of the screw threads when the top of the rod is cut off,
to place the suspension spring by measurement from the center of gravity as
has been already described; also a zinc and iron compensation is within
range of the screw if the compensating rods are not made in undue weight
to the bob. The whole weight of the compensating parts of a pendulum can
be safely made within one and a half pounds or lighter, and carry a bob of
twenty-five pounds or over without buckling the rods, and the two points,
the center of gravity and the center of oscillation, will be within the range of
the screw.
There are still some other forces to be considered as affecting the
performance of our pendulum. These are the resistance to its momentum
offered by the air and the resistance of the suspension spring.
Barometric Error.—If we adjust a pendulum in a clock with an air-
tight case so that the pendulum swings a certain number of degrees of arc,

as noted on the degree plate in the case at the foot of the pendulum, and
then start to pump out the air from the case while the clock is running, we
shall find the pendulum swinging over longer arcs as the air becomes less
until we reach as perfect a vacuum as we can produce. If we note this point
and slowly admit air to the case again we shall find that the arcs of the
pendulum’s swing will be slowly shortened until the pressure in the case
equals that of the surrounding air, when they will be the same as when our
experiment was started. If we now pump air into our clock case, the
vibrations will become still shorter as the pressure of the air increases,
proving conclusively that the resistance of the air has an effect on the
swinging of the pendulum.
We are accustomed to measure the pressure of the air as it changes in
varying weather by means of the barometer and hence we call the changes
in the swing of the pendulum due to varying air pressure the “barometric
error.” The barometric error of pendulums is only considered in the very
finest of clocks for astronomical observatories, master clocks for watch
factories, etc., but the resistance of the air is closely considered when we
come to shape our bob. This is why bobs are either double-convex or
cylindrical in shape, as these two forms offer the least resistance to the air
and (which is more important) they offer equal resistance on both sides of
the center of the bob and thus tend to keep the pendulum swinging in a
straight line back and forth.

Fig. 4. A, arc of circle. B, cycloid path of pendulum, exaggerated.
The Circular Error.—As the pendulum swings over a greater arc it
will occupy more time in doing it and thus the rate of the clock will be
affected, if the barometric changes are very great. This is called the circular
error. In ancient times, when it was customary to make pendulums vibrate
at least fifteen degrees, this error was of importance and clock makers tried

to make the bob take a cycloidal path, as is shown in Fig. 4, greatly
exaggerated. This was accomplished by suspending the pendulum by a cord
which swung between cycloidal checks, but it created so much friction that
it was abandoned in favor of the spring as used to-day. It has since been
proved that the long and short arcs of the pendulum’s vibration are
practically isochronous (with a spring of proper length and thickness) up to
about six degrees of arc (three degrees each side of zero on the degree plate
at the foot of the pendulum) and hence small variations of power in spring
operated clocks and also the barometric error are taken care of, except for
greatly increased variations of power, or for too great arcs of vibration.
Here we see the reasons for and the amount of swing we can properly give
to our pendulum.
Temperature Error.—The temperature error is the greatest which we
shall have to consider. It is this which makes the compound pendulum
necessary for accurate time, and we shall consequently give it a great
amount of space, as the methods of overcoming it should be fully
understood.
Expansion of Metals.—The materials commonly used in making
pendulums are wood (deal, pine and mahogany), steel, cast iron, zinc, brass
and mercury. Wood expands .0004 of its length between 32° and 212° F.;
lead, .0028; steel, .0011; mercury, .0180; zinc, .0028; cast iron, .0011; brass,
.0020. Now the length of a seconds pendulum, by our tables (3600 beats per
hour) is 0.9939 meter; if the rod is brass it will lengthen .002 with such a
range of temperature. As this is practically two-thousandths of a meter, this
is a gain of two millimeters, which would produce a variation of one minute
and forty seconds every twenty-four hours; consequently a brass rod would
be a very bad one.
If we take two of these materials, with as wide a difference in expansion
ratios as possible, and use the least variable for the rod and the other for the
bob, supporting it at the bottom, we can make the expansion of the rod
counterbalance the expansion of the bob and thus keep the effective length
of our pendulum constant, or nearly so. This is the theory of the
compensating pendulum.

CHAPTER III.
COMPENSATING PENDULUMS.

As the pendulum is the means of regulating the time consumed in
unwinding the spring or weight cord by means of the escapement, passing
one tooth of the escape wheel at each end of its swing, it will readily be
seen that lengthening or shortening the pendulum constitutes the means of
regulating the clock; this would make the whole subject a very simple
affair, were it not that the reverse proposition is also true; viz.; Changing the
length of the pendulum will change the rate of the clock and after a proper
rate has been obtained further changes are extremely undesirable. This is
what makes the temperature error spoken of in the preceding chapter so
vexatious where close timing is desired and why as a rule, a well
compensated pendulum costs more than the rest of the clock. The sole
reason for the business existence of watch and clockmakers lies in the
necessity of measuring time, and the accuracy with which it may be done
decides in large measure the value of any watchmaker in his community.
Hence it is of the utmost importance that he shall provide himself with an
accurate means of measuring time, as all his work must be judged finally by
it, not only while he is working upon time-measuring devices, but also after
they have passed into the possession of the general public.
A good clock is one of the very necessary foundation elements,
contributing very largely to equip the skilled mechanic and verify his work.
Without some reliable means to get accurate mean time a watchmaker is
always at sea—without a compass—and has to trust to his faith and a large
amount of guessing, and this is always an embarrassment, no matter how
skilled he may be in his craft, or adept in guessing. What I want to call
particular attention to is the unreliable and worthless character of the
average regulator of the present day. A good clock is not necessarily a high
priced instrument and it is within the reach of most watchmakers. A
thoroughly good and reliable timekeeper of American make is to be had
now in the market for less than one hundred dollars, and the only serious
charge that can be made against these clocks is that they cost the consumer

too much money. Any of them are thirty-three and a third per cent higher
than they should be. About seventy-five dollars will furnish a thoroughly
good clock. The average clock to be met with in the watchmakers’ shops is
the Swiss imitation gridiron pendulum, pin escapement, and these are of the
low grades as a rule; the best grades of them rarely ever get into the
American market. Almost without exception, the Swiss regulator, as
described, is wholly worthless as a standard, as the pendulums are only an
imitation of the real compensated pendulum. They are an imitation all
through, the bob being hollow and filled with scrap iron, and the brass and
steel rods composing the compensating element, along with the cross-pieces
or binders, are all of the cheapest and poorest description. If one of these
pendulums was taken away from the movement and a plain iron bob and
wooden rod put to the movement, in its place, the possessor of any such
clock would be surprised to find how much better average rate the clock
would have the year through, although there would then be no
compensating mechanism, or its semblance, in the make-up of the
pendulum. In brief, the average imitation compensation pendulum of this
particular variety is far poorer than the simplest plain pendulum, such as the
old style, grandfather clocks were equipped with. A wood rod would be far
superior to a steel one, or any metal rod, as may be seen by consulting the
expansion data given in the previous chapter.
Many other pendulums that are sold as compensating are a delusion in
part, as they do not thoroughly compensate, because the elements
composing them are not in equilibrium or in due proportion to one another
and to the general mechanism.
To all workmen who have a Swiss regulator, I would say that the
movement, if put into good condition, will answer very well to maintain the
motion of a good pendulum, and that it will pay to overhaul these
movements and put to them good pendulums that will pretty nearly
compensate. At least a well constructed pendulum will give a very useful
and reliable rate with such a motor, and be a great help and satisfaction to
any man repairing and rating good watches.
The facts are, that one of the good grade of American adjusted watch
movements will keep a much steadier rate when maintained in one position
than the average regulator. Without a reliable standard to regulate by, there
is very little satisfaction in handling a good movement and then not be able

to ascertain its capabilities as to rate. Very many watch carriers are better up
in the capabilities of good watches than many of our American repairers
are, because a large per cent of such persons have bought a watch of high
grade with a published rate, and naturally when it is made to appear to
entirely lack a constant rate when compared with the average regulator, they
draw the conclusion that the clock is at fault, or that the cleaning and
repairing are. Many a fair workman has lost his watch trade, largely on
account of a lack of any kind of reliable standard of time in his
establishment. There are very few things that a repairer can do in the way of
advertising and holding his customers more than to keep a good clock, and
furnish good watch owners a means of comparison and thus to confirm their
good opinions of their watches.
We have along our railroads throughout the country a standard time
system of synchronized clocks, which are an improvement over no standard
of comparison; but they cannot be depended upon as a reliable standard,
because they are subject to all the uncertainties that affect the telegraph
lines—bad service, lack of skill, storms, etc. The clocks furnished by these
systems are not reliable in themselves and they are therefore corrected once
in twenty-four hours by telegraph, being automatically set to mean time by
the mechanism for that purpose, which is operated by a standard or master
clock at some designated point in the system.
Now all this is good in a general way; but as a means to regulate a fine
watch and use as a standard from day to day, it is not adequate. A standard
clock, to be thoroughly serviceable, must always, all through the twenty-
four hours, have its seconds hand at the correct point at each minute and
hour, or it is unreliable as a standard. The reason is that owing to train
defects watches may vary back and forth and these errors cannot be
detected with a standard that is right but once a day. No man can compare
to a certainty unless his standard is without variation, substantially; and I do
not know of any way that this can be obtained so well and satisfactorily as
through the means of a thoroughly good pendulum.
Compensating seconds pendulums are, it might be said, the standard
time measure. Mechanically such a pendulum is not in any way difficult of
execution, yet by far the greater portion of pendulums beating seconds are
not at all accurate time measures, as independently of their slight variations
in length, any defects in the construction or fitting of their parts are bound

to have a direct effect upon the performance of the clock. The average
watchmaker as a mechanic has the ability to do the work properly, but he
does not fully understand or realize what is necessary, nor appreciate the
fact that little things not attended to will render useless all his efforts.
The first consideration in a compensated pendulum is to maintain the
center of oscillation at a fixed distance from the point of suspension and it
does not matter how this is accomplished.
So, also, the details of construction are of little consequence, so long as
the main points are well looked after—the perfect solidity of all parts, with
very few of them, and the free movement of all working surfaces without
play, so that the compensating action may be constantly maintained at all
times. Where this is not the case the sticking, rattling, binding or cramping
of certain parts will give different rates at different times under the same
variations of temperature, according as the parts work smoothly and evenly
or move only by jerks.
The necessary and useful parts of a pendulum are all that are really
admissible in thoroughly good construction. Any and all pieces attached by
way of ornament merely are apt to act to the prejudice of the necessary
parts and should be avoided. In this chapter we shall give measurements
and details of construction for a number of compensated pendulums of
various kinds, as that will be the best means of arriving at a thorough
understanding of the subject, even if the reader does not desire to construct
such a pendulum for his own use.
Principles of Construction.—Compensation pendulums are
constructed upon two distinct principles. First, those in which the bob is
supported by the bottom, resting on the adjusting screw with its entire
height free to expand upward as the rod expands downward from its fixed
point of suspension. In this class of pendulums the error of the bob is used
to counteract that of the rod and if the bob is made of sufficiently
expansible metal it only remains to make the bob of sufficient height in
proportion to its expansibility for one error to offset the other. In the second
class the attempt is made to leave out of consideration any errors caused by
expansion of the bob, by suspending it from the center, so that its expansion
downward will exactly balance its expansion upward and hence they will
balance each other and may be neglected. Having eliminated the bob from

consideration by this means we must necessarily confine our attempt at
compensation to the rod in the second method.
The wood rod and lead bob and the mercurial pendulums are examples
of the first-class and the wood rod with brass sleeve having a nut at the
bottom and reaching to the center of the iron bob and the common gridiron,
or compound tubular rod, or compound bar of steel and brass, or steel and
zinc, are examples of the second class.
Wood Rod and Zinc Bob.—We will suppose that we have one of the
Swiss imitation gridiron pendulums which we want to discard, while
retaining the case and movement. As these cases are wide and generally
fitted with twelve-inch dials, we shall have about twenty inches inside our
case and we may therefore use a large bob, lens-shaped, made of cast zinc,
polished and lacquered to look like brass.
The bobs in such imitation gridiron pendulums are generally about
thirteen inches in diameter and swing about five inches (two and a half
inches each side). The pendulums are generally light, convex in front and
flattened at the rear, and the entire pendulum measures about 56 inches
from the point of suspension to the lower end of the adjusting screw. We
will also suppose that we desire to change the appearance of the clock as
little as possible, while improving its rate. This will mean that we desire to
retain a lens-shaped bob of about the same size as the one we are going to
remove.
We shall first need to know the total length of our pendulum, so that we
can calculate the expansion of the rod. A seconds pendulum measures 39.2
inches from the point in the suspension spring at the lower edge of the
chops to the center of oscillation. With a lens-shaped bob the center of
gravity will be practically at the center of the bob, if we use a light wooden
rod and a steel adjusting screw and brass nut, as these metal parts, although
short, will be heavy enough to nearly balance the suspension spring and that
portion of the rod which is above the center. We shall also gain a little in
balance if we leave the steel screw long enough to act as an index over the
degree plate, in the case, at the bottom of the pendulum, by stripping the
thread and turning the end to a taper an inch or so in length.
We shall only be able to use one-half of the expansion upwards of our
bob, because the centers of gravity and oscillation will be practically

together at the center of the bob. We shall find the center of gravity easily
by balancing the pendulum on a knife edge and thus we will be able to
make an exceedingly close guess at the center of oscillation.
Now, looking over our data, we find that we have a suspension spring of
steel, then some wood and steel again at the other end. We shall need about
one inch of suspension spring. The spring will, of course, be longer than
one inch, but we shall hold it in iron chops and the expansion of the chops
will equal that of the spring between them, so that only the free part of the
spring need be considered. Now from the adjusting screw, where it leaves
the last pin through the wood, to the middle position of the rating nut will
be about one inch, so we shall have two inches of steel to consider in our
figures of expansion.
Now to get the length of the rod. We want to keep our bob about the size
of the other, so we will try 14 inches diameter, as half of this is an even
number and makes easy figuring in our trials. 39.2 inches, plus 7 (half the
diameter of the bob) gives us 46.2 inches; now we have an inch of
adjustment in our screw, so we can discard the .2; this leaves us 46 inches
of wood and steel for which we must get the expansion.

Wood expands .0004 of its length between 32° and 212° F.
Steel expands .0011 of its length between 32° and 212° F.
Lead expands .0028 of its length between 32° and 212° F.
Brass expands .0020 of its length between 32° and 212° F.
Zinc expands .0028 of its length between 32° and 212° F.
Tin expands .0021 of its length between 32° and 212° F.
Antimony expands .0011 of its length between 32° and 212° F.
Total length of pendulum to adjusting nut 46 inches.
Total length of steel to adjusting nut 2 inches.
Total length of wood to adjusting nut 44 inches.
.0011 × 2 = .0022 inch, expansion of our steel.
.0004 × 44 = .0176 inch, expansion of our wood.
.0198 total expansion of rod.

We have 7 inches as half the diameter of our bob .0198 ÷ 7 = .0028, ²⁄₇,
which we find from our tables is very close to the expansion of zinc, so we

will make the bob of that metal. Now let us check back; the upward
expansion of 7 inches of zinc equals .0028 × 7 = .0196 inch, as against
.0198 inch downward expansion of the rod. This gives us a total difference
of .0002 inch between 32° and 212° or a range of 180° F. This is a
difference of .0001 inch for 90° of temperature and is closer than most
pendulums ever get.
The above figures are for dry, clear white pine, well baked and
shellacked, with steel of average expansion, and zinc of new metal, melted
and cast without the admixtures of other metals or the formation of oxide.
The presence of tin, lead, antimony and other admixtures in the zinc would
of course change the results secured; so also will there be a slight difference
in the expansion of the rod if other woods are used. Still the jeweler can
from the above get a very close approximation.

Fig. 5. Zinc bob and wood rod to replace
imitation gridiron pendulum.
Such a bob, 14 inches diameter and 1.5 inches thick, alike on both sides,
with an oval hole 1 × .5 inches through its center, see Fig. 5, would weigh
about 30 to 32 pounds, and would have to be hung from a cast iron bracket,
Fig. 6, bolted through the clock case to the wall behind it, so as to get a
steady rate. It would be nearly constant, as the metal is spread out so as to
be quickly affected by temperature; and the shape would hold it well in its
plane of oscillation, if both sides were of exactly the same curvature, while

the weight would overcome minor disturbances due to vibration of the
building. It would require a little heavier suspension spring, in order to be
isochronous in the long and short arcs and this thickening of the spring
would need the addition of from one and a half to two pounds more of
driving weight.

Fig. 6. Cast iron bracket for heavy pendulums and movements.
If so heavy a pendulum is deemed undesirable, the bob would have to
be made of cylindrical form, retaining the height, as necessary to
compensation, and varying the diameter of the cylinder to suit the weight
desired.

Fig. 7. Wood rod Fig. 8. Bob of metal casing
and lead bob. filled with shot.
Wood Rod and Lead Bob.—The wood should be clear, straight-grained
and thoroughly dried, then given several coats of shellac varnish, well
baked on. It may be either flat, oval or round in section, but is generally
made round because the brass cap at the upper end, the lining for the crutch,
and the ferrule for the adjusting screw at the lower end may then be readily
made from tubing. For pendulums smaller than one second, the wood is
generally hard, as it gives a firmer attachment of the metal parts.
Inches.
Length, top of suspension spring to bottom of bob 44.5
Length to bottom of nut 45.25

Diameter of bob 2.0
Length of bob 10.5
Weight of bob, 8 lbs.
Acting length of suspension spring 1.0
Width of spring .45
Thickness .008
Diameter of rod .5

The top of the rod should have a brass collar fixed on it by riveting
through the rod and it should extend down the rod about three inches, so as
to make a firm support for the slit to receive the lower clip of the
suspension spring. The lower end should have a slit or a round hole drilled
longitudinally three inches up the rod to receive the upper end of the
adjusting screw and this should also fit snugly and be well pinned or riveted
in place. See Fig. 7. A piece of thin brass tube about one inch in length is
fitted over the rod where the crutch works.
In casting zinc and lead bobs, especially those of lens-shapes, the
jeweler should not attempt to do the work himself, but should go to a
pattern maker, explain carefully just what is wanted and have a pattern
made, as such patterns must be larger than the casting in order to take care
of the shrinkage due to cooling the molten metal. It will also be better to use
an iron core, well coated with graphite when casting, as the core can be
made smooth throughout and the exact shape of the pendulum rod, and
there will then be no work to be done on the hole when the casting is made.
The natural shrinkage of the metal on cooling will free the core, which can
be easily driven out when the metal is cold and it will then leave a smooth,
well shaped hole to which the rod can be fitted to work easily, but without
shake. Lens-shaped bobs, particularly, should be cast flat, with register pins
on the flask, so as to get both sides central with the hole, and be cast with a
deep riser large enough to put considerable pressure of melted metal on the
casting until it is chilled, so as to get a sound casting; it should be allowed
to remain in the sand until thoroughly cold, for the same reason, as if cooled
quickly the bob will have internal stresses which are liable to adjust
themselves sometime after the pendulum is in the clock and thus upset the
rate until such interior disturbances have ceased. Cylinders may be cast in a
length of steel tubing, using a round steel core and driven out when cold.

If using oval or flat rods of wood, the adjusting screw should be
flattened for about three inches at its upper end, wide enough to conform to
the width of the rod; then saw a slot in the center of the rod, wide and deep
enough to just fit the flattened part of the screw; heat the screw and apply
shellac or lathe wax and press it firmly into the slot with the center of the
screw in line with the center of the rod; after the wax is cold select a drill of
the same size as the rivet wire; drill and rivet snugly through the rod,
smooth everything carefully and the job is complete.
If by accident you have got the rod too small for the hole, so that there
is any play, give the rod another coat of shellac varnish and after drying
thoroughly, sand paper it down until it will fit properly.
Round rods may be treated in the same manner, but it is usual to drill a
round hole in such a rod to just fit the wire, then insert and rivet as before
after the wax is cold, finishing with a ferrule or cap of brass at the end of
the rod.
The slot for the suspension spring is fitted to the upper end of the rod in
the same manner.
Pendulum with Shot.—Still another method of making a compensating
pendulum, which gives a lighter pendulum, is to make a case of light brass
or steel tubing of about three inches diameter. Fig. 8, with a bottom and top
of equal weight, so as to keep the center of oscillation about the center of
gravity, for convenience in working. The bottom may be turned to a close
fit, and soldered, pinned, or riveted into the tube. It is pierced at its center
and another tube of the same material as the outer tube, with an internal
diameter which closely fits the pendulum rod is soldered or riveted into the
center of the bottom, both bottom and top being pierced for its admission
and the other parts fitted as previously described.
The length of the case or canister should be about 11.5 inches so as to
give room for a column of shot of 10.5 inches (the normal compensating
height for lead) and still leave room for correction. Make a tubular case for
the driving weight also and then we have a flexible system. If it is necessary
to add or subtract weight to obtain the proper arcs of oscillation of the
pendulum, it can be readily done by adding to or taking from the shot in the
weight case.

Fill the pendulum to 10.5 inches with ordinary sportsmen’s shot and try
it for rate. If it gains in heat and loses in cold it is over-compensated and
shot must be taken from it. If it loses in heat and gains in cold it is under-
compensated and shot should be added.
The methods of calculation were given in full in describing the zinc
pendulum and hence need not be repeated here, but attention should be
called to the fact that there are three materials here, wood, steel or brass and
lead and each should be figured separately so that the last two may just
counterbalance the first. If the case is made light throughout the effect upon
the center of oscillation will be inappreciable as compared with that of the
lead, but if made heavier than need be, it will exert a marked influence,
particularly if its highest portion (the cover) be heavy, as we then have the
effect of a shifting weight high up on the pendulum rod. If made of thin
steel throughout and nickel plated, we shall have a light and handsome case
for our bob. If this is not practicable, or if the color of brass be preferred, it
may be made of that material.
The following table of weights will be of use in making calculations for
a pendulum or for clock weights.
Weight of Lead, Zinc and Cast Iron Cylinders One-Half Inch
Long.

Diameter Weight in Pounds.
in Inches. Lead Zinc Iron
.25 .020 .012 .012
.5 .080 .049 .050
.75 .180 .111 .114
1. .321 .198 .204
1.25 .503 .310 .319
1.5 .724 .447 .459
1.75 .984 .607 .624
2. 1.287 .794 .816
2.25 1.630 1.005 1.033
2.5 2.009 2.239 1.274

Diameter Weight in Pounds.
in Inches. Lead Zinc Iron
2.75 2.434 1.502 1.544
3. 2.897 1.788 1.837
3.25 3.400 2.098 2.156
3.5 3.944 2.434 2.491
3.75 4.51 2.783 2.865
4. 5.149 3.177 3.265
4.25 5.813 3.587 3.686
4.5 6.519 3.922 4.134
4.75 7.265 4.483 4.607
5. 8.048 4.966 5.103
5.25 8.872 5.474 5.626
5.5 9.737 6.008 5.175
5.75 10.643 6.567 6.749
6. 11.590 7.152 7.350

Example:—Required, the weight of a
lead pendulum bob, 3 inches diameter, 9
inches long, which has a hole through it .75
inch in diameter. The weight of a lead
cylinder 3 inches diameter in the table is
2.897, which multiplied by 9 (the length
given) = 26.07 lbs. Then the weight in the
table of a cylinder .75 inch diameter is .18
and .18 × 9 = 1.62 lbs. And 26.07 -
1.62 = 24.45, the weight required in lbs.

Auxiliary Weights.—If for any reason our pendulum does not turn out
with a rating as calculated and we find after getting it to time that it is over-
compensated, it is a comparatively simple matter to turn off a portion from
the bottom of a solid bob. By doing this in very small portions at a time and
then testing carefully for heat and cold every time any amount has been

removed, we shall in the course of a few weeks arrive at a close
approximation to compensation, at least as close as the ordinary standards
available to the jeweler will permit. This is a matter of weeks, because if the
pendulum is being rated by the standard time which is telegraphed over the
country daily at noon, the jeweler, as soon as he gets his pendulum nearly
right, will begin to discover variations in the noon signal of from .2 to 5
seconds on successive days. Then it becomes a matter of averages and
reasoning, thus: If the pendulum beats to time on the first, second, third,
fifth and seventh days, it follows that the signal was incorrect—slow or fast
—on the fourth and sixth days.
If the pendulum shows a gain of one second a week on the majority of
the days, the observation must be continued without changing the pendulum
for another week. If the pendulum shows two seconds gain at the end of this
time, we have two things to consider. Is the length right, or is the pendulum
not fully compensated? We cannot answer the second query without a
record of the temperature variations during the period of observations.
To get the temperature record we shall require a set of maximum and
minimum thermometers in our clock case. They consist of mercurial
thermometer tubes on the ordinary Fahrenheit scales, but with a marker of
colored wood or metal resting on the upper end of the column of mercury in
the tube. The tube is not hung vertically, but is placed in an inclined
position so that the mark will stay where it is pushed by the column of
mercury. Thus if the temperature rises during the day to 84 degrees the
mark in the maximum thermometer will be found resting in the tube at 84°
whether the mercury is there when the reading is taken or not. Similarly, if
the temperature has dropped during the night to 40°, the mark in the
minimum thermometer will be found at 40°, although the temperature may
be 70° when the reading is taken. After reading, the thermometers are
shaken to bring the marks back to the top of the column of mercury and the
thermometers are then restored to their positions, ready for another reading
on the following day.
These records should be set down on a sheet every day at noon in
columns giving date, rate, plus or minus, maximum, minimum, average
temperature and remarks as to regulation, etc., and with these data to guide
us we shall be in a position to determine whether to move the rating nut or
not. If the temperature has been fairly constant we can get a closer rate by

moving the nut and continuing the observations. If the temperature has been
increasing steadily and our pendulum has been gaining steadily it is
probably over-compensated and the bob should be shortened a trifle and the
observations renewed.
It is best to “make haste slowly” in such a matter. First bring the
pendulum to time in a constant temperature; that will take care of its proper
length. Then allow the temperature to vary naturally and note the results.
If the pendulum is under-compensated, so that the bob is too short to
take care of the expansion of the rod, auxiliary weights of zinc in the shape
of washers (or short cylinders) are placed between the bottom of the bob
and the rating nut. This of course makes necessary a new adjustment and
another course of observations all around, but it will readily be seen that it
places a length of expansible metal between the nut and the center of
oscillation and thus makes up for the deficiency of expansion of the bob.
Zinc is generally chosen on account of its high rate of expansion, but brass,
aluminum and other metals are also used. It is best to use one thick washer,
rather than a number of thinner ones, as it is important to keep the
construction as solid at this point as possible.
Top Weights.—After bringing the pendulum as close as possible by the
compensation and the rating nuts, astronomers and others requiring exact
time get a trifle closer rating by the use of top weights. These are generally
U-shaped pieces of thin metal which are slipped on the rod above the bob
without stopping the pendulum. They raise the center of oscillation by
adding to the height of the bob when they are put on, or lower it when they
are removed, but they are never resorted to until long after the pendulum is
closer to time than the jeweler can get with his limited standards of
comparison. They are mentioned here simply that their use may be
understood when they may be encountered in cleaning siderial clocks.
Mercurial pendulums also belong to the class of compensation by
expansion of the bobs, but they are so numerous and so different that they
will be considered separately, later on.
Compensated Pendulum Rods.—We will now consider the second class,
that in which an attempt is made to obtain a pendulum rod of unvarying
length.

The oldest form of compensated rod is undoubtedly the gridiron of
either nine, five or three rods. As originally made it was an accurate but
expensive proposition, as the coefficients of expansion of the brass or zinc
and iron or steel had all to be determined individually for each pendulum.
Each rod had to be sized accurately, or if this was not done, then each rod
had to be fitted carefully to each hole in the cross bars so as to move freely,
without shake. The rods were spread out for two purposes, to impress the
public and to secure uniform and speedy action in changes of temperature.
The weight, which increased rapidly with the increase of diameter of the
rod, made a long and large seconds pendulum, some of them measuring as
much as sixty-two inches in length, and needing a large bob to look in
proportion. Various attempts were made to ornament the great expanse of
the gridiron, harps, wreaths and other forms in pierced metal being screwed
to the bars. The next advance was in substituting tubes for rods in the
gridiron, securing an apparently large rod that was at the same time stiff and
light. Then came the era of imitation, in which the rods were made of all
brass, the imitation steel portion being nickel plated. With the development
of plating they were still further cheapened by being made of steel, with the
supposedly brass rods plated with brass and the steel ones with nickel.
Thousands of such pendulums are in use to-day; they have the rods riveted
to the cross-pieces and are simply steel rods, subject to change of length
with every change in temperature. It does no harm to ornament such
pendulums, as the rods themselves are merely ornaments, usually all of one
metal, plated to change the color.
As three rods were all that were necessary, the clockmaker who desired
a pendulum that was compensated soon found his most easily made rod
consisted of a zinc bar, wide, thin and flat, placed between two steel parts,
like the meat and bread of a sandwich. This gives a flat and apparently solid
rod of metal which if polished gives a pleasing appearance, and combines
accurate performance with cheapness of construction, so that any
watchmaker may make it himself, without expensive tools.

A, the lens-shaped bob; T P, the total length of the
compensating part.
R, the upper round part of rod.

The side showing the
heads of the screws is the
face side and is finished. The
screws 1, 2, 3, 4 hold the
three pieces from separating,
but do not confine the front
and middle sections in their
lengthwise expansion along
the rod, but are screwed into
the back iron section, while
the holes in the other two
sections are slotted smaller
than the screw heads.
The holes at the lower
extreme of combination 5, 6,
7, 8, 9 are for adjustments in
effecting a compensation.
The pin at 10 is the steel
adjusting pin, and is only
tight in the front bar and zinc
bars, being loose in the back
bar.
O and P show the angles
in the back rod, T shows the
angle in the rod at the top, m
shows the pin as placed in the
Fig. 9. Pendulum with compensated iron and zinc sections where
rod of steel and zinc. they have been soldered as
described.
h shows the regulating nut carried by the tube, as
described, and terminating in the nut D.
l and i show the screw of 36 threads.
The nut D is to be divided on its edge into 30 divisions.
n is the angle of the back bar to which zinc is soldered.

Flat Compensated Rod.—One of the most easily made zinc and iron
compensating pendulums, shown in detail in Fig. 9, is as follows: A lead or
iron bob, lens-shaped, that is, convex equally on each side, 9 inches
diameter and an inch and one-quarter thick at the center. A hole to be made
straight through its diameter ½ inch. One-half through the diameter this
hole is to be enlarged to ⅝ inch diameter. This will make the hole for half of
its length ½ inch and the remaining half ⅝ inch diameter. The ⅝ hole must
have a thin tube, just fitting it, and 5 inches long. At one end of this tube is
soldered in a nut, with a hole tapped with a tap of thirty-six threads to the
inch, and ¼ inch diameter, and at the other end of the tube is soldered a
collar or disc one inch diameter, which is to be divided into thirty divisions,
for regulating purposes, as will be described later on. The whole forms a nut
into which the rod screws, and the tube allows the nut to be pushed up to
the center of the diameter of the bob, through the large hole, and the nut can
be operated then by means of the disc at its lower end. The rod, of flat iron,
is in two sections, as follows: That section which enters the bob and
terminates in the regulating screw is flat for twenty-six inches, and then
rounded to ½ inch for six inches, and a screw cut on its end for two inches,
to fit the thread in the nut. The upper end of this section is then to be bent at
a right angle, flatwise. This angle piece will be long enough if only ³⁄₁₆ inch
long, so that it covers the thickness of the zinc center rod. The zinc center
rod is a bar of the metal, hammered or rolled, 25 inches long, ³frasl;₁₆ inch
thick, and ¾ inch wide, and comes up against the angle piece bent on the
flat part of the lower section of the rod. Now the upper section of the rod
may be an exact duplicate of the lower section, with the flat part only a little
longer than the zinc bar, say ½ inch, and the angle turned on the end, as
previously described. The balance of the bar may be forged into a rod of ⁵⁄₁₆
inch diameter. As has been stated, the zinc bar is placed against the angle
piece bent on the upper end of the lower section of the rod, P, n, Fig. 9, and
pins must be put through this angle piece into the end of the zinc bar, to
hold it in close contact with the iron bar. The upper section of the rod is
now to be laid on the opposite side of the zinc bar, with its angle at the other
end of the zinc, but not in contact with it, say ¹⁄₁₆ inch left between the angle
and the zinc bar. Now all is ready to clamp together—the two flat iron bars

with the zinc between them. After clamping, taking care to have the pinned
end of the zinc in contact with the angle and the free, or lower end, removed
from the other angle about ¹⁄₁₆ inch, three screws should be put through all
three bars, with their heads all on the side selected for the front, and one
screw may be an inch from the top, another 3 inches from the bottom, and
one-half way between the two first mentioned. Now the rod is complete in
its composite form, and there is left only the little detail to attend to. Two
flat bars, with their ends angled in one case and rounded in the other into
rods of given diameter, confining between them, as described, a flat bar of
wrought zinc of stated length and of the same thickness and width as the
iron bars, comprises the active or compensating elements of the pendulum’s
rod. The screws that are put through the three bars are each to pass through
the front iron bar, without threads in the bar, and only the back iron bar is to
have the holes tapped, fitting the screws. All the corresponding holes in the
zinc are to be reamed a little larger than the diameter of the screws, and to
be freed lengthwise of the bar, to allow of the bar’s contracting and
expanding without being confined in this action by the screws. At the lower
or free end of the zinc bar are to be holes carried clear through all three
bars, while the combination is held firmly together by the screws. These
holes are to start at ½ inch from the end of the zinc, and each carried
straight through all three bars, and then broached true and a steel pin made
to accurately fit them from the front side. These holes may be from three to
five in number, extending up to a safe distance from the lower screw. The
holes in the back bar, after boring, are to be reamed larger than those in the
front bar and zinc bar. These holes and the pin serve for adjusting the
compensation. The pin holds the front bar and zinc from slipping, or
moving past one another at the point pinned, and also allows the back bar to
be free of the pin, and not under the influence of the two front bars. The
upper end of the second iron section is, as has been mentioned, forged into a
round rod about ⁵⁄₁₆ inch diameter, and this rod or upper end is to receive
the pendulum suspension spring, which may be one single spring, or a
compound spring, as preferred.
Now that the pendulum is all ready to balance on the knife edge,
proceed as in the case of the simple pendulum, and ascertain at what point
up the rod the spring must be placed. In this pendulum the rod will be
heavier in proportion than the wood rod was to its bob, and the center of
gravity of the whole will be found higher up in the bob. However, wherever

in the bob the center of gravity is found, that is the starting point to measure
from to find the total length of the rod, and the point for the spring. The
heavier the rod is in relation to the bob, the higher will the center of gravity
of the whole rise in the bob, and the greater will be the total length of the
entire pendulum.
In getting up a rod of the kind just described, the main item is to get the
parts all so arranged that there will be very little settling of the joints in
contact, particularly those which sustain the weight of the bob and the
whole dead weight of the pendulum. The nut in the center of the pendulum
holds the weight of the bob only, but it should fit against the shoulder
formed for the purpose by the juncture of the two holes, and the face of the
nut should be turned true and flat, so that there may not be any uneven
motion, and only the one imparted by the progressive one of the threads.
When this nut is put to its place for the last time, and after all is finished,
there should be a little tallow put on to the face of the nut just where it
comes to a seat against the shoulder of the bob, as this shoulder being not
very well finished, the two surfaces coming in contact, if left dry, might cut
and tear each other, and help to make the nut’s action slightly unsteady and
unreliable. A finished washer can be driven into this lower hole up to the
center, friction-tight, and serve as a reliable and finished seat for the nut.
In reality, the zinc at the point of contact, where pinned to the angle
piece at the top of the lower section, is the point of greatest importance in
the whole combination, and if the joint between the angle and the end of the
zinc bar is soldered with soft solder, the result will be that of greater
certainty in the maintenance of a steady rate. This joint just mentioned can
be soldered as follows: File the end of the zinc and the inside surface of the
angle until they fit so that no appreciable space is left between them. Then,
with a soldering iron, tin the end of the zinc thoroughly and evenly, and
then put into the holes already made the two steady pins. Now tin in the
same manner the surface of the angle, and see that the holes are free of
solder, so that the zinc bar will go to its place easily; then between the zinc
and the iron, place a piece of thin writing paper, so that the flat surfaces of
the zinc and iron may not become soldered. Set the iron bar upright on a
piece of charcoal, and secure it in this position from any danger of falling,
and then put the zinc to its place and see that the pins enter and that the
paper is between the surfaces, as described. Put the screws into their places,

and screw down on the zinc just enough to hold it in contact with the iron
bar, but not so tight that the zinc will not readily move down and rest firmly
on the angle. Put a little soldering fluid on the tinned joint, and blow with a
blow pipe against the iron bar (not touching the zinc with the flame). When
the solder in the joint begins to flow, press the zinc down in close contact
with the angle, and then cool gradually, and if all the points described have
been attended to the joint will be solidly soldered, and the two bars will be
as one solid bar bent against itself. The tinning leaves surplus solder on the
surfaces sufficient to make a solid joint, and to allow some to flow into the
pin holes and also solder the pin to avoid any danger of getting loose in
after time, and helps make a much stronger joint. At the time the solder is
melted the zinc is sufficiently heated to become quite malleable, and care
must be taken not to force it down against the angle in making the joint, or
it may be distorted and ruined at the joint. If carefully done the result will
be perfect. The paper between the surfaces burns, and is got rid of in
washing to remove the soldering fluid. Soda or ammonia will help to
remove all traces of the fluid. However, it is best, as a last operation, to put
the joint in alcohol for a minute.
This soldering makes the lower section and the zinc practically one
piece and without loose joint, and the next joint is that made by the pin
pinning the outside bar and the zinc together. This is necessarily formed this
way, as in this stage of the operation we do not know just what length the
zinc bar will be to exactly compensate for the expansion and contraction of
the balance of the pendulum. By the changing of the pin into the different
holes, 5, 6, 7, 8, 9, 10, Fig. 9, the zinc is made relatively longer or shorter,
and so a compensation is arrived at in time after the clock has been running.
After it is definitely settled where the pin will remain to secure the
compensation of the rod, then that hole can have a screw put in to match the
three upper ones. This screw must be tapped into the front bar and the zinc,
and be very free in the back bar to allow of its expansion. It is supposed that
in this example given of a zinc and steel compensation seconds pendulum
that there has been due allowance made in the lengths of the several bars to
allow for adjustment to temperature by the movements of the pin along the
course of the several holes described, but the zinc is a very uncertain
element, and its ultimate action is largely influenced by its treatment after
being cast. Differences of working cast zinc under the hammer or rolls
produce wide differences practically, and therefore materially change the

results in its combination with iron in their relative expansive action.
Wrought zinc can be obtained of any of the brass plate factories, of any
dimensions required, and will be found to be satisfactory for the purpose in
hand.
The adjusting pin should be well fitted to the holes in the front iron bar,
and also fit the corresponding ones in the zinc bar closely, and if the holes
are reamed smooth and true with an English clock broach, then the pin will
be slightly tapering and fit the iron hole perfectly solid. After one pair of
these holes have been reamed, fit the pin and drive it in place perfectly firm,
and then with the broach ream all the remaining holes to just the same
diameter, and then the pin will move along from one set of holes to another
with mechanically accurate results. Otherwise, if poorly fitted, the full
effect would not be obtained from the compensating action in making
changes in the pin from one set of holes to another. This pin, if made of cast
steel, hardened and drawn to a blue, will on the whole be a very good
device mechanically.
Many means are used to effect the adjustments for compensation, of
more or less value, but whatever the means used, it must be kept in mind
that extra care must be taken to have the mechanical execution first class, as
on this very much depends the steady rate of the pendulum in after time.
Tubular Compensated Rods.—There are tubular pendulums in the
market which have a screw sleeve at the top of the zinc element, and by this
means the adjustments are effected, and this is thought to be a very accurate
mechanism. The most common form of zinc and iron compensation is
where the zinc is a tube combined with one iron tube and a central rod, as
shown in Figs. 10, 11, 12. The rod is the center piece, the zinc tube next,
followed by the iron tube enveloping both. The relative lengths may be the
same as those just given in the foregoing example with the compensating
elements flat. The relative lengths of the several members will be virtually
the same in both combinations.
Tubular Compensation with Aluminum.—The pendulum as seen by an
observer appears to him as being a simple single rod pendulum. Figs. 10
and 12 are front and side views; Fig. 11 is an enlarged view of its parts, the
upper being a sectional view. Its principal features are: The steel rod S, Fig.
11, 4 mm. in diameter, having at its upper end a hook for fastening to the

suspension spring in the usual way; the lower end has a pivot carrying the
bushing, T, which solidly connects the steel rod, S, with the aluminum tube,
A, the latter being 10 mm. in diameter and its sides 1.5 mm. in thickness of
the wall.
The upper end of the aluminum tube is very close to the pendulum hook
and is also provided with a bushing, P, Fig. 11. This bushing is permanently
connected at the upper end of the aluminum tube with a steel tube, R, 16
mm. in diameter and 1 mm. in thickness. The outer steel tube is the only
one that is visible and it supports the bob, the lower part being furnished
with a fine thread on which the regulating nut, O, is movable, at the center
of the bob.
For securing a central alignment of the steel rod, S, at its lowest part,
where it is pivoted, a bushing, M, Fig. 11, is screwed into the steel tube, R.
The lower end of the steel tube, R, projects considerably below the
lenticular bob (compare Figs. 10 and 12); and is also provided with a thread
and regulating weight, G (Figs. 10 and 12), of 100 grammes in weight,
which is only used in the fine regulation of small variations from correct
time.
The steel tube is open at the bottom and the index at its lower end is
fastened to a bridge. Furthermore all three of the bushings, P, T and M, have
each three radial cuts, which will permit the surrounding air to act equally
and at the same time on the steel rod, S, the aluminum tube. A, and the steel
tube, R, and as the steel tube, R, is open at its lower end, and as there is also
a certain amount of space between the tubes, the steel rod, and the radial
openings in the bushings, there will be a draught of air passing through
them, which will allow the thin-walled tubes and thin steel rod to promptly
and equally adapt themselves to the temperature of the air.

Fig. 10. Fig. 11. Fig. 12.
The lenticular pendulum bob has a diameter of 24 cm., and is made of
red brass. The bob is supported at its center by the regulating nut, O, Figs.
10 and 12. That the bob may not turn on the cylindrical pendulum rod, the
latter is provided with a longitudinal groove and working therein are the
ends of two shoulder screws which are placed on the back of the bob above
and below the regulating nut, O; and thus properly controlling its
movements.

From the foregoing description the action of the compensation is readily
explained. For the purpose of illustration of its action we will accept the
fact that there has been a sudden rise in temperature. The steel rod, S, and
the tube, R, will lengthen in a downward direction (including the
suspension spring and the pendulum hook), conversely the aluminum tube,
A, which is fastened to the steel rod at one end and the steel tube at the
other, will lengthen in an upward direction and thus equalize the expansion
of the tube, R, and rod, S.
As the coefficients of expansion of steel and aluminum are
approximately at the ratio of 1:2.0313 we find that with such a pendulum
construction—accurate calculations presumed—we shall have a complete
and exact coincidence in its compensation; in other words, the center of
oscillation of the pendulum will be under all conditions at the same distance
from the bending point of the suspension spring.
This style of pendulum is made for astronomical clocks in Europe and is
furnished in two qualities. In the best quality, the tubes, steel rod, and the
bob are all separately and carefully tested as to their expansion, and their
coefficients of expansion fully determined in a laboratory; the bushings, P
and M, are jeweled, all parts being accurately and finely finished. In the
second quality the pendulum is constructed on a general calculation and
finished in a more simple manner without impairing its ultimate efficiency.
At the upper part of the steel tube, R, there is a funnel-shaped piece
(omitted in the drawing) in which are placed small lead and aluminum balls
for the final regulation of the pendulum without stopping it.
The regulation of this pendulum is effected in three ways:
1. The preliminary or coarse regulation by turning the
regulating nut, O, and so raising or lowering the bob.
2. The finer regulation by turning the 100 grammes
weight, g, having the shape of a nut and turning on the
threaded part of the tube, R. 3. The precision regulation is
effected by placing small lead or aluminum balls in a small
funnel-shaped receptacle attached to the upper part of the
tube, R, or by removing them therefrom.

It will readily be seen that this form of pendulum can be used with zinc
or brass instead of aluminum, by altering the lengths of the inner rod and
the compensating tube to suit the expansion of the metal it is decided to use;
also that alterations in length may be made by screwing the bushings in or
out, provided that the tube be long enough in the first place. After securing
the right position the bushings should have pins driven into them through
the tube, in order to prevent further shifting.

CHAPTER IV.
THE CONSTRUCTION OF MERCURIAL PENDULUMS.

Owing to the difficulty of calculating the expansive ratios of metal
which (particularly with brass and zinc) vary slightly with differences of
manufacture, the manufacture of compensated pendulums from metal rods
cannot be reduced to cutting up so many pieces and assembling them from
calculations made previously, so that each must be separately built and
tested. While this is not a great draw-back to the jeweler who wants to make
himself a pendulum, it becomes a serious difficulty to a manufacturer, and
hence a cheaper combination had to be devised to prevent the cost of
compensated pendulums from seriously interfering with their use. The
result was the pendulum composed of a steel rod and a quantity of mercury,
the latter forming the principal weight for the bob and being contained in
steel or glass jars, or jars of cast iron for the heavier pendulums. Other
metals will not serve the purpose, as they are corroded by the mercury,
become rotten and lose their contents.
Mercury has one deficiency which, however, is not serious, except for
the severe conditions of astronomical observatories. It will oxidize after
long exposure to the air, when it must be strained and a fresh quantity of
metal added and the compensation freshly adjusted. To an astronomer this is
a serious objection, as it may interfere with his work for a month, but to the
jeweler this is of little moment as the rates he demands will not be seriously
affected for about ten years, if the jars are tightly covered.
To construct a reliable gridiron pendulum would cost about fifty dollars
while a mercurial pendulum can be well made and compensated for about
twenty-five dollars, hence the popularity of the latter form.
Zinc will lengthen under severe variations of temperature as the
following will show: Zinc has a decided objectionable quality in its
crystalline structure that with temperature changes there is very unequal
expansion and contraction, and furthermore, that these changes occur
suddenly; this often results in the blending of the zinc rod, causing a

binding to take place, which naturally enough prevents the correct working
of the compensation.
It is probably not very well known that zinc can change its length at one
and the same temperature, and that this peculiar quality must not be
overlooked. The U. S. Lake Survey, which has under its charge the
triangulation of the great lakes of the United States, has in its possession a
steel meter measure, R, 1876; a metallic thermometer composed, of a steel
and zinc rod, each being one meter in length, marked M. T., 1876s, and M.
T. 1876z; and four metallic thermometers, used in connection with the base
apparatus, which likewise are made of steel and zinc rods, each of these
being four meters in length. All of these rods were made by Repsold, of
Hamburg. Comparisons between these different rods show peculiar
variations, and which point to the fact that their lengths at the same degree
of temperature are not constant. For the purpose of determining these
variations accurate investigations were undertaken. The metallic
thermometer M. T. 1876 was removed from an observatory room having an
equal temperature of about 2° C. and placed for one day in a temperature of
+24° C., and also for the same period of time in one of -20° C; it was then
replaced in the observatory room, where it remained for twenty-four hours,
and comparisons were made during the following three days with the steel
thermometer 1876, which had been left in the room. From these
observations and comparisons the following results were tabulated, which
give the mean lengths of the zinc rods of the metallic thermometer. The
slight variations of temperature in the observatory room were also taken
into consideration in the calculations:
M. T. 1876s. M. T. 1876z.
mm. mm.
February 16-24 - 0.0006 + 0.0152, previous 7 days at + 24°C
February 25-27 - 0.0017 - 0.0011, previous 1 day at - 20°C.
March 2-4 + 0.0005 + 0.0154, previous 1 day at + 24°C.
March 5-8 - 0.0058 - 0.0022, previous 1 day at - 20°C.
These investigations clearly indicate, without doubt, that the zinc rod at
one and the same temperature of about 2° C., is 0.018 mm. longer after
having been previously heated to 24° C. than when cooled before to -20° C.

A similar but less complete examination was made with the metallic
thermometer four meters in length. These trials were made by that efficient
officer, General Comstock, gave the same results, and completely prove that
in zinc there are considerable thermal after-effects at work.
To prove that zinc is not an efficient metal for compensation pendulums
when employed for the exact measurement of time, a short calculation may
be made—using the above conclusions—that a zinc rod one meter in
length, after being subjected to a difference of temperature of 44° C. will
alter its length 0.018 mm. after having been brought back to its initial
degree. For a seconds pendulum with zinc compensation each of the zinc
rods would require a length of 64.9 cm. With the above computations we
get a difference in length of 0.0117 mm. at the same degree of temperature.
Since a lengthening of the zinc rods without a suitable and
contemporaneous expansion of the steel rods is synonymous with a
shortening of the effectual pendulum length, we have, notwithstanding the
compensation, a shortening of the pendulum length of 0.017 mm., which
corresponds to a change in the daily rate of about 0.5 seconds.
This will sufficiently prove that zinc is unquestionably not suitable for
extremely accurate compensation pendulums, and as neither is permanent
under extremes of temperature the advantages of first cost and of correction
of error appear to lie with the mercurial form.
The average mercurial compensation pendulums, on sale in the trade are
often only partially compensated, as the mercury is nearly always deficient
in quantity relatively, and not high enough in the jar to neutralize the action
of the rigid metallic elements, composing the structure. The trouble
generally is that the mercury forms too small a proportion of the total
weight of the pendulum bob. There is a fundamental principle governing
these compensating pendulums that has to be kept in mind, and that is that
one of the compensating elements is expected to just undo what the other
does and so establish through the medium of physical things the condition
of the ideal pendulum, without weight or elements outside of the bob. As
iron and mercury, for instance, have a pretty fixed relative expansive ratio,
then whatever these ratios are after being found, must be maintained in the
construction of the pendulum, or the results cannot be satisfactory.

First, there are 39.2 inches of rod of steel to hold the bob between the
point of suspension and the center of oscillation, and it has been found that,
constructively, in all the ordinary forms of these pendulums, the height of
mercury in the bob cannot usually be less than 7.5 inches. Second, that in
all seconds pendulums the length of the metal is fixed substantially, while
the height of the mercury is a varying one, due to the differing weights of
the jars, straps, etc.
Third, the mercury, at its minimum, cannot with jars of ordinary weight
be less in height in the jar than 7.5 inches, to effectually counteract what the
39.2 inches of iron does in the way of expanding and contracting under the
same exposure.
Whoever observes the great mass of pendulums of this description on
sale and in use will find that the height of the mercury in the jar is not up to
the amount given above for the least quantity that will serve under the most
favorable circumstances of construction. The less weight there is in the rod,
jar and frame, the less is the height of mercury which is required; but with
most of the pendulums made in the present day for the market, the height
given cannot be cut short without impairing the quality and efficiency of the
compensation. Any amount less will have the effect of leaving the rigid
metal in the ascendancy; or, in other words, the pendulum will be under
compensated and leave the pendulum to feel heat and cold by raising and
lowering the center of oscillation of the pendulum and hence only partly
compensating. A jar with only six inches in height of mercury will in round
numbers only correct the temperature error about six-sevenths.
Calculations of Weights.—As to how to calculate the amount of
mercury required to compensate a seconds pendulum, the following
explanation should make the matter clear to anyone having a fair
knowledge of arithmetic only, though there are several points to be
considered which render it a rather more complicated process than would
appear at first sight.
1st. The expansion in length of steel and cast iron, as given in the tables
(these tables differ somewhat in the various books), is respectively .0064
and .0066, while mercury expands .1 in bulk for the same increase of
temperature. If the mercury were contained in a jar which itself had no
expansion in diameter, then all its expansion would take place in height, and

in round numbers it would expand sixteen times more than steel, and we
should only require (neglecting at present the allowance to be explained
under head 3) to make the height of the mercury—reckoned from the
bottom of the jar (inside) to the middle of the column of mercury contained
therein—one-sixteenth of the total length of the pendulum measured from
the point of suspension to the bottom of the jar, assuming that the rod and
the jar are both of steel, and that the center of oscillation is coincident with
the center of the column of mercury. Practically in these pendulums, the
center of oscillation is almost identical with the center of the bob.
2d. As we cannot obtain a jar having no expansion in diameter, we must
allow for such expansion as follows, and as cast iron or steel jars of
cylindrical shape are undoubtedly the best, we will consider that material
and form only.
As above stated, cast iron expands .0066, so that if the original diameter
of the jar be represented by 1, its expanded diameter will be 1.0066. Now
the area of any circle varies as the square of its diameter, so that before and
after its expansion the areas of the jar will be in the ratio of 1² to 1.0066²;
that is, in the proportion of 1 to 1.013243; or in round numbers it will be
one-seventy-sixth larger in area after expansion than before. It is evident
that the mercury will then expand sideways, and that its vertical rise will be
diminished to the same extent. Deduct, therefore, the one-seventy-sixth
from its expansion in bulk (one-tenth) and we get one-eleventh (or more
exactly .086757) remaining. This, then, is the actual vertical rise in the jar,
and when compared with the expansion of steel in length it will be found to
be about thirteen and a half times greater (more exactly 13.556).
The mercury, therefore (still neglecting head No. 3), must be thirteen
and a half times shorter than the length of the pendulum, both being
measured as explained above. The pendulum will probably be 43.5 inches
long to the bottom of the jar; but as about nine inches of it is cast iron,
which has a slightly greater rate of expansion than steel, we will call the
length 44 inches, as the half inch added will make it about equivalent to a
pendulum entirely of steel. If the height of the mercury be obtained by
dividing 44 by 13.5, it will be 3.25 inches high to its center, or 6.5 inches
high altogether; and were it not for the following circumstance, the
pendulum would be perfectly compensated.

3d. The mercury is the only part of the bob which expands upwards; the
jar does not rise, its lower end being carried downward by the expansion of
the rod, which supports it. In a well-designed pendulum, the jar, straps, etc.,
will be from one-fourth to one-third the weight of the mercury. Assume
them to be seven pounds and twenty-eight pounds respectively; therefore,
the total weight of the bob is thirty-five pounds; but as it is only the
mercury (four-fifths) of this total that rises with an increase of temperature,
we must increase the weight of the mercury in the proportion of five to four,
thus 6.5 × 5 ÷ 4 = 8⅛ inches. Or, what is the same thing, we add one-fourth
to the amount of mercury, because the weight of the jar is one-fourth of that
of the mercury. Eight and one-eighth inches is, therefore, the ultimate
height of the mercury required to compensate the pendulum with that
weight of jar. If the jar had been heavier, say one-third the weight of the
mercury, then the latter would have to be nearly 8.75 inches high.
If the jar be required to be of glass, then we substitute the expansion of
that material in No. 2 and its weight in No. 3.
In the above method of calculating, there are two slight elements of
uncertainty: 1st. In assuming that the center of oscillation is coincident with
the center of the bob; however, I should suppose that they would never be
more than .25 inch apart, and generally much nearer. 2d. The weight of the
jar cannot well be exactly known until after it is finished (i. e., bored
smooth and parallel inside, and turned outside true with the interior), so that
the exact height of the mercury cannot be easily ascertained till then.
I may explain that the reason (in Nos. 1 and 2) we measure the mercury
from the bottom to the center of the column, is that it is its center which we
wish to raise when an increase of temperature occurs, so that the center may
always be exactly the same distance from the point of suspension; and we
have seen that 3.25 inches is the necessary quantity to raise it sufficiently.
Now that center could not be the center without it had as much mercury
over it as it has under it; hence we double the 3.25 and get the 6.5 inches
stated.
From the foregoing it will be seen that the average mercury pendulums
are better than a plain rod, from the fact that the mercury is free to obey the
law of expansion, and so, to a certain degree, does counteract the action of
the balance of the metal of the pendulum, and this with a degree of certainty

that is not found in the gridiron form, provided always that the height and
amount of the mercury are correctly proportional to the total weight of the
pendulum.
Compensating Mercurial Pendulums.—To compensate a pendulum of
this kind takes time and study. The first thing to do is to place maximum
and minimum thermometers in the clock case, so that you can tell the
temperature.
Then get the rate of the clock at a given temperature. For example, say
the clock gains two seconds in twenty-four hours, the temperature being at
70°. Then see how much it gains when the temperature is at 80°. We will
say it gains two seconds more at 80° than it does when the temperature is at
70°.
In that case we must remove some of the mercury in order to
compensate the pendulum. To do this take a syringe and soak the cotton or
whatever makes the suction in the syringe with vaseline. The reason for
doing this is that mercury is very heavy and the syringe must be air-tight
before you can take any of the mercury up into it.
You want to remove about two pennyweights of mercury to every
second the clock gains in twenty-four hours. Now, after removing the
mercury the clock will lose time, because the pendulum is lighter. You must
then raise the ball to bring it to time. You then repeat the same operation by
getting the rate at 70° and 80° again and see if it gains. When the
temperature rises, if the pendulum still gains, you must remove more
mercury; but if it should lose time when the temperature rises you have
taken out too much mercury and you must replace some. Continue this
operation until the pendulum has the same rate, whether the temperature is
high or low, raising the bob when you take out mercury to bring it to time,
and lowering the bob when you put mercury in to bring it to time.
To compensate a pendulum takes time and study of the clock, but if you
follow out these instructions you will succeed in getting the clock to run
regularly in both summer and winter.
Besides the oxidation, which is an admitted fault, there are two
theoretical questions which have to do with construction in deciding
between the metallic and mercurial forms of compensation. We will present

the claims of each side, therefore, with the preliminary statement that (for
all except the severest conditions of accuracy) either form, if well made will
answer every purpose and that therefore, except in special circumstances,
these objections are more theoretical than real.
The advocates of metallic compensation claim that where there are great
differences of temperature, the compensated rod, with its long bars will
answer more quickly to temperature changes as follows:
The mercurial pendulum, when in an unheated room and not subjected
to sudden temperature changes, gives very excellent results, but should the
opposite case occur there will then be observed an irregularity in the rate of
the clock. The causes which produce these effects are various. As a
principal reason for such a condition it may be stated that the compensating
mercury occupies only about one-fifth the pendulum length, and it
inevitably follows that when the upper strata of the air is warmer than the
lower, in which the mercury is placed, the steel pendulum rod will expand
at a different ratio than the mercury, as the latter is influenced by a different
degree of temperature than the upper part of the pendulum rod. The natural
effect will be a lengthening of the pendulum rod, notwithstanding the
compensation, and therefore, a loss of time by the clock.
Two thermometers, agreeing perfectly, were placed in the case of a
clock, one near the point of suspension, and the other near the middle of the
ball, and repeated experiments, showed a difference between these two
thermometers of 7° to 10½° F., the lower one indicating less than the higher
one. The thermometers were then hung in the room, one at twenty-two
inches above the floor, and the other three feet higher, when they showed a
difference of 7° between them. The difference of 2.5° more which was
found inside the case proceeds from the heat striking the upper part of the
case; and the wood, though a bad conductor, gradually increases in
temperature, while, on the contrary, the cold rises from the floor and acts on
the lower part of the case. The same thermometers at the same height and
distance in an unused room, which was never warmed, showed no
difference between them; and it would be the same, doubtless, in an
observatory.
From the preceding it is very evident that the decrease of rate of the
clock since December 13 proceeded from the rod of the pendulum

experiencing 7° to 10.5° F. greater heat than the mercury in the bob, thus
showing the impossibility of making a mercurial pendulum perfectly
compensating in an artificially heated room which varies greatly in
temperature. I should remark here that during the entire winter the
temperature in the case is never more than 68° F., and during the summer,
when the rate of the clock was regular, the thermometer in the case has
often indicated 72° to 77° F.
The gridiron pendulum in this case would seem preferable, for if the
temperature is higher at the top than at the lower part, the nine
compensating rods are equally affected by it. But in its compensating action
it is not nearly as regular, and it is very difficult to regulate it, for in any
room (artificially heated) it is impossible to obtain a uniform temperature
throughout its entire length, and without that all proofs are necessarily
inexact.
These facts can also be applied to pendulums situated in heated rooms.
In the case of a rapid change in temperature taking place in the observatory
rooms, under the domes of observatories, especially during the winter
months, and which are of frequent occurrence, a mercurial compensation
pendulum, as generally made, is not apt to give a reliable rate. Let us accept
the fact, as an example, of a considerable fall in the temperature of the
surrounding air; the thin pendulum rod will quickly accept the same
temperature, but with the great mass of mercury to be acted upon the
responsive effects will only occur after a considerable lapse of time. The
result will be a shortening of the pendulum length and a gain in the rate
until the mercury has had time to respond, notwithstanding the
compensation.
Others who have expressed their views in writing seem to favor the idea
that this inequality in the temperature of the atmosphere is unfavorable to
the accurate action of the mercurial form of compensation; and however
plausible and reasonable this idea may seem at first notice, it will not take a
great amount of investigation to show that, instead of being a disadvantage,
its existence is beneficial, and an important element in the success of
mercurial pendulums.
It appears that the majority of those who have proposed, or have tried to
improve Graham’s pendulum have overlooked the fact that different

substances require different quantities of heat to raise them to the same
temperature. In order to warm a certain weight of water, for instance, to the
same degree of heat as an equal weight of oil, or an equal weight of
mercury, twice as much heat must be given to the water as to the oil, and
thirty times as much as to the mercury; while in cooling down again to a
given temperature, the oil will cool twice as quick as the water, and the
mercury thirty times quicker than the water. This phenomenon is accounted
for by the difference in the amount of latent heat that exists in various
substances. On the authority of Sir Humphrey Davy, zinc is heated and
cooled again ten and three-quarters times quicker than water, brass ten and a
half times quicker, steel nine times, glass eight and a half times, and
mercury is heated and cooled again thirty times quicker than water.
From the above it will be noticed that the difference in the time steel
and mercury takes to rise and fall to a given temperature is as nine to thirty,
and also that the difference in the quantity of heat that it takes to raise steel
and mercury to a given temperature is in the ratio of nine to thirty.
Now, without entering into minute details on the properties which
different substances possess for absorbing or reflecting heat, it is plain that
mercury should move in a proportionally different atmosphere from steel in
order to be expanded or contracted a given distance in the same length of
time; and to obtain this result the amount of difference in the temperature of
the atmosphere at the opposite ends of the pendulum must vary a little more
or less according to the nature of the material the mercury jars are
constructed from.
Differences in the temperature of the atmosphere of a room will
generally vary according to its size, the height of the ceiling, and the
ventilation of the apartment; and if the difference must continue to exist, it
is of importance that the difference should be uniformly regular. We must
not lose sight of the fact, however, that clocks having these pendulums, and
placed in apartments every way favorable to an equal temperature, and in
some instances, the clocks and their pendulums encased in double casing in
order to more effectually obtain this result, still the rates of the clock show
the same eccentricities as those placed in less favorable position. This
clearly shows that many changes in the rates of fine clocks are due to other
causes than a change in the temperature of the surrounding atmosphere.
Still it must be admitted that any change in the condition of the atmosphere

that surrounds a pendulum is a most formidable obstacle to be overcome by
those who seek to improve compensated pendulums, and it would be of
service to them to know all that can possibly be known on the subject.
The differences spoken of above have resulted in some practical
improvements, which are: 1st, the division of the mercury into two, three or
four jars in order to expose as much surface as possible to the action of the
air, so that the expansion of the mercury should not lag behind that of the
rod, which it will do if too large amounts of it are kept in one jar. 2nd, the
use of very thin steel jars made from tubing, so that the transmission of heat
from the air to the mercury may be hastened as much as possible. 3rd, the
increase in the number of jars makes a thinner bob than a single jar of the
same total weight and hence gives an advantage in decreasing the resistant
effect of air friction in dense air, thereby decreasing somewhat the
barometric error of the pendulum.
The original form of mercurial pendulums, as made by Graham, and
still used in tower and other clocks where extraordinary accuracy is not
required, was a single jar which formed the bob and had the pendulum rod
extending into the mercury to assist in conducting heat to the variable
element of the pendulum. It is shown in section in Fig. 13, which is taken
from a working drawing for a tower clock.
The pendulum, Fig. 13, is suspended from the head or cock shown in
the figure, and supported by the clock frame itself, instead of being hung on
a wall, since the intention is to set the clock in the center of the clockroom,
and also because the weight, forty pounds, is not too much for the clock
frame to carry. The head, A, forms a revolving thumb-nut, which is divided
into sixty parts around the circumference of its lower edge, and the
regulating screw, B, is threaded ten to the inch. A very fine adjustment is
thus obtained for regulating the time of the pendulum. The lower end of the
regulating screw, B, holds the end of the pendulum spring, E, which is
riveted between two pieces of steel, C, and a pin, C′, is put through them
and the end of the regulating screw, by which to suspend the pendulum.
The cheeks or chops are the pieces D, the lower edges of which form
the theoretical point of suspension of the pendulum. These pieces must be
perfectly square at their lower edges, otherwise the center of gravity would

describe a cylindrical curve. The chops are clamped tightly in place by the
setscrews, D′, after the pendulum has been hung.
The lower end of the regulating screw is squared to fit the ways and
slotted on one side, sliding on a pin to prevent its turning and therefore
twisting the suspension spring when it is raised or lowered.
The spring is three inches long between its points of suspension, one
and three-eighths inches wide, and one-sixtieth of an inch thick. Its lower
end is riveted between two small blocks of steel, F, and suspended from a
pin, F′, in the upper end of the cap, G, of the pendulum rod.
The tubular steel portion of the pendulum rod is seven-eighths of an
inch in diameter and one-thirty-second of an inch thickness of the wall. It is
enclosed at each end by the solid ends, G and L, and is made as nearly air-
tight as possible.
The compensation is by mercury inclosed in a cast iron bob. The
mercury, the bob and the rod together weigh forty pounds. The bob of the
pendulum is a cast iron jar, K, three inches in diameter inside, one-quarter
inch thick at the sides, and five-sixteenths thick at the bottom, with the cap,
J, screwed into its upper end. The cap, J, forms also the socket for the lower
end of the pendulum rod, H. The rod, L, one-quarter inch in diameter,
screws into the cap, J, and its large end at the same time forms a plug for
the lower end of the pendulum tube, H. The pin, J′, holds all these parts
together. The rod, L, extends nearly to the bottom of the jar, and forms a
medium for the transmission of the changes in temperature from the
pendulum tube to the mercury. The screw in the cap, J, is for filling or
emptying the jar. The jar is finished as smoothly as possible, outside and
inside, and should be coated with at least three coats of shellac inside. Of
course if one was building an astronomical clock, it would be necessary to
boil the mercury in the jar in order to drive off the layer of air between the
mercury and the walls of the jar, but with the smooth finish the shellac will
give, in addition to the good work of the machinist, the amount of air held
by the jar can be ignored.
The cast iron jar was decided upon because it was safer to handle, can
be attached more firmly to the rod with less multiplication of parts, and also
on account of the weight as compared with glass, which is the only other
thing that should be used, the glass requiring a greater height of jar for

equal weight. In making cast iron jars, they should
always be carefully turned inside and out in order that
the walls of the jar may be of equal thickness
throughout; then they will not throw the pendulum out of
balance when they are screwed up or down on the
pendulum rod in making the coarse regulation before
timing by the upper screw. The thread on the rod should
have the cover of the jar at about the center of the thread
when nearly to time and that portion which extends into
the jar should be short enough to permit this.
Ignoring the rod and its parts for the present, and
calling the jar one-third of the weight of the mercury, we
shall find that thirty pounds of mercury, at .49 pounds
per cubic inch, will fill a cylinder which is three inches
inside diameter to a height of 8.816 inches, after
deducting for the mass of the rod L, when the
temperature of the mercury is 60 degrees F. Mercury
expands one-tenth in bulk, while cast iron expands .0066
in diameter: so the sectional area increases as 1.0066² or
1.0132 to 1, therefore the mercury will rise .1-.013243,
or .086757; then the mercury in our jar will rise .767 of
an inch in the ordinary changes of temperature, making a
total height of 9.58 inches to provide for; so the jar was
made ten inches long.
Pendulums of this pattern as used in the high grade
English clocks, are substantially as follows: Rod of steel
⁵⁄₁₆inch diameter jar about 2.1 inches diameter inside and
Fig. 13. 8¾ inches deep inside. The jar may be wrought or cast
iron and about ⅜ of an inch thick with the cover to screw
on with fine thread, making a tight joint. The cover of the jar is to act as a
nut to turn on the rod for regulation. The thread cut on the rod should be
thirty-six to the inch, and fit into the jar cover easily, so that it may turn
without binding. With a thirty-six thread one turn of the jar on the rod
changes the rate thirty seconds per day and by laying off on the edge of the
cover 30 divisions, a scale is made by which movements for one second per
day are obtained.

We will now describe (Fig. 14) the method of making a mercurial
pendulum to replace an imitation gridiron pendulum for a Swiss, pin
escapement regulator, such as is commonly found in the jewelry stores of
the United States, that is, a clock in which the pendulum is supported by the
plates of the movement and swings between the front plate and the dial of
the movement. In thus changing our pendulum, we shall desire to retain the
upper portion of the old rod, as the fittings are already in place and we shall
save considerable time and labor by this course. As the pendulum is
suspended from the movement, it must be lighter in weight than if it were
independently supported by a cast iron bracket, as shown in Fig. 6, so we
will make the weight about that of the one we have removed, or about
twelve pounds. If it is desired to make the pendulum heavier, four jars of
the dimensions given would make it weigh about twenty pounds, or four
jars of one inch diameter would make a thinner bob and one weighing about
fourteen pounds. As the substitution of a different number or different sizes
of jars merely involves changing the lengths of the upper and lower bars of
the frame, further drawings will be unnecessary, the jeweler having
sufficient mechanical capacity to be able to make them for himself. I might
add, however, that the late Edward Howard, in building his astronomical
clocks, used four jars containing twenty-eight pounds of mercury for such
movements, and the perfection of his trains was such that a seven-ounce
driving weight was sufficient to propel the thirty pound pendulum.
The two jars are filled with mercury to a height of 7⅝ inches, are 1⅜
inches in diameter outside and 8⅜ inches in height outside. The caps and
foot pieces are screwed on and when the foot pieces are screwed on for the
last time the screw threads should be covered with a thick shellac varnish
which, when dry, makes the joint perfectly air-tight. The jars are best made
of the fine, thin tubing, used in bicycles, which can be purchased from any
factory, of various sizes and thickness. In the pendulum shown in the
illustration, the jar stock is close to 14 wire gauge, or about 2 mm. in
thickness. In cutting the threads at the ends of the jars they should be about
36 threads to the inch, the same number as the threads on the lower end of
the rod used to carry the regulating nut. A fine thread makes the best job
and the tightest joints. The caps to the jars are turned up from cold rolled
shafting, it being generally good stock and finishes well. The threads need
not be over ³⁄₁₆ inch, which is ample. Cut the square shoulder so the caps
and foot pieces come full up and do not show any thread when screwed

home. These jars will hold ten pounds of mercury and this weight is about
right for this particular style of pendulum. The jars complete will weigh
about seven ounces each.

Fig. 14.
The frame is also made of steel and square finished stock is used as far
as possible and of the quality used in the caps. The lower bar of the frame is
six inches long and ⅝ inch square at the center and tapered, as shown in the
illustration. It is made light by being planed away on the under side, an end
view being shown at 3. The top bar of the frame, shown at 4, is planed away
also and is one-half inch square the whole length and is six inches long. The

two side rods are to bind the two bars together, and with the four thumb
nuts at the top and bottom make a strong light frame.
The pendulum described is nickel plated and polished, except the jars,
which are left half dead; that is, they are frosted with a sand blast and
scratch brushed a little. The effect is good and makes a good contrast to the
polished parts. The side rods are five inches apart, which leaves one-half
inch at the ends outside.
The rod is ⁵⁄₁₆ of an inch in diameter and 33 inches long from the
bottom of the frame at a point where the regulating nut rests against it to the
lower end of the piece of the usual gridiron pendulum shown in Fig. 14 at
10. This piece shown is the usual style and size of those in the majority of
these clocks and is the standard adopted by the makers. This piece is 11⅛
inches long from the upper leaf of the suspension spring, which is shown at
12, to the lower end marked 10. By cutting out the lower end of this piece,
as shown at 10, and squaring the upper end of the rod, pinning it into the
piece as shown, the union can be made easily and any little adjustments for
length can be made by drilling another set of holes in the rod and raising the
pendulum by so doing to the correct point. A rod whose total length is 37
inches will leave 2 inches for the prolongation below the frame carrying the
regulating nut, 9, and for the portion squared at the top, and will then be so
long that the rate of the clock will be slow and leave a surplus to be cut off
either at the top or bottom, as may seem best.
The screw at the lower end carrying the nut should have 36 threads to
the inch and the nut graduated to 30 divisions, each of which is equal in
turning the nut to one minute in 24 hours, fast or slow, as the case may be.
The rod should pass through the frame bars snugly and not rattle or
bind. It also should have a slot cut so that a pin can be put through the upper
bar of the frame to keep the frame from turning on the rod and yet allow it
to move up and down about an inch. The thread at the lower end of the rod
should be cut about two inches in length and when cutting off the rod for a
final length, put the nut in the middle of the run of the thread and shorten
the rod at the top. This will be found the most satisfactory method, for when
all is adjusted the nut will stand in the middle of its scope and have an equal
run for fast or slow adjustment. With the rod of the full length as given, this
pendulum had to be cut at the top about one inch to bring to a minute or two

in twenty-four hours, and this left all other points below corrected. The pin
in the rod should be adjusted the last thing, as this allows the rod to slide on
the pin equal distances each way. One inch in the raising or lowering of the
frame on the rod will alter the rate for twenty-four hours about eighteen
minutes.
Many attempts have been made to combine the good qualities of the
various forms of pendulums and thus produce an instrument which would
do better work under the severe exactions of astronomical observatories and
master clocks controlling large systems. The reader should understand that,
just as in watch work, the difficulties increase enormously the nearer we get
towards absolute accuracy, and while anybody can make a pendulum which
will stay within a minute a month, it takes a very good one to stay within
five seconds per month, under the conditions usually found in a store, and
such a performance makes it totally unfit for astronomical work, where
variations of not over five-thousandths of a second per day are demanded.
In order to secure such accuracy every possible aid is given to the
pendulum. Barometric errors are avoided by enclosing it in an air-tight case,
provided with an air pump; the temperature is carefully maintained as
nearly constant as possible and its performance is carefully checked against
the revolutions of the fixed stars, while various astronomers check their
observations against each other by correspondence, so that each can get the
rate of his clock by calculations of observations and the law of averages,
eliminating personal errors.
One of the successful attempts at such a combination of mercury and
metallic pendulums is that of Riefler, as shown in Fig. 15, which illustrates
a seconds pendulum one-thirtieth of the actual size.
It consists of a Mannesmann steel tube (rod), bore 16 mm., thickness of
metal 1 mm., filled with mercury to about two-thirds of its length, the
expansion of the mercury in the tube changing the center of weight an
amount sufficient to compensate for the lengthening of the tube by heat, or
vice versa. The pendulum, has further, a metal bob weighing several
kilograms, and shaped to cut the air. Below the bob are disc shaped weights,
attached by screw threads, for correcting the compensation, the number of
which may be increased or diminished as appears necessary.

Whereas in the Graham pendulum regulation for temperature is effected
by altering the height of the column of mercury, in this pendulum it is
effected by changing the position of the center of weight of the pendulum
by moving the regulating weights referred to, and thus the height of the
column of mercury always remains the same, except as it is influenced by
the temperature.
A correction of the compensation should be
effected, however, only in case the pendulum is to
show sidereal time, instead of mean solar time, for
which latter it is calculated. In this case a weight of
110 to 120 grams should be screwed on to correct the
compensation.
In order to calculate the effect of the
compensation, it is necessary to know precisely the
coefficients of the expansion by heat of the steel rod,
the mercury, and the material of which the bob is
made.
The last two of these coefficients of expansion are
of subordinate importance, the two adjusting screws
for shifting the bob up and down being fixed in the
middle of the latter. A slight deviation is, therefore, of
no consequence. In the calculation for all these
pendulums the co-efficient for the bob is, therefore,
fixed at 0.000018, and for the mercury at 0.00018136,
being the closest approximation hitherto found for
chemically pure mercury, such as that used in these
pendulums.
The co-efficient of the expansion of the steel rod
is, however, of greater importance. It is therefore,
Fig. 15. ascertained for every pendulum constructed in Mr.
Riefler’s factory, by the physikalisch-technische
Reichsanstalt at Charlottenburg, examinations showing, in the case of a
large number of similar steel rods, that the co-efficient of expansion lies
between 0.00001034 and 0.00001162.

The precision with which the measurements are carried out is so great
that the error in compensation resulting from a possible deviation from the
true value of the co-efficient of expansion, as ascertained by the
Reichsanstalt, does not amount to over ± 0.0017; and, as the precision with
which the compensation for each pendulum may be calculated absolutely
precludes any error of consequence, Mr. Riefler is in a position to guarantee
that the probable error of compensation in these pendulums will not exceed
± 0.005 seconds per diem and ± 1° variation in temperature.
A subsequent correction of the compensation is, therefore, superfluous,
whereas, with all other pendulums it is necessary, partly because the
coefficients of expansion of the materials used are arbitrarily assumed; and
partly because none of the formulæ hitherto employed for calculating the
compensation can yield an exact result, for the reason that they neglect to
notice certain important influences, in particular that of the weight of the
several parts of the pendulum. Such formulæ are based on the assumption
that this problem can be solved by simple geometrical calculation, whereas,
its exact solution can be arrived at only with the aid of physics.
This is hardly the proper place for details concerning the lengthy and
rather complicated calculations required by the method employed. It is
intended to publish them later, either in some mathematical journal or in a
separate pamphlet. Here I will only say that the object of the whole
calculation is to find the allowable or requisite weight of the bob, i. e., the
weight proportionate to the coefficients of expansion of the steel rod,
dimensions and weight of the rod and the column of mercury being given in
each separate case. To this end the relations of all the parts of the pendulum,
both in regard to statics and inertia, have to be ascertained, and for various
temperatures.
A considerable number of these pendulums have already been
constructed, and are now running in astronomical observatories. One of
them is in the observatory of the University of Chicago, and others are in
Europe. The precision of this compensation which was discovered by
purely theoretical computations, has been thoroughly established by the
ascertained records of their running at different temperatures.
The adjustment of the pendulums, which is, of course, almost wholly
without influence on the compensation, can be effected in three different

ways;
(1.) The rough adjustment, by screwing the bob up or
down.
(2.) A finer adjustment, by screwing the correction discs
up or down.
(3.) The finest adjustment, by putting on additional
weights.
These weights are to be placed on a cup attached to a special part of the
rod of the pendulum. Their shape and size is such that they can be readily
put on or taken off while the pendulum is swinging. Their weight bears a
fixed proportion to the static momentum of the pendulum, so that each
additional weight imparts to the pendulum, for twenty-four hours, an
acceleration expressed in even seconds and parts of seconds, and marked on
each weight.
Each pendulum is accompanied with additional weights of German
silver, for a daily acceleration of 1 second each, and ditto of aluminum for
an acceleration of 0.5 and 0.1 second respectively.
A metal clasp attached on the rear side of the clock case, may be pushed
up to hold the pendulum in such a way that it can receive no twisting
motion during adjustment.
Further, a pointer is attached to the lower end of the pendulum, for
reading off the arc of oscillation.
The essential advantages of this pendulum over the mercurial
compensation pendulums are the following:
(1.) It follows the changes of temperature more rapidly,
because a small amount of mercury is divided over a greater
length of pendulum, whereas, in the older ones the entire
(and decidedly larger) mass of mercury is situated in a vessel
at the lower end of the pendulum rod.
(2.) For this reason differences in the temperature of the
air at different levels have no such disturbing influence on
this pendulum as on the others.

(3.) This pendulum is not so strongly influenced as the
others by changes in the atmospheric pressure, because the
principal mass of the pendulum has the shape of a lens, and
therefore cuts the air easily.

CHAPTER V.
REGULATIONS, SUSPENSIONS, CRUTCHES
AND MINOR POINTS.

Regulation.—The reader will have noticed that in describing the
various forms of seconds pendulums we have specified either eighteen or
thirty-six threads to the inch; this is because a revolution of the nut with
such a thread gives us a definite proportion of the length of the rod, so that
it means an even number of seconds in twenty-four hours.
Moving the bob up or down ¹⁄₁₈ inch makes the clock having a seconds
pendulum gain or lose in twenty-four hours one minute, hence the selecting
definite numbers of threads has for its reason a philosophical standpoint,
and is not a matter of convenience and chance, as seems to be the practice
with many clockmakers. With a screw of eighteen threads, we shall get one
minute change of the clock’s rate in twenty-four hours for every turn of the
nut, and if the nut is divided into sixty parts at its edge, each of these
divisions will make a change of the clock’s rate of one second in twenty-
four hours. Thus by using a thread having a definite relation to the length of
the rod regulating is made comparatively easy, and a clock can be brought
to time without delay. Suppose, after comparing your clock for three or four
days with some standard, you find it gains twelve seconds per day, then,
turning the nut down twelve divisions will bring the rate down to within one
second a day in one operation, if the screw is eighteen threads. With the
screw thirty-six threads the nut will require moving just the same number of
divisions, only the divisions are twice as long as those with the screw of
eighteen threads.
The next thing is the size and weight of the nut. If it is to be placed in
the middle of the bob as in Figs. 10, 12 and 15, it should project slightly
beyond the surface and its diameter will be governed by the thickness of the
bob. If it is an internal nut, worked by means of a sleeve and disc, as in Fig.
9, the disc should be of sufficient diameter to make the divisions long
enough to be easily read. If the nut is of the class shown in Fig. 5, 6, 7, a nut

is most convenient, 1 inch in diameter, and cut on its edge into thirty equal
divisions, each of which is equal to one second in change of rate in twenty-
four hours, if the screw has thirty-six threads to the inch. This gives 3.1416
inches of circumference for the thirty divisions, which makes them long
enough to be subdivided if we choose, each division being a little over one-
tenth of an inch in length, so that quarter-seconds may be measured or
estimated.
With some pendulums, Fig. 13, the bob rotates on the rod, and is in the
form of a cylinder, say 8½ inches long by 2½ inches in diameter, and the
bob then acts on its rod as the nut does, and moves up and down when
turned, and in this form of bob the divisions are cut on the outside edge of
the cover of the bob, and are so long that each one is subdivided into five or
ten smaller divisions, each altering the clock .2 or .1 second per day.
On the top of the bob turn two deep lines, close to the edge, about ⅛-
inch apart, and divide the whole diameter into thirty equal divisions, and
subdivide each of the thirty into five, and this will give seconds and fifths of
seconds for twenty-four hours. Each even seconds division should be
marked heavier than the fraction, and should be marked from one to thirty
with figures. Just above the cover on the rod should slide a short tube,
friction-tight, and to this a light index or hand should be fastened, the point
of which just reaches the seconds circle on the bob cover, and thus indicates
the division, its number and fraction. The tube slides on the rod because the
exact place of the hand cannot be settled until it has been settled by
experiment. After this it can be fastened permanently, if thought best,
though as described it will be all sufficient. While the bob is being raised or
lowered to bring the clock to its rate, the bob might get too far away or too
near to the index and necessitate its being shifted, and if friction-tight this
can be readily accomplished, and the hand be brought to just coincide with
the divisions and look well and be a means of accomplishing very accurate
minute adjustments.
Suspensions.—Suspensions are of four kinds, cord, wire loop, knife
edges and springs. Cords are generally of loosely twisted silk and are
seldom found except in the older clocks of French or Swiss construction.
They have been entirely displaced in the later makes of European
manufactures by a double wire loop, in which the pendulum swings from a
central eye in the loop, while the loop rocks upon a round stud by means of

an eye at each end of the loop. The eyes should all be in planes parallel to
the plane of oscillation of the pendulum, otherwise the bob will take an
elliptical path instead of oscillating in a plane. They should also be large
enough to roll without friction upon the stud and center of the loop, as any
slipping or sliding of either will cause them to soon wear out, besides
affecting the rate of the pendulum. Properly constructed loops will give
practically no friction and make a very free suspension that will last as long
as the clock is capable of keeping time, although it seems to be a very weak
and flimsy method of construction at first sight. Care should be taken in
such cases to keep the bob from turning when regulating the clock, or the
effect upon the pendulum will be the same as if the eyes were not parallel.
Knife edge suspensions are also rare now, having been displaced by the
spring, as it was found the vibrations were too free and any change in power
introduced a circular error (See Fig. 4) by making the long swings in longer
time. They are still to be found, however, and in repairing clocks containing
them the following points should be observed: The upper surface of the stud
on which the pendulum swings should carry the knife edge at its highest
point, exactly central with the line of centers of the stud, so that when the
pendulum hangs at rest the stud shall taper equally on both sides of the
center, thus giving equal freedom to both sides of the swing. Care should be
taken that the stud is firmly fixed, with the knife edge exactly at right angles
to the movement, and also to the back of the case. The suspension stud and
the block on the rod should be long enough to hold the pendulum firmly in
line, as the angle in the top of the rod must be the sole means of keeping the
pendulum swinging in plane. The student will also perceive the necessity of
making the angle occupy the proper position on the rod, especially if the
latter be flat. In repairing this suspension it is usual to make the plate, fasten
it in place and then drill and file out the hole, as it is easier to get the angles
exactly in this way than to complete the plate and then attempt to fasten it in
the exact position in which it should be. After fastening the plates in
position on the rod, two holes should be drilled, a small one at the apex of
the angle (which must be exactly square and true with the rod), and a larger
one below it large enough to pass the files easily. The larger hole can then
be enlarged to the proper size, filing the angle at the top in such a way that
the small hole first drilled forms the groove at the apex of the angle in
which the knife edge of the stud shall work when it is completed. Knife
edge suspensions are unfitted for heavy pendulums, as the weight causes

the knife edge to work into the groove and cut it, even if the latter be
jeweled. Both the edge and groove should be hardened and polished.
Pendulum Suspension Springs.—Next in importance to the pendulum is
its suspension spring. This spring should be just stiff enough to make the
pendulum swing in all its vibrations in the same time; that is, if the
pendulum at one time swung at the bottom of the jar 1¼ inch each side of
the center, and at another time it swung only 1 inch each side, that the two
should be made in exactly one second. The suspension springs are a point in
the construction of a fine pendulum, that there has been very much
theorizing on, but the experiments have never thus far exactly corroborated
the theories and there are no definite rules to go by, but every maker holds
to that plan and construction that gives his particular works the best results.
A spring of sufficient strength to materially influence the swing of the
pendulum is of course bad, as it necessitates more power to give the
pendulum its proper motion and hence there is unnecessary wear on the
pallets and escape wheel teeth, and too weak a spring is also bad, as it
would not correct any inequalities in the time of swing and would in time
break from overloading, as its granular structure would finally change, and
rupture of the spring would follow. The office of a spring is to sustain the
weight without detriment to strength and elasticity, and if so proportioned to
the weight as to be just right, it will make the long and short swings of the
pendulum of equal duration. When a pendulum hung by a cord or knife
edge instead of a spring is regulated to mean time and swings just two
inches at the bottom, any change in the power that swings the pendulum
will increase its movement or decrease it, and in either case the rate will
change, but with a proper spring the rate will be constant under like
conditions. The action of the spring is this: In the long swings the spring, as
it bends, lifts the pendulum bob up a little more than the arc of the normal
circle in which it swings, and consequently when the bob descends, in
going to the center of its swing, it falls a little quicker than it does when
held by a cord, and this extra quick drop can be made to neutralize the extra
time taken by the bob in making extra long swings. See Fig. 4. This action
is the isochronal action of the spring, the same that is attained in isochronal
hair springs in watches.
As with the hairspring, it is quite necessary that the pendulum spring be
accurately adjusted to isochronism and my advice to every jeweler is to

thoroughly test his regulator, which can easily be done by changing the
weight or motive power. If the test should prove the lack of isochronism he
can adjust it by following these simple rules. Fig. 16 is the pendulum spring
or leaf. If the short arcs should prove the slowest, make the spring a trifle
thinner at B; if fastest, reduce the thickness of the spring at A. Continue the
test until the long and short arcs are equal. In doing this care must be taken
to thin each spring equally, if it is a double spring, and each edge equally, if
a single spring, as if one side be left thicker than the other the pendulum
will wabble.

Fig. 16.
The cause of a pendulum wobbling is that there must be something
wrong with the suspension spring, or the bridge that holds the spring. If the
suspension spring is bent or kinked, the pendulum will wabble; or if the
spring should be of an unequal thickness it will have the same effect on the
pendulum; but the main cause of the pendulum wobbling in American
clocks is that the slot in the bridge that holds the spring, or the slot in the
slide that works up and down on the spring (which is used to regulate the
clock) is not parallel. When this slot is not parallel it pinches the spring,
front or back, and allows it to vibrate more where it is the freest, causing the
pendulum to wabble. We have found that by making these slots parallel the
wobbling of the pendulum has ceased in most all cases. If the pallet staff is
not at right angles to the crutch, wobbling may be caused by the oblique
action of the crutch. This often happens when the movement is not set
square in the case.

It occasionally happens in mantel clocks that the pendulum when
brought to time is just too long for the case when too thick a spring is used.
In such a case thinning the spring will require the bob to be raised a little
and also give a better motion. If compelled to make a spring use a piece of
mainspring about .007 thick and ⅜ wide for small pendulums and the same
spring doubled for heavier pendulums, making the acting part of the spring
about 1.5 inches long.
The suspension spring for a rather heavy pendulum is better divided,
that is, two springs, held by two sets of clamps, and jointly acting as one
spring. The length will be the same as to the acting part, and that part held
at each end by the clamps may be ¾ inch long; total length, 1.5 inches with
⅜ inch at each end held in the clamps. These clamps are best soldered on to
the spring with very low flowing solder so as not to draw the temper of the
spring, and then two rivets put through the whole, near the lower edge of
the clamps. The object of securing the clamps so firmly is so that the spring
may not bend beyond the edge of the clamps, as if this should take place the
clock will be thrown off of its rate. After a time the rate would settle and
become steady, but it only causes an extra period of regulating that does not
occur when the clamps hold the spring immovable at this point. About in
the center of each of the clamps, when soldered and riveted, is to be a hole
bored for a pin, which pins the clamp into the bracket and holds the weight
of the pendulum.
The width of this compound spring for a seconds’ pendulum of average
weight may be .60 inch, from outside to outside, each spring .15 inch wide.
This will separate the springs .30 inch in the center. With this form of
spring, the lower end of each spring being held in a pair of clamps, the
clamps will have to be let into the top of the rod, and held in by a stout pin,
or the pendulum finished with a hook which will fit the clamp. In letting the
clamp into the rod, the clamp should just go into the mortise and be without
side shake, but tilt each way from the center a little on the pin, so that when
the pendulum is hung it may hang perpendicular, directly in the center of
both springs. Also, the top pair of clamps should fit into a bracket without
shake, and tilt a little on a pin, the same as the lower clamps. These two
points, each moving a little, helps to take any side twist away, and allows
the whole mechanism to swing in line with the center of gravity of the mass
from end to end. With the parts well made, as described, the bob will swing

in a straight line from side to side, and its path will be without any other
motion except the one of slight curvature, due to being suspended by a
fixed point at the upper clamp.
Pendulum Supports.—Stability in the movement and in the suspension
of the pendulum is very necessary in all forms of clocks for accurate
timekeeping. The pendulum should be hung on a bracket attached to the
back of the case (see Fig. 6), and not be subject to disturbance when the
movement is cleaned. Also the movement should rest on two brackets
attached to the bracket holding the pendulum and the whole be very firmly
secured to the back board of the case. Screws should go through the foot
pieces of the brackets and into a stone or brick wall and be very firmly held
against the wall just back of the brackets. Any instability in this part of a
clock is very productive of poor rates. The bracket, to be in its best form, is
made of cast iron, with a large foot carrying all three separate brackets, well
screwed to a strong back board and the whole secured to the masonry by
bolts. Too much firmness cannot be attained, as a lack of it is a very great
fault, and many a good clock is a very poor timekeeper, due to a lack of
firmness in its supports and fastenings. The late Edward Howard used to
make his astronomical clocks with a heavy cast iron back, to which the rest
of the case was screwed, so that the pendulum should not swing the case.
Any external influence that vibrates a wall or foundation on which a clock
is placed, is a disturbing influence, but an instability in a clock’s attachment
to such supports is a greater one. Many pendulums swing the case in which
they hang (from unstable setting up) and never get down to or maintain a
satisfactory rate from that cause. This is also aggravated by the habit of
placing grandfather clocks on stair landings or other places subject to
jarring. The writer knows of several clocks which, after being cleaned, kept
stopping until raised off the floor and bolted to the wall, when they at once
took an excellent rate. The appearance of resting on the floor may be
preserved, if desirable, by raising the clock only half an inch or so, just
enough to free it from the floor.
Crutches.—The impulse is transmitted to the pendulum from the pallet
staff by means of a wire, or slender rod, fastened at its upper end to the
pallet staff and having its lower end terminating in a fork (crutch), loop, or
bent at right angles so as to work freely in a slot in the rod. It is also called
the verge wire, owing to the fact that older writers and many of the older

workmen called the pallet fork the verge, thus continuing the older
nomenclature, although of necessity the verge disappeared when the crown
wheel was discarded.
In order to avoid friction at this very important point, the centers of both
axes of oscillation, that of the pallet arbor and that of the pendulum spring,
where it bends, should be in a straight horizontal line. If, for instance, the
center of suspension of the pendulum be higher, then the fork and the
pendulum describe two different arcs of circles; that of the pendulum will
be greater than that of the fork at their meeting point. If, however, the center
of suspension of the pendulum be lower than that of the fork, they will also
describe two different arcs, and that of the pendulum will be smaller than
that of the fork at their point of meeting. This, as can be readily understood,
will cause friction in the fork, the pendulum going up and down in it. This
is prevented when, as stated before, the center of suspension of the
pendulum is in the prolonged straight imaginary line going through the
center of the pivots of the fork, which will cause the arcs described by the
fork and the pendulum to be the same. It will be well understood from the
foregoing that the pendulum should neither be suspended higher nor lower,
nor to the left, nor to the right of the fork.
If the centers of motion do not coincide, as is often the case with cheap
clocks with recoil escapements, any roughness of the pendulum rod where
it slides on the crutch will stop the clock, and repairers should always see to
it that this point is made as smooth as possible and be very slightly oiled
when setting up. If putting in a new verge wire, the workman can always
tell where to bend it to form the loop by noticing where the rod is worn and
forming the loop so that it will reach the center of that old crutch or loop
mark on the pendulum rod. If the verge wire is too long, it will give too
great an arc to the pendulum if the latter is hung below the pallet arbor, as is
generally the case with recoil escapements of the cheap clocks, and if it is
too short there will not be sufficient power applied to the pendulum when
the clock gets dirty and the oil dries, in which case the clock will stop
before the spring runs down.
An important thing to look after when repairing is in the verge wire and
loop (the slot the pendulum rod goes through). After the clock is set up and
oiled, put it on a level shelf; have a special adjusted shelf for this level
adjusting, one that is absolutely correct. Have the dial off. If the beat is off

on one side, so that it bangs up heavily on one side of the escape wheel,
bend the verge wire the same way. That will reverse the action and put it in
beat. So far so good—but don’t stop now. Just notice whether if that shelf
were tipped forward or back, as perhaps your customer’s may, that the
pendulum should still hang plumb and free. Now if the top of your clock
tips forward, the pendulum ball inclines to hang out toward the front. We
will suppose you put two small wedges under the back of the case. Now
notice in its hanging out whether the pendulum rod pinches or bears in the
throat of the verge; or if it tips back, see if the rod hits the other end of the
slot. This verge slot should be long enough, with the rod hanging in the
middle when adjusted to beat on a level, to admit of the clock pitching
forward or back a little without creating a friction on the ends of the slot.
This little loop should be open just enough to be nice and free; if open too
much, you will notice the pallet fork will make a little jump when carrying
the ball over by hand. This is lost motion. If this little bend of wire is not
parallel it may be opened enough inside, but if pitched forward a little it
will bind in the narrowest part of the V and then the clock will stop. The
clock beat and the tipping out or in of the clock case, causing a binding or
bearing of the pendulum rod in this verge throat, does more towards
stopping clocks just repaired than all other causes.
Putting in Beat.—To put a clock in beat, hang the clock in such a
position that when the pendulum is at rest one tooth of the escape wheel
will rest on the center of a pallet stone. Screwed on the case of the clock at
the bottom of the pendulum there is, or should be, an index marked with
degrees. Now, while the escape wheel tooth is resting on the pallet, as
explained above, the index of the pendulum should point to zero on the
index. Move the pendulum until the tooth just escapes and note how many
degrees beyond zero the pendulum point is. Say it escapes 2° to the left;
now move the pendulum until the next tooth escapes—it should escape 2°
to the right. But let us suppose it does not escape until the index of the
pendulum registers 5° to the right of zero. In this case the rod attached to
the pallets must be bent until the escape wheel teeth escape when the
pendulum is moved an even number of degrees to the right and left of zero,
when the clock will be in beat.
Close Rating with Shot.—Very close rating of a seconds’ pendulum,
accompanied by records in the book, may be got with the nut alone, but

there is the inconvenience of stopping the clock to make an alteration. This
may be avoided by having a small cup the size of a thimble or small pill
box on the pendulum top. This can be lifted off and put back without
disturbing the motion of the pendulum. In using it a number of small shot,
selected of equal size, are put in, say 60, and the clock brought as nearly as
possible to time by the nut. After a few days the cup may be emptied and
put back, when on further trial the value of the 60 shot in seconds a day will
be found. This value divided by 60 will give the value of a single shot, by
knowing which very small alterations of rate may be made with a definite
approach towards accuracy, and in much less time than by putting in or
taking out one or more shot at random.

CHAPTER VI.
TORSION PENDULUMS FOR FOUR-HUNDRED DAY CLOCKS.

As this pendulum is only found in the 400-day, or annual wind, or
anniversary clocks (they are known by all of these names), it is best to
describe the pendulum and movement together, as its relations to the work
to be done may be more easily perceived.
Rotating pendulums of this kind—that is, in which the bob rotates by
the twisting of the suspension rod or spring—will not bear comparison with
vibrating pendulums for accurate timekeeping. They are only used when a
long period between windings is required. Small clocks to go for twelve
months with one winding have the torsion pendulum ribbons of flat steel
about six inches long, making 15 beats per minute. The time occupied in the
beat of such a pendulum depends on the power of the suspending ribbon to
resist twisting, and the weight and distance from the center of motion of the
bob. In fact, the action of the bob and suspending ribbon is very analogous
to that of a balance and balance spring.

Fig. 17.
In order to get good time from a clock of this character, it should be
made with a dead-beat escapement. With such an escapement there is no
motion of the escape wheel, after the tooth drops on the locking face of the
pallet; the escape wheel is dead and does not move again until it starts to
give the pallet impulse. This style of an escapement allows the pendulum as
much freedom to vibrate as possible, as the fork in one form of this
escapement may leave the pallet pin as soon as the latter strikes the guard
pins, as in the ordinary lever escapement of a watch, and it will remain in
that position until the return of the fork unlocks the escapement to receive
another impulse. B, Fig. 17, represents the escape wheel; C, the pallet; E,

pallet staff; D, the pallet pin rivetted on to the pallet staff E, which works in
the slot or fork H; this fork is screwed fast to the spring. The spring G is
made of a piece of flat steel wire and looks like a clock hairspring
straightened out. G is fast to the collar I and rests on a seat screwed to the
plate of the clock, as shown at P; the spring is also fastened to the pendulum
ball O with screws; the ball makes about one and one-half revolutions each
beat, which causes the spring to twist. It twists more at the point S than it
does at L; as it twists at L it carries the fork with it, so that the latter vibrates
from one side to the other, similar to a fork in a watch. This fork H carries
the pin D, which is fast to the pallet staff E, far enough to allow the teeth to
escape.

Fig. 18.
In the most common form of this escapement, see Fig. 18, the fork does
not allow the pin D to leave the slot H, and the beat pins are absent, the
pendulum not being as highly detached as in the form previously
mentioned. In this case great care must be taken to have the edges of the
slot, which slide on the pallet pin, smooth, parallel and properly beveled, so

as not to bind on the pin. The pendulum ball makes from eight to sixteen
vibrations a minute. Of course the number depends upon the train of the
clock.
In suspending the pendulum it is necessary to verify the drop of the
teeth of the escape wheel as follows: The pendulum is suspended and the
locking position of the pallets marked, taking as a guiding point the long,
regulating screw, which, fixed transversely in the support, serves for
adjusting the small suspension block. An impulse of about a third of a turn
is given to the pendulum while observing the escapement. If the oscillations
of the pendulum, measured on the two sides, taking the locking point as the
base, are symmetrical, the drop is also equal, and the rate of the clock
regular and exact; but if the teeth of the escape wheel are unlocked sooner
on one side than on the other, so that the pendulum in its swing passes
beyond the symmetrical point on one of the pallets and does not reach it on
the other, it is necessary to correct the unequal drop.

Fig. 19.

The suspension block B, Fig. 18, between the jaws of which the steel
ribbon is pressed by two screws, has a lower cylindrical portion, which is
fitted in a hole made in the seat, and is kept immovable by the screw A. If
the vibration of the pendulum passes beyond the proper point on the left
side, it is necessary to loosen A and turn the suspension block slightly to the
right. If the deviation is produced in the opposite direction, it is necessary to
turn it to the left. These corrections should be repeated until the drop of the
escape wheel teeth on the pallets is exactly equal on the two sides. As the
drop is often disturbed by the fact that the long thin steel ribbon has been
twisted in cleaning, taking apart or handling by unskilled persons before
coming to the watchmaker, it is desirable to test the escapement again,
when the clock is put into position on the premises of the buyer.

Fig. 20.
The timing adjustment of the pendulum is effected with the aid of
regulating weights, placed on the ball. By moving these away from the
center by means of a right and left hand screw on the center of the disk (see
Fig. 19), the centrifugal force is augmented, the oscillations of the
pendulum slackened, and the clock goes slower. The contrary effect is
produced if the weights are brought nearer the center. In one form of ball
the shifting of the regulating weights is accomplished by a compensating
spring of steel and brass like the rim of a watch balance, Fig. 20.

If necessary to replace the pendulum spring, the adjustment is
commenced by shortening or lengthening the steel ribbon to a certain
extent. For this purpose the end of the spring is allowed to project above the
suspension block as a reserve until adjustment has been completed, when it
may be cut off. If the space between the ball and the bottom of the case, or
the bottom of the movement plates, does not allow of attaining this end, it is
necessary to increase or decrease the weight of the disk, adding one or
several plates of metal in a depression made in the under side of the ball,
and removing the plates screwed to it, which are too light.
There are some peculiarities of the trains of these clocks. The cannon
pinion is provided with a re-enforcing spring, serving as guide to the dial
work, on which it exercises a sufficient pressure to assure precise working.
The pressure of this spring is important, because if the dial work presses too
hard on the pinion of the minute wheel, the latter engaging directly with the
escape wheel, would transmit to the latter all the force employed in setting
the hands. The teeth of the escape wheel would incur damage and the
consequent irregularity or even stopping of the clock would naturally
follow.
In order that it may run for so long a time, the motive force is
transmitted through the train by the intervention of three supplementary
wheels between the minute wheel and the barrel, in order to avoid the
employment of too large a barrel; the third wheel is omitted; the motion
work is geared immediately with the arbor of the escape wheel. It is evident
that the system of the three intermediate wheels, of which we have spoken,
requires for the motive force a barrel spring much stronger than that of
ordinary clocks.
The points which we have noticed are of the most importance with
reference to the repair and keeping in order of an annual clock. It very often
happens that when the repairer does not understand these clocks,
irregularities are sought for where they do not exist. The pivot holes are
bushed and the depthings altered, when a more intelligent examination
would show that the stopping, or the irregular rate of the clock, proceeds
only from the condition of the escapement. Unless, however, they are
perfectly adjusted, a variation of five minutes a week is a close rate for
them, and most of those in use will vary still more.

Annual clocks are enjoying an increased favor with the public; their
good qualities allow confidence, the rate being quite regular when in proper
order. They are suitable for offices; their silent running recommends them
for the sick chamber, and the subdued elegance of their decoration causes
the best of them to be valued ornaments in the home.

CHAPTER VII.
PECULIARITIES OF ANGULAR MEASUREMENT—
HOW TO READ DRAWINGS.

We now come to a point at which, if we are to keep our pendulum
vibrating, we must apply power to it, evenly, accurately and in small doses.
In order to do this conveniently we must store up energy by raising a weight
or winding a spring and allow the weight to fall or the spring to unwind
very slowly, say in thirty hours or in eight days. This brings about the
necessity of changing rotary motion to reciprocating motion, and the several
devices for doing this are called “escapements” in horology, each being
further designated by the names of their inventors, or by some peculiarity of
the devices themselves; thus, the Graham is also called the dead beat
escapement; Le Paute’s is the pin wheel; Dennison’s in its various forms is
called the gravity; Hooke’s is known as the recoil; Brocot’s as the visible
escapement, etc.
The Mechanical Elements.—We shall understand this subject more
clearly, perhaps, if we first separate these mechanical devices into their
component parts and consider them, not as parts of clocks, but as various
forms of levers, which they really are. This is perhaps the best place to
consider the levers we are using to transmit the energy to the pendulum, as
at this point we shall find a greater variety of forms of the lever than in any
other place in the clock, and we shall have less difficulty in understanding
the methods of calculating for time and power by a thorough preliminary
understanding of leverage and the peculiarities of angular or circular
motion.
If we take a bar, A, Fig. 21, and place under it a fulcrum, B, then by
applying at C a given force, we shall be able to lift at D a weight whose
amount will be governed by the relative distances of C and D from the
fulcrum B. If the distance CB is four times that of BD, then a force of 10
pounds at C will lift 40 pounds at D, for one-fourth of the distance through
which C moves, minus the power lost by friction. The reverse of this is also

true; that is, it will take 40 pounds at D to exert a force of 10 pounds at C
and the 10 pounds would be lifted four times as far as the 40 pound weight
was depressed.

Fig. 21.

Fig. 22.
If instead of a weight we substitute other levers, Fig. 22, the result
would be the same, except that we should move the other levers until the
ends which were in contact slipped apart.

Fig. 23.
If we divide our lever and attach the long end to one portion of an axle,
as at A, Fig. 23, and the short end to another part of it at B, the result will be
the same as long as the proportions of the lever are not changed. It will still
transmit power or impart motion according to the relative lengths of the two
parts of the lever. The capacity of our levers, Fig. 22, will be limited by that
point at which the ends of the levers will separate, because they are held at
the points of the fulcrums and constrained to move in circles by the
fulcrums. If we put more levers on the same axles, so spaced that another

set will come into action as the first pair are disengaged, we can continue
our transmission of power, Fig. 24; and if we follow this with still others
until we can add no more for want of room we shall have wheels and
pinions, the collection of short levers forming the pinion and the group of
long levers forming the wheel, Fig. 25. Thus every wheel and pinion
mounted together on an arbor are simply a collection of levers, each wheel
tooth and its corresponding pinion leaf forming one lever. This explains
why the force decreases and the motion increases in proportion to the
relative lengths of the radii of the wheels and pinions, so that eight or ten
turns of the barrel of a clock will run the escape wheel all day.

Fig. 24.
We now come to the verge or anchor, and here we have the same sort of
lever in a different form; the verge wire, which presses on the pendulum rod
and keeps it going is the long arm of our lever, but instead of many there is
only one. The short arm of our lever is the pallet, and there are two of these.
Therefore we have a form of lever in which there is one long arm and two
short ones; but as the two are never acting at the same time they do not
interfere with each other.

Fig. 25.
These systems of levers have another advantage, which is that one arm
need not be on the opposite side of the fulcrum from the other. It may be on
the same side as in the verge or at any other convenient point. This enables
us to save space in arranging our trains, as such a collection of wheels and
pinions is called, by placing them in any position which, on account of
other facts, may seem desirable.
Peculiarities of Angular Motion.—Now our collections of levers must
move in certain directions in order to be serviceable and in order to describe
these things properly, we must have names for these movements so that we
can convey our thoughts to each other. Let us see how they move. They will

not move vertically (up or down) or horizontally (sidewise), because we
have taken great pains to prevent them from doing so by confining the
central bars of our levers in a fixed position by making pivots on their ends
and fitting them carefully into pivot holes in the plates, so that they can
move only in one plane, and that movement must be in a circular direction
in that predetermined plane. Consequently we must designate any
movement in terms of the portions of a circle, because that is the only way
they can move.
These portions of a circle are called angles, which is a general term
meaning always a portion of a circle, measured from its center; this will
perhaps be plainer if we consider that whenever we want to be specific in
mentioning any particular size of angle we must speak of it in degrees,
minutes and seconds, which are the names of the standard parts into which
a circle is divided. Now in every circle, large or small, there are 360
degrees, because a degree is ¹⁄₃₆₀th part of a circle, and this measurement is
always from its center. Consequently a degree, or any angle composed of a
number of degrees, is always the same, because, being measured from its
center, such measurements of any two circles will coincide as far as they
go. If we draw two circles having their centers over each other at A, Fig. 26,
and take a tenth part of each, we shall have 360° ÷ 10 = 36°, which we shall
mark out by drawing radial lines to the circumference of each circle, and we
shall find this to be true; the radii of the smaller circle AB and AC will
coincide with the radii AD and AE as far as they go. This is because each is
the tenth part of its circle, measured from its center. Now that portion of the
circumference of the circle BC will be smaller than the same portion DE of
the larger circle, but each will be a tenth part of its own circle, although
they are not the same size when measured by a rule on the circumference.
This is a point which has bothered so many people when taking up the
study of angular measurement that we have tried to make it absurdly clear.
An angle never means so many feet, inches or millimeters; it always means
a portion of a circle, measured from the center.

Fig. 26.
There is one feature about these angular (or circular) measurements that
is of great convenience, which is that as no definite size is mentioned, but
only proportionate sizes, the description of the machine described need not
be changed for any size desired, as it will fit all sizes. It thus becomes a
flexible term, like the fraction “one-half,” changing its size to suit the
occasion. Thus, one-half of 300,000 bushels of wheat is 150,000 bushels;
one-half of 10 bushels is 5 bushels; one-half of one bushel is two pecks; yet
each is one-half. It is so with our angles.
There are some other terms which we shall do well to investigate before
we leave the subject of angular measurements, which are the relations
between the straight and curved lines we shall need to study in our drawings
of the various escapements. A radius (plural radii) is a straight line drawn
from the center of a circle to its circumference. A tangent is a straight line
drawn outside the circumference, touching (but not cutting) it at right
angles (90 degrees) to a radius drawn to the point of tangency (point where
it touches the circumference). A general misunderstanding of this term
(tangent) has done much to hinder a proper comprehension of the writers
who have attempted to make clear the mysteries of the escapements. Its
importance will be seen when we recollect that about the first thing we do
in laying out an escapement is to draw tangents to the pitch circle of the
escape wheel and plant our pallet center where these tangents intersect on
the line of centers. They should always be drawn at right angles to the radii
which mark the angles we choose for the working portion of our escape

wheel. If properly drawn we shall find that the pallet arbor will then locate
itself at the correct distance from the escape wheel center for any desired
angle of escapement. We shall also discover that it will take a different
center distance for every different angle and yet each different position will
be the correct one for its angle, Fig. 27.
Because an angle is always the same, no matter how far from the center
the radii defining it are carried, we are able to work conveniently with large
drawing instruments on small drawings. Thus we can use an eight or ten
inch protractor in laying off our angles, so as to get the degrees large
enough to measure accurately, mark the degrees with dots on our paper and
then draw our lines with a straight edge from the center towards the dots, as
far as we wish to go. Thus we can lay off the angles on a one-inch escape
wheel with a ten inch protractor more easily and correctly than if we were
using a smaller instrument.

Fig. 27.
Another thing which will help us in understanding these drawings is that
the effective length of a lever is its distance from the center to the working
point, measured in a straight line. Thus in a pallet of a clock the distance of
the pallets from the center of the pallet arbor is the effective length of that
arm of the lever, no matter how it may be curved for ornament or for other
reasons.
The lines and circles drawn to enable us to take the necessary
measurements of angles and center distances are called “construction lines”
and are generally dotted on the paper to enable us to distinguish them as
lines for measurement only, while the lines which are intended to define the

actual shapes of the pieces thus drawn are solid lines. By observing this
distinction we are enabled to show the actual shapes of the objects and all
their angular measurements clearly on the one drawing.
With these explanations the student should be able to read clearly and
correctly the many drawings which follow, and we will now turn our
attention to the escapements. In doing this we shall meet with a constant use
of certain terms which have a peculiar and special meaning when applied to
escapements.
The Lift is the amount of angular motion imparted to the verge or
anchor by the teeth of the escape wheel pressing against the pallets and
pushing first one and then the other out of the way, so that the escape wheel
teeth may pass. According as the angular motion is more or less the “lift” is
said to be greater or less; as this motion is circular, it must be expressed in
degrees. The lifting planes are those surfaces which produce this motion; in
clocks with pendulums the lifting planes are generally on the pallets, being
those hard and smoothly polished surfaces over which the points of the
escape wheel teeth slide in escaping. In lever escapements the lifting planes
are frequently on the escape wheel, the pallets being merely round pins.
Such an escape wheel is said to have club teeth, as distinguished from the
pointed teeth used when the lifting planes are on the pallets. In the cylinder
escapement the lifting planes are on the escape wheel; they are curved
instead of being straight; and there is but one pallet, which is on the lip of
the cylinder. In the forms of lever escapement used in watches and some
clocks the lift is divided, part of the lifting planes being also on the pallets;
in this case both sets of planes are shorter than if they were entirely on one
or the other, but they must be long enough so that combined they will
produce the requisite amount of angular motion of the pallets, so as to give
the requisite impulse to the pendulum or balance.
The Drop is the amount of circular motion, measured in degrees, which
the escape wheel has from the instant the tooth escapes from one pallet to
that point at which it is stopped by the other pallet catching another tooth.
During this period the train is running down without imparting any power
to the pendulum or balance, hence the drop is entirely lost motion. We must
have it, however, as it requires some time for the other pallet to move far
enough within the pitch circle of the escape wheel to safely catch and stop
the next tooth under all circumstances. It is the freedom and safety of the

working plan of our escapement, but it is advisable to keep the drop as
small as is possible with safe locking.
The Lock is also angular motion and is measured in degrees from the
center of the pallet arbor. It is the distance which the pallet has moved
inside of the pitch circle of the escape wheel before being struck by the
escape wheel tooth. It is measured from the edge of the lifting plane to the
point of the tooth where it rests on the locking face of the pallet. A safe lock
is necessary in order to prevent the points of the escape wheel teeth butting
against the lifting planes, stopping the clock and injuring the teeth. We want
to point out that from the instant of escaping to the instant of locking we
have the two parts of our escapement propelled by different and entirely
separate forces and moving at different speeds. The pallets, after having
given impulse to the pendulum, are controlled by the pendulum and moved
by it; in the case of a heavy pendulum ball at the end of a 40-inch lever, this
control is very steady, powerful and quite slow. The escape wheel, the
lightest and fastest in the train, is driven by the weight or spring and moves
independently of the pallets during the drop, so that safe locking is
important. It should never be too deep, as it would increase the swing of the
pendulum too much; this is especially true with short and light pendulums
and strong mainsprings.
The Run.—After locking the pallet continues to move inward towards
the escape wheel center as the pendulum continues its course, and the
amount of this motion, measured in degrees from the center of the pallet
arbor, is called the run.
When the escapement is properly adjusted the lifting planes are of the
same length on both pallets, when they are measured in degrees of motion
given to the pallet arbor. They may or may not be equal in length when
measured by a rule on the faces of the pallets. There should also be an equal
and safe lock on each pallet, as measured in degrees of movement of the
pallet arbor. The run should also be equal.
The reason why one lifting plane may be longer than the other and still
give the same amount of lift is that some escapements are constructed with
unequal lockings, so that one radius is longer than the other, and this, as we
explained at length in treating of angles, Fig. 26, would make a difference

in the length of arc traversed by the longer arm for the same angle of
motion.

CHAPTER VIII.
THE GRAHAM OR DEAD BEAT ESCAPEMENT.

This escapement is so-called because the escape wheel remains “dead”
(motionless) during the periods between the impulses given to the
pendulum. It is the original or predecessor of the well known detached lever
escapement so common in watches, and it is surprising how many
watchmakers who are fairly well posted on the latter form exhibit a
surprising ignorance of this escapement as used in clocks. It has like the
latter a “lock,” “lift” and “run”; the only difference being that it has no
“draw,” the control by the verge wire rendering the draw unnecessary.
It may be made to embrace any number of teeth of the escape wheel,
but, owing to the peculiarities of angular motion referred to in the last
chapter, see Fig. 26, B C, D E, the increased arcs traveled as the pallet arms
lengthen introduce elements of friction which counterbalance and in some
cases exceed the advantage gained by increasing the length of the lever
used to propel the pendulum. Similarly, the too short armed escapements
were found to cause increased difficulty from faulty fitting of the pivots and
their holes, and other errors of workmanship, which errors could not be
reduced in the same proportion as the arms were shortened, so that it has
been determined by practice that a pallet embracing ninety degrees, or one-
fourth of the circumference of the escape wheel, offers perhaps the best
escapement of this nature that can be made. Therefore the factories
generally now make them in this way. But as many clocks are coming in for
repair with greater or less arcs of escapement and the repairers must fix
them satisfactorily, we will begin at the beginning by explaining how to
make the escapement of any angle whatever, from one tooth up to 140
degrees, or nearly half of the escape wheel.
It is quite a common thing for some workmen to imagine that in making
an escapement, the pallets ought to take in a given number of teeth, and that
the number which they suppose to be right must not be departed from; but
there seems to be no rule that necessarily prescribes any number of teeth to
be used arbitrarily. The nearer that the center of motion of the pallets is to

the center of the escape wheel, the less will be the number of teeth that will
be embraced by the pallets. Fig. 28 is an illustration of the distances
between the center of motion of the pallets and the center of the wheel
required for 3, 5, 7, 9 and 11 teeth in a wheel of the same size as the circle;
but although we have adopted these numbers so as to make a symmetrical
diagram, any other numbers that may be desirable can be used with equal
propriety. All that is necessary to be done to find the proper center of
motion of the pallets is first to determine the number of teeth that are to be
embraced, and draw lines (radii) from the points of the outside ones of the
number to the center of the wheel, and at right angles to these lines draw
other two lines (tangents), and the point where they intersect each other on
the line of centers will be the center of motion of the pallets.

Fig. 28.

Fig. 29. Note the difference in
length of arc for the same angle.

It will be seen by the diagram, Fig. 28, that by this method the distance
between the centers of motion of the pallets and that of the scape wheel
takes care of itself for a given number of teeth and that it is greater when
eleven and one-half teeth are to be embraced than for eight or for a less
number. These short pallet arms are imagined by some workmen to be
objectionable, on the supposition that it will take a heavier weight to drive
the clock; but it can easily be shown that this objection is altogether
imaginary. Now, bearing in mind the principles of leverage, if the distance
between the pallets and escape wheel centers is very long, as in Graham’s
plan, in which the pallets embraced 138° of the escape wheel, the value of
the impulse received from the scape wheel and communicated through the
pallets to the pendulum is no doubt greater with a proper length of verge
wire, for, the lifting planes being longer, the leverage is applied to the
pendulum for a longer arc of its vibration, yet we must not suppose that

from this fact the clock will go with less weight, for it is easy to see that the
longer the pallet arms are the greater will be the distance the teeth of the
escape wheel will have to move (run) on the circular part of the pallets. See
Fig. 29. The extra amount of friction, and the consequent extra amount of
resistance offered to the pendulum, caused by the extra distance the points
of the teeth run on the circular locking planes of the pallets and back again,
destroys all the value of the extra amount of impulse given to the pendulum
in the first instance by means of the long arms of the pallets. The escape
wheel tooth resting on the locking plane of the pallet is quite variable in its
effective action, and since it rests on the pallet during a part of each swing
of the pendulum and the pendulum is called on to move the pallet back and
forth under the tooth, any change in the friction between the tooth and pallet
is felt by the pendulum and when the clock gets dirty and the friction
between the tooth and pallet is increased, the rate of the clock gets slow, as
the friction holds the pendulum from moving as fast as it would without
friction. Now, as this friction increases by dirt and thickening of the oil, all
these forms of escapements are subject to changes and so change the
clock’s rate. An increase of the driving weight, or force of the mainspring,
of clocks with dead-beat escapements always tends to make their rate slow,
from the action mentioned.
It is for this reason that moderately short arms are used in clocks having
dead-beat escapements of modern construction. Most of the first-class
modern makers of astronomical clocks only embrace seven and one-half
teeth, on a 30-tooth wheel, with the centers of motion of the pallets and
scape wheel proportionately nearer, as it can be mathematically
demonstrated that with the pallets embracing an arc of 90° the application
of the power to the pendulum is at right angles to the rod and therefore is
most effective.
To Draw the Escapement.—In order to make the matter clearer we
show in Fig. 30 the successive stages of drawing an escapement and also
the completed work in Figs. 32 and 33 embracing different numbers of
teeth. Draw a line, A B, Fig. 30, to serve as a basis for measurements. With
a compass draw from some point C on this line a circle to represent the
diameter of our escape wheel. Now we shall require to know how many
teeth there will be in our escape wheel. There may be 60, 40, 33, 32, 30, or
any other number we desire to give it; seconds pendulums generally have

30 teeth in this wheel, because this allows the second hand to be mounted
directly on the escape wheel arbor and thus avoids complications. We
divide the number of degrees in a circle (360) by the number of teeth we
have selected, say 30. 360 ÷ 30 = 12° for each tooth and space. One-fourth
of 360° equals 90° and one-fourth of 30 teeth equals seven and one-half
teeth; each tooth equaling 12 degrees, we have 12 × 7 = 84°, which gives us
six degrees for drop, to ensure the safety of our actions.

Fig. 30.
We now take 90° and, dividing it, set off 45° each side of our center line
and draw radii, R, from the center to the circumference of our circle; this
marks the beginnings of our pallets. Now to find our pallet center distance
we draw tangents, T (at right angles), from the ends of these radii toward
the line of centers. The point where they intersect on the line of centers is
the pallet center.
Now we must determine how much motion we are going to give our
pendulum, so that we can give the proper lift to our pallets. Four degrees of
swing is usual for a seconds pendulum, so we will take four degrees and,
dividing it, give two degrees of lift to each pallet. To do this we draw a line
two degrees inside the tangent, T (towards the escape wheel center), from
our pallet center on the entering pallet side and another line from the pallet
center two degrees outside of the tangent, T, on the exit pallet side. Next,
from the pallet center we draw arcs of circles cutting the tangents, T, and
the radii, R, where they intersect; this gives us the locking planes on which
the teeth of the escape wheel “run” (slide) during the excursions of the
pendulum, if the escapement is to have unequal lockings; if the lockings are
to be equidistant (if the pallet arms are to be of equal length) the arc for the
entering pallet is drawn three degrees below (outside) the radius, R, while

that on the exit pallet is drawn three degrees above (inside) the exit radius.
Finally the lifting planes are drawn from the intersection of the arcs of
circles struck from the pallet center with their tangents, T, to the lines,
marking the limits of the lift, two degrees away. These lifting planes should
be at an angle of 60° from the radii, R, and as a tangent is always at right
angles (90°) to its radius, they are consequently at 30° to the tangents
running to the pallet center. Thus we can measure these angles from either
the escape wheel or the pallet center, as may be most convenient.
When making a new pallet fork, it is most convenient to mark out the
lifting planes on the steel at 30° from the tangents, T, as we then do not
have to bother with the escape wheel further than to get its center distance
and the degrees of arc the lifting planes are to embrace. The workman who
is not familiar with this rule is apt to have his ideas upset at first by the
angles of inclination toward the center line which the lifting planes will take
for different center distances, as owing to the fact that the tangents meet on
the center line at different angles for different distances, the lifting planes
assume different positions with regard to the center line and he may think
that they do not “look right.” They are right, however, when drawn at 30° to
their tangents. Fig. 31 shows several pallets with different arcs arranged in
line for purposes of comparison, each being drawn according to the above
rule, as measurements with a protractor will show.

Fig. 31.
We have now arrived at the complete escapement, having finished our
pallets. We have, however, nothing to hold them in position; they must be
rigidly held in position with regard to each other and the escape wheel,

consequently we will make a yoke to connect them to the pallet arbor out of
the same steel, giving it any desired shape that will not interfere with the
working of the clock. Two of the most usual forms are shown at Figs. 32
and 33.

Fig. 32.

Fig. 33.
Let us see how this rule will work in repairs. Suppose we have a clock
brought in with the pallet fork missing, and that the movement is one of
those in which the pallet arbor is held by adjustable cocks which have been
misplaced or lost, so that we don’t know the center distance of the pallet
arbor and escape wheel. We shall have to make a new part.
Measure the escape wheel, getting its diameter carefully, take half of
this as a radius, and mark out the circle with a fine needle point on some
copper, brass or sheet steel, drawing the escapement as detailed in Figs. 30
and 32. Then measure carefully the angles made by the tangents with the
center line; take the steel which is to be used in making the pallets and fork;
draw on it a center line; lay off the tangents and the lift lines; draw the

locking arcs and the lifting planes carefully from the tangents and give the
rest of the fork a symmetrical shape. Use needle points to draw with and
have your protractor large enough to measure your angles accurately. Then
drill or saw out and file to your lines, except on the locking and lifting
planes; leave these large enough to stand grinding or polishing after
hardening. Harden; draw to a straw color and polish the planes. Your verge
will fit if it has not warped in hardening. If this is the case, soften the center,
keeping the heat away from the pallets, and bend or twist the arms until the
verge will fit the drawing, when laid on top of it. In grinding the pallets the
fork should be mounted on its arbor and the latter held between the centers
of a rounding-up tool while the grinding is done by a lap in the lathe. This
insures that the planes will be parallel to the pallet arbor and hence square
with the escape wheel teeth, so that they will not create an end thrust on
either escape or pallet arbor. It is also the quickest, easiest and most reliable
way of doing the job. When clocks come in with the pallets badly cut;
soften the center of the fork, place the ends between the jaws of a vise,
squeeze enough to bring them closer, mount in the rounding-up tool and lap
off the cut planes until they are smooth and stand at the proper angle; then
polish. This is done quickly.

Fig. 34. Drawing escape wheel to fit a tracing from a pallet fork.
Can we work the rule backwards? Suppose we get a clock in which we
have the pallet arbor adjustable as before, and we have the pallet fork all in
good shape, but we have lost the escape wheel, or it has been butchered by
somebody before coming to us, so that a new one is required.
Take off the pallet fork; lay it on a sheet of brass and trace around it
carefully with a needle point. Fig. 34. Mark the center carefully at the pallet
arbor hole and measure carefully the distance between the pallets and mark
that center. Draw a center line cutting these centers and extending beyond.
Now draw the tangent from the beginning of the entering pallet (as shown
by the tracing on our brass) to the pallet center; do the same with the exit
pallet. Now take a metal square and place it on one of the tangents exactly,
with the end at the beginning of the entering pallet; trace a line cutting the
line of centers and we have the radius of our escape wheel. Trace a circle
from the intersection of the radius and the center line and we have the
circumference of our escape wheel. This circle should also cut the
intersection of the tangent and radius on the other side if it is drawn
correctly; if it does not do this an error has been made in the drawing.

Fig. 35. Drawing an escape wheel to cut.
The last drawing shows the complete wheel.
Having found the diameter and circumference of our escape wheel it
may be sawed out and mounted for wheel cutting; or, if we have no wheel
cutter and must make the wheel, we must draw it on the brass by hand with
a fine needle point before proceeding to saw it out by hand, Fig. 35. Say
that the wheel is to have thirty-two teeth, which is a common number; then
360° ÷ 32 = 11¼° as the space between the points of our teeth. Take a large
protractor, one with the degrees large enough to be divided (I use a ten
inch); place its center on the center of our escape wheel, set off 11¼° and
mark them on the brass with the needle point, at the edge of the protractor.
Then take a straight edge and draw a radius from the center to the
circumference; change the straight edge to the other mark and mark the
point where it crosses the circumference; set your dividers accurately by
this mark and space off the teeth on your circumference. If they are set at
eleven degrees and fifteen minutes they will come out exactly at the end.
Now take your protractor and with its center at the junction of the radius
and circumference set off ten degrees and draw a line past the center of the
wheel; set off twenty degrees and draw another line the same way. From the
center of the escape wheel draw two circles just touching these lines.
Outside of these draw two circles defining the inner and outer edges of the
rim of the wheel. With the straight edge just touching the inner circle draw
in the fronts of the teeth; these will all be set at ten degrees from a radius, so
that only the extreme points will touch the locking planes of the pallets and
thus reduce the friction during the run. The backs of the teeth are marked
out in the same way from the twenty-degree circle. The hub is made to
coincide with the ten-degree circle; the spokes are traced in and we are
ready to begin sawing out.
If the workman has a wheel cutter the job is much simpler. A piece of
brass is mounted on a cement brass with soft solder, faced off, centered and
the pitch circle, inner and outer edges of the rim and the hub are traced with
the T-rest and graver. The extra metal is then cut away and a suitable index
placed on the spindle and locked. The wheel cutter is set up with a fine-
toothed, smooth cutting saw on the spindle, horizontal, with its upper edge
at the line of centers of the lathe. It is then run out to the circumference of
the wheel, turned upwards ten degrees and the wheel cut around, Fig. 36.

This makes the fronts of the teeth. Turn the saw ten degrees more and cut
the backs of the teeth. Then turn the saw so that it will reach from the front
of one tooth to the root of the back of the next one, without touching either
tooth, and cut round again; this cuts out a triangular piece of waste metal
between the teeth. Turn the saw again so that it reaches from the bottom of
the front of a tooth to the top of the back of the next one and cut around
again, thus removing another portion of the waste metal, and leaving only a
small triangle between the teeth. Lower the saw its own thickness and cut
around the wheel again, repeating the operation until the waste metal is all
removed and you have a smooth circular rim between the teeth, Fig. 36.

Fig. 36. Making an escape wheel with a saw, showing the successive cuts.
Set the saw horizontally at the lathe center; raise it one-half the
thickness of the spokes; set the index pin of the lathe head firmly at O; feed
in the saw the thickness of the wheel and make straight cuts across from the
circle of the inner rim to the circle marking the hub, but not cutting either;
set the index pin at 30 and repeat; next lower your saw and cut the other
side of the spokes the same way.
Next you can mount a lap in place of the saw and smooth the fronts and
backs of the teeth and if you have a rather thick disc the outer edge of the
rim, between the teeth, may also be smoothed.
If you have a good strong pivot polisher, mount a triangular end mill in
the spindle, lock the yoke, and cut the arcs of circles of the hub and rim
from edge to edge of the spokes, feeding carefully against the mill with the
hand on the lathe pulley.
Put on your jeweling tailstock and open the wheel to fit the pinion,
collet, or arbor, if there is no collet.
You now have the wheel all done, except facing the side that was
soldered to the cement brass and trimming up the corners of the spokes at
the rim and hub, and you have got it round, true and correct in much less
time than you could have done in any other way, while an immense amount
of work with the file and eye-glass has been avoided. It is true because it
was soldered in position at the beginning and has not been removed until
finished.

Sometimes what are known from their appearance as club-shaped teeth
are used in the wheels of Graham’s escapements. Pendulums receive their
impulse from escapements made in this manner partly from the lifting
planes on the pallets, and partly from the planes on the scape wheel. The
advantage gained by this method is, that wheels made in this way will work
with the least possible drop, and consequently, power is saved; but the
power saved is thrown away again in the increased friction of the planes of
the wheel against those of the pallets, which is considerably more than
when plain-pointed teeth are used on the escape wheel.
Clock pallets are usually made of steel, and on the finer classes of work
jewels are often set into them to prevent the oil from drying, after the same
fashion as jewels are placed in steel pallets in a lever watch; but it is
obvious that stone pallets made in this way have to be finished with
polishers held in the hand, and that, except in factories, they cannot be
made so perfectly regular, especially that pallet that is struck downwards, as
the particular action of a fine Graham escapement requires. When great
accuracy is required, the pallets are usually made of separate pieces, and the
acting circles ground and polished on laps, running in a lathe. This method
of constructing pallets also allows a means of adjustment which in some
particular instances is very convenient.
There is also a plan of making jeweled pallets adjustable, which is
practiced on fine work, such as astronomical and master clocks. The pallet
fork consists of two pieces of thin, hard, sheet brass, cut out in the usual
form and two mounted on one arbor. Circular grooves are cut in the sides of
both plates, at the proper distance, and of the proper size to receive the
jewels which are the acting parts of the pallets. When jewels cannot be
made of the desired size, pallets of steel are made, and the jewels are then
set into the steel large enough for the teeth of the wheel to act upon. The
two parts of the fork are fastened at a given distance apart, and the jewels,
or pieces of steel, go in between them, and, after they have been adjusted to
the proper position, are fastened by screws that pull the frames close
together and press against the edges of the jewels. Pallets made in this
manner have a very elegant appearance. Another method is to have only one
frame, and to have it thick enough, where the jewels have to be set in, to
allow a groove to be cut in its side as deep as the jewels (or the pieces of
steel that hold the jewels) are broad, and which are held in their proper

position by screws. This system of jeweling pallets is frequently adopted by
the makers of fine mantel clocks.

Fig. 37. Brocot’s visible escapement, escaping over
120° with pointed teeth. Dotted lines on pallets
show where they are cut to avoid stopping.
Brocot’s Visible Escapement.—Fig. 37 represents a system of making
and jeweling pallets much used by the French in their small work,
especially in visible escapements. The acting parts of the pallets are simply
cylinders, generally of colored stones, usually garnets, one-half of each
cylinder being cut away. These cylinders extend some distance from the
front of the pallet frame, and work into the escape wheel the same as the

pallets of a Graham escapement—the round parts of the pallets serving as
impulse planes. The neck of the brass pallet frame is cut up in the center,
and the width between the pallets is sometimes adjusted by a screw,
sometimes by bending the arms.
Clock movements with this escapement, of a careful construction, will
frequently come for repairs, accompanied by the complaint of constant
stopping and that no attempt at closely regulating can succeed with them,
although they appear to have no visible disturbing cause. In such cases the
depthing of the escapement is generally wrong. With proper depthing the
point of the escape wheel tooth should drop on the center or a little beyond
the center of the pallet stone. If it is set in this way the clock will stop when
wound, especially if it has a strong spring, as the light pendulum will not
then have momentum enough to unlock it against the full power of the
spring. If the pallets are set shallow, in order to avoid this difficulty, then,
the pendulum will take too short a swing and thus the clock will have a
gaining rate. Generally the pendulum ball cannot be made enough heavier
to correct the defect.

Fig. 38. Brocot’s visible escapement escaping over
90° with a small lift on the escape wheel teeth.
In these movements, in which the length of the pendulum does not
exceed 4 inches, the pallet fork embraces, generally about 120°, or the one-
third part of the wheel; it will be seen that unless there are stop works on
the barrel of the main spring no manner of regulating is possible with these
conditions, in view of the considerable influence exercised by the
mainspring through the train on the very light pendulum, and by replacing
this unduly high anchor by a lower one, I have always been able to produce
a very satisfactory rate with movements having pendulums of three and a
half to four inches. Fig. 38 shows a 90° escapement with a small lift on the
escape wheel teeth.

In spite of its incontestable qualities, the visible escapement possesses
one inherent fault. I refer to the formation of its pallets, the semi-circular
shape of which renders unequal the action of the train in giving impulse to
the pendulum exceeding 50 centimeters (20 inches), since to make it to
describe arcs of from one to two degrees only, with pendulums of from 60
centimeters to one meter in length, it became necessary to make the anchor
arms extremely long, which considerably impeded the freedom of action,
especially when the oil became thick, and this disposition would, therefore,
stand in direct contradiction with the principles of modern horology. Both
stopping and the irregularity of rate can be obviated by changing the semi-
circular form of the pallets for one of an inclined plane, either by grinding a
new plane or turning the stones in such manner as to offer an inclined plane
to the action of the wheel, analogous to that of the Graham escapement. See
Fig. 37, the dotted lines on the pallets showing the portion to be ground
away.
The importance of this transformation will readily be understood; it
suffices to give to these planes a more or less large inclination in order to
obtain a greater regularity of lifting, and, at desire, a lifting arc more or less
considerable without being compelled to modify the proportions of the fork
or to exaggerate the center distance of wheel and pallet arbor.
In adjusting an escapement, perhaps it may be advisable to mention that
moving the pallets closer together, or opening them wider, will only adjust
the drop on one side, while the other drop can only be affected by altering
the distance between the centers of the pallets and scape wheel. This is
accomplished in various ways. The French method consists of an eccentric
bush, riveted in the frame just tight enough to be turned by a screwdriver.
Another plan, common in America, is simply pieces of brass (cocks)
fastened on the sides of the frames. The pivots of the pallet axis are hung in
holes in these cocks, and an adjustment of great accuracy may be quickly
obtained by loosening the clamping screws. Lock, drop and run should be
of the same amount on each pallet. However, we do not approve of
adjustments of any kind, except in the very highest class of clocks, where
they are always likely to be under the care of skillful people, who
understand how to use the adjustments to obtain nicety of action in the
various parts.

In making escapements, lightness of all the parts ought to be an object
always in view in the mind of the workman, and such materials should be
used as will best serve that purpose. The scape wheel, and the pallets and
fork, should have no more metal in them than is necessary for stiffness. The
pallet arbor, and also the escape wheel arbor, should be left pretty thick
when the wheel and pallets are placed in the center between the plates, to
prevent their springing when giving impulse to the pendulum. We have
often been puzzled to find out the necessity or the utility of placing them in
the center between the plates, as they are so generally done in English
clockwork. The escapement acts much more firmly when it is placed near
one of the plates, and it is just as easy to make it in this way as in the other.
It is often assumed that the friction of the teeth on the circular part of
the pallets of a dead-beat escapement is small in amount and unimportant in
its value. With respect to its amount, we believe it is often not far short of
being equal to one-half of the combined retarding forces presented to the
pendulum; and with respect to its being unimportant, this assumption is
founded on the supposition that it is always a uniform force, when it is easy
to show that it is not a uniform force. It is very well known that the force
transmitted in clock trains, from each wheel to the next, is very far from
being constant. Small defects in the forms of the teeth of the wheels and of
the leaves of the pinions, and also in the depths to which they are set into
each other, cause irregularities in the amount of power transmitted from
each wheel to the next; and the accidental combination of these
irregularities in a train of four or five wheels, makes the force transmitted
from the first to the last exceedingly variable. The wearing of the parts and
the change in the state of the oil, are causes of further irregularities; and,
from these causes, it must be admitted that the propelling power of the
scape wheel on the pallets is of a variable amount, and a more important
question for consideration than it is usually supposed to be. To avoid the
consequences of this irregular pressure of the scape wheel on the pallets
being communicated to the pendulum, is a problem that has puzzled skillful
mechanicians for many years; for, although we find the Graham escapement
to be pronounced both theoretically and mechanically correct, and by some
authorities little short of perfection, we find some of these same authorities
—both theoretically and practically—testify their dissatisfaction with it by
endeavoring to improve on it. In Europe the experience of generations and
the expenditure of small fortunes, in pursuit of this improvement, through

the agency of the gravity, and other forms of escapements, proves this fact;
while of late years, in the United States, much time and money has been
spent on the same subject, and results have been reached which have raised
questions that ten years ago were little dreamed of by those clockmakers
who are generally engaged on the highest class of work.
While considering this class of escapements, we would say a few words
in regard to the sizes of escape wheels generally used. Small wheels can
now be cut as accurately as larger ones and there is now no reason or
necessity for continuing the use of a wheel of the size Graham and Le Paute
used, and which has been the size generally adopted by most European
makers who use these escapements. The Germans and Swiss make wheels
much smaller for Graham escapements than the English makers do; and the
American factories make them smaller still. On the continent of Europe the
wheels of Le Paute’s escapement are made much larger than they are made
in England and in the United States. No wheel, and more especially a scape
wheel, should be larger than will just give sufficient strength for the number
of teeth it has to contain, in proportion to the amount of work that it has to
perform. The amount of work a scape wheel has to perform in giving
motion to the pendulum is of the lightest description, and not more than
one-tenth of what it is popularly supposed to be, which is shown by its
variation under slight increase of friction; therefore we do not consider that
we take extreme ground in recommending wheels for these escapements to
be made nearly half the size their originators made them, and the pallets
drawn off in proportion to the reduced size of the wheel. It is plain that by
reducing the size of the wheel its inertia will be reduced. When the teeth
begin to act on the inclined planes of the pallets, the wheel will be set in
motion with greater ease, as it has a shorter leverage, and the amount of the
dead friction of the scape wheel teeth on the inclined planes and circular
part of the pallets will also be proportionately reduced by making the wheel
smaller. Factory experience and examination of a large number of clocks in
repair shops have also shown that smaller and thicker escape wheels will
wear much longer than larger and thinner ones, as all the wear is at the
points of the teeth and this is the portion to be protected.

CHAPTER IX.
LE PAUTE’S PIN WHEEL ESCAPEMENT.

Probably in no other escapement, except the lever, has there been so
many modifications as in the pin wheel; this is so to such an extent that it
will be found by the student that nearly every escapement of this kind
which he will examine will differ from its fellows if it has been made by a
different maker. They will be found to vary in the lengths of the pallet arms
from three-fourths to one and a half times the diameter of the escape wheel;
some of them will have the longer arm of the pallets outside and some
inside; some will have the lift for both pallets laid out on one side of the
perpendicular P, Fig. 39, while others will have the lift divided, with the
perpendicular in the center. Very old escapements have the pallet center
directly over the escape wheel center, while the pallet arms work at an angle
of 45°, while others have them with the pallet center planted on a
perpendicular, tangent to the pitch line of the escape wheel. Some have the
circular rest or locking faces of the pallets rounded slightly to hold the oil in
position while others have them flat and still others have them made of hard
stone, polished. More than half have the pins in the escape wheel cut away
for one-half of their diameters, leaving the bottoms round, as shown in Fig.
39, while others use a wider pin and trim away the bottoms also, as in Fig.
40, leaving the lifting surface on the pins not more than one-fourth the arc
of the circle. This is especially true of the larger escapements used in tower
clocks, though they are also found in regulators.

Fig. 39. Pin Wheel Escapement.

Fig. 40. Pin Wheel With Flattened Teeth.
In view of the wide variation in practice, therefore, we have endeavored
to present in Fig. 39 a conservative statement of the general practice as
found in existing clocks. We say existing, because very few of these
escapements are made now—none at all in America—and those in use are
generally in imported regulators, which have come from Switzerland or
Germany. The Waterbury Clock Co. at one time made this escapement for
its regulators and the Seth Thomas Clock Company made a number of its
early tower clocks with it, but both have discontinued it for some years, and
it is safe to say that any movement coming into the watchmaker’s hands
which has this escapement is imported; or if American, it is out of the
market. Le Paute claimed as an advantage the fact that the impact of the
escape wheel teeth is downward on both pallets, whereas in the gravity and
recoil escapements one blow is struck upwards and the other downwards.

He claimed that by this means a better action was secured after the pivot
holes began to wear, as there was less lost motion with both blows in the
same direction and any shake would not affect the amount of impulse given
to the pendulum. The difference is more theoretical than practical, however,
and the escapement possesses one serious fault, which is that the pins
forming the escape wheel teeth conduct the oil away from the pallets, so
that the clock changes its rate in from eight months to one year after being
oiled and cleaned. The most effective means of counteracting this is to
round the locking planes of the pallets slightly, so that the oil will be held
on them by capillary attraction. Another method is to turn the pins so that
they are thicker in diameter at the point of contact with the pallets, but this
is seldom tried. The best plan is to keep the pallets as close as they can be to
the face of the wheel without touching.
To Draw the Escapement.—In laying out this escapement the first thing
to consider is the arc of swing of the pendulum, because one-half of the lift
is on the pin and consequently one-half the lift must equal one-half the
diameter of the pin, as shown in Fig. 39. If the pendulum swings four
degrees, then the diameter of each pin must equal four degrees of the pallet
movement. This establishes the size of our pin; it is measured from the
pallet staff hole. There are 30 of these pins for a second’s pendulum, and
unless it is a very large escapement the pins cannot be made less in diameter
than one-fourth the distance between the pins, or they will be too weak and
will spring; consequently 360 ÷ 30 = 12° and 12° ÷ 4 = 3°, so that three
degrees of the pitch line of the escape wheel equals the swing of the pallet
fork. This establishes the relation as to size between the escape wheel and
the opening, or swing of the pallet fork. Draw a perpendicular, P, from the
pallet center and on one side of it lay out the lift lines L, L; draw a line at
right angles to the perpendicular and where it crosses the inner lift line draw
a circle touching the outer lift line. The diameter of this circle equals three
degrees of the circumference of the wheel, on its pitch line, and this
multiplied by 120 gives 360° or the pitch circumference of the escape
wheel. Dividing the sum so found by 3.1416 gives the diameter of the
escape wheel and half of this is the radius. After finding the radius draw the
pitch circle and set out the other twenty-nine teeth spaced twelve degrees
apart, and drawn in half circles as shown in Fig. 39.

Now to get the thickness of the pallet arms. When the pin shown in
action in Fig. 39 has just cleared the lower edge of the inner pallet, the
succeeding pin should fall safely on the upper corner of the outer pallet;
consequently the thickness of these two arms, the pin between them, and
the drop (clearance between the pin and the lower edge of the upper pallet)
should just equal the distance between two pins, from center to center, or
12° of the escape wheel. With the first or inner lift line as a starting point,
draw the lower arcs of the pallets and draw the upper or locking planes
from the perpendicular and the outer lift line. Then draw the lifting planes
of the pallets by connecting the ends of these arcs. The enlarged view above
the escape wheel in Fig. 39 will show how this is done more clearly than
the main drawing.
It is best to make the pallet fork of steel, in two pieces, screwed to a
collet on the pallet arbor, as the inner arm must be bent, or offset, so that it
will clear the pins of the escape wheel, and the pallets should lie in the same
plane, as close to the wheel as is possible without touching it. The pallets
are hardened.
In tower clocks the escapement is so large that a pin having a diameter
of three degrees of the escape wheel gives a half pin of greater strength than
is necessary for the work to be done and such pins are cut away on the
bottom, as in Fig. 40. In making the wheel it should be drilled in the lathe
with the proper index to divide the wheel and the pins riveted in; then the
pins are cut with a wheel cutter as if they were teeth of a wheel. Pins should
be of hard brass.
Care should be used in handling clocks with this escapement while the
pendulum is connected with the pallet fork, as, if the motion of the fork
should be reversed while a pin was on one of the lifting planes, it would
bend or break the pin.

CHAPTER X.
THE RECOIL OR ANCHOR ESCAPEMENT.

This escapement, always a favorite with clockmakers, has had a long
and interesting history and development. Because it started with a suddenly
achieved reputation, and because it is adapted to obtain fair results with the
cheapest and consequently most unfavorable working conditions, it has won
its way into almost universal use in the cheaper classes of clock work; that
is to say, it is used in about ninety per cent of the pendulum clocks which
are manufactured to-day.
It achieved a sudden reputation at its birth, because it was designed to
replace the old verge, which, with its ninety degree pallets close to the
arbor, and working into the crown wheel, required a very large swing of the
pendulum. This necessitated a light ball, a short rod, required a great force
to drive it, and made it impossible to do away with the circular error, while
leaving the clock sensitive to variations in power. The recoil escapement
was therefore the first considerable advance in accuracy, as its use involved
a longer and heavier pendulum, shorter arcs of vibration and less motive
power than was practicable with the verge; and as the pendulum was less
controlled by the escapement, it was less influenced by variations of power.
In the early escapements the entrance pallet was convex and the exit
pallet concave. Escapements of this description may still be met with
among the antiquities that occasionally drift into the repair shop. Later on
both pallets were made straight, as shown in Fig. 41. It will be seen by
studying the direction of the forces that the effect is to wear off the points of
the teeth very rapidly, and for this reason the pallets were both made convex
(See Fig. 42), so as to bring the rubbing action of the recoil more on the
sides of the teeth and do away to a large extent with the butting on the
points which destroyed them so rapidly.

Fig. 41. Recoil Escapement with Straight Lifting Planes.
The rather empirical methods of laying out the recoil escapement, which
have gained general circulation in works on horology, have had much to do
with bad depthings of this escapement and the consequent undue wear of
the escape wheel teeth and great variation in timekeeping of the movements
in which such faulty depthings occur, particularly in eight-day movements
with short and light pendulums. The escapement will invariably drive the
clock faster for an increase of power and slower for a decrease; an unduly
great depthing will greatly increase the arc of vibration of the pendulum, as
the train exerts pressure on the pendulum for a longer period during the
vibration; the consequence is that instead of the pendulum being as highly
detached as possible, we have the opposite state of affairs and a

combination of a strong spring, light pendulum and excessive depthing will
easily make a variation of five minutes a week in an eight-day clock.
The generally accepted method of laying out this escapement is shown
in Figs. 41 and 42, as follows: “Draw a circle representing the escape
wheel; multiply the radius of the escape wheel by 1.4 and set off this as the
center distance between the pallet and escape wheel centers. From the pallet
staff center describe a circle with a radius equal to half the distance between
escape wheel and pallet centers. Set off on each side of the center line one-
half the number of teeth to be embraced by the pallets and from the points
of the outside teeth draw lines tangent to the circle described from the pallet
center. These lines would then form the faces of the pallets if they were left
flat.”
We wonder how much information this description and the drawing
conveys to the average reader. How long should the pallets be? What is the
drop? How much will the escape wheel recoil with such a depthing? What
arc will the pallets give the pendulum? Why should the center distance
always be the same (seven tenths of the diameter of the wheel) whether the
escapement embraces eight, or ten, or six teeth? As a matter of fact it should
not be the same. We could ask a few more questions as to other details of
this formula, but it will be seen that such a description is practically useless
to all but those who are already so skilled that they do not need it.

Fig. 42. Recoil Escapement with Curved Lifting Planes.

Fig. 43. Drawing the Lock Lift and Recoil of the Usual Form.
Let us analyze these drawings. A little study of Figs. 41, 42 and 43 will
show that there is really only one point of difference between them and Fig.
32, which shows the elements of the Graham, or dead beat. The sole
difference is in the fact that there are no separate locking planes in the
recoil, the locking and run taking place on an extension of the lifting planes.
Otherwise we have the same elements in our problem and it may therefore
be laid out and handled in the same manner; indeed, if we were to set off on
Fig. 32, the amount of angular motion of the pallet fork which is taken up
by the run of the escape wheel teeth on the locking planes, by drawing
dotted lines above the tangents, T, we should then have measured all the
angles necessary to intelligently set out the recoil escapement. We should
have the lock at the tangent, T, the lift and the run (or recoil) being defined
by the lines on either side of it, and the length of our running and lifting
planes would be found for the entering pallet by drawing a straight line

between the points of the two acting teeth of the escape wheel and noting
where this line cut the lines of recoil and lift. A similar line traced at right
angles to this would in the same way define the limits of run and lift on the
exit pallet. It will therefore be seen that our center distances for any desired
angle of escapement may be found in the same way (Fig. 28), for either
escapement, and thus the method of making the pallets for the ordinary
American clock, Fig. 43, becomes readily intelligible. The sole object of
curving the pallets, as explained previously, was to decrease the butting
effect of the run on the points of the teeth. This is accomplished in Fig. 43
by straight planes on the pallets and straight sides to the teeth with 20° teeth
on the escape wheel; merely inclining the plane of the entering pallet about
six degrees toward the escape wheel center, thus serving all purposes, while
the gain in the cost of manufacture by using straight instead of curved
pallets and wheel teeth is very great.

Fig. 45. Showing the Usual Position in Cheap Clocks and the Verge Wire.

Fig. 44. Recoil with Curved Planes.
One factory in the United States is turning out 2,000,000 annually of
two movements, or about 1,000,000 of each movement; there are four other
larger factories and several with a less product; so it will readily be seen
that any decrease in cost, however small it may be on a single movement,
will run up enormously on a year’s output. Suppose the factory mentioned
were enabled to save only one-eighth of a cent on one of its million
movements manufactured last year, this would amount to $1,250 per year, a
little over $100 per month. Thus it will be seen that close figuring on costs
of production is a necessity.

Fig. 46. Drum Escapement.
Fig. 44 shows the method of drawing the escapement according to the
common sense deductions given above. As the methods of laying out the
angle of escapement, lock, lift, and run, were given in detail in Figs. 28 to
32, they need not be repeated here.
Fig. 46 shows the escapement frequently used in French “drum” clocks
and hence called the “Drum” escapement. These are clocks fitted to go in
any hole of the diameter of the dial and hence they have very short, light
pendulums. An attempt is made to gain control over the pendulum by
decreasing the arc of escapement to not more than two and sometimes to
only one tooth. This gives an impulse to the pendulum only on one-half of
the vibrations, the escape wheel teeth resting and running on the long

circular locking pallet during alternate swings of the pendulum. The idea is
that the friction of the long lock will tend to reduce the effect of the extra
force of the mainspring when the clock is freshly wound. Such clocks often
stop when the clock is nearly run down, from deficiency of power, and stop
when wound, because the friction of the escape wheel teeth on the locking
plane is such as to destroy the momentum of the light pendulum. All that
can be done in such cases is to alter the locking planes as shown by the
dotted lines, so that the “drum” becomes virtually a recoil escapement of
two teeth.

CHAPTER XI.
THE DENNISON OR GRAVITY ESCAPEMENT.

The distinguishing feature of this escapement lies in the fact that it aims
to drive the pendulum by applying to it a falling weight at each excursion
on each side. As the weight is lifted by the train and applied to the
pendulum on its return stroke and there is no other connection, it follows
that the pendulum is more highly detached than in any other form of
pendulum escapement. This should make it a better timekeeper, as the
application of the weight should give a constant impulse and hence errors
and variations in the power which drives the train may be neglected.
On tower clocks this is undoubtedly true, as these clocks are interfered
with by every wind that blows against the hands, so that a detached
pendulum enables a surplus of power to be applied to the train to meet all
emergencies. With a watchmaker’s regulator, however, the case is different.
Here every effort is made to favor the clock, vibrations, variations of
temperature, variations of power, dirt, dust, wind pressure and irregularities
of the mechanism are all carefully excluded and the consequence is that the
special advantages of the gravity escapement are not apparent, for the
reason that there are practically no variations for the escapement to take
care of. Added to this we must consider that the double three-legged form,
which is the usual one, is practically an escape wheel of but six teeth, so
that another wheel and pinion must be added to the train and this, with the
added complications of the fan and the heavier driving weight required,
counterbalance its advantages and bring it back to an equality of
performance with the simpler mechanism of the well made and properly
adjusted dead beat escapement. Theoretically it should work far better than
the dead beat, as it is more detached; but theory is always modified by
working conditions and if the variations are lacking there is no special
advantage in constructing a mechanism to take care of them. This is the
reason why so many watchmakers have constructed for themselves a
regulator with this escapement, used in the making all the care and skill of
which they were capable and then been disappointed to find that it gave no

better results with the same pendulum than the dead beat it was to replace.
They had eliminated all the conditions under which the detached
escapement would have shown superiority.
Although the gravity escapement will not
give a superior performance under the most
favorable conditions for timekeeping, it is
distinctly superior when these conditions are
unfavorable and therefore fully merits its high
place in the estimation of the horological
fraternity. We have instanced its value in tower
clock work; it has another advantage in running
cheap and poorly made (home made) regulators
with rough and poor trains; therefore, it is a
favorite escapement with watchmakers who
build their own regulators while they are still
working at the bench, before entering into
business for themselves. As the price of a first-
class clock for this purpose is about $300 and
the cheapest that is at all reliable is about $75, it
will be seen that the temptation to build a clock
is very strong and many of them are built
annually.
Regulators with the gravity escapement are
built by the Seth Thomas Clock Co., the
Howard, and one or two others in this country,
but they are furnished simply to supply the
demand and sales are never pushed for the
Fig. 47. reasons given previously. Clocks with this
escapement are quite common in England and
many of them have found their way to America.
It is one of the anomalies of trade that our clockmakers are supplying
Europe with cheap clocks, while we are importing practically all the high
priced clocks sold in the United States and among them are a few having
the three-legged and four-legged gravity escapements, therefore the chances
are that when a repairer finds such a clock it is likely to be either of English
origin or homemade, unless it be a German regulator.

Figs. 47 and 48 show plans and side views of the three-legged
escapement. Fig. 48 also shows an enlarged view of the escape wheel,
showing how the three-leaved pinion between the two escape wheels, is
made where it is worked out of the solid. A, B and C and a, b and c show
the escape wheel which is made up of two three-armed wheels, one on each
side of a three-leaved pinion marked D¹ and D² in the enlarged view of Fig.
48. The pallets in this escapement consist of the two arms of metal
suspended from points opposite the point of bending of the pendulum
spring and the lifting planes are found on the ends of the center arms in
these pallets, which press against the three leaves of the pinion, while the
impulse pins e¹ and e², Fig. 47 and 48 act directly upon the pendulum in
place of the verge wire. The pallets act between the wheels in the same
plane as each other. The lifting pins or pinion leaves act on the lifting planes
after the line of centers when the long teeth or legs of the escape wheels
have been released from the stops, F and G, Figs. 47 and 48, which are
placed one on each side of the pallets and act alternately on the wheels.
These pallets are pivoted one on each side of the bending point of the
suspension spring. To lay out the escapement, draw a circle representing the
escape wheel diameter, then draw the line of centers and set off on the
diameter of the escape wheel from each side of the line of centers 60° of its
circumference, thus marking the positions for the pallet stops 120° apart.
Draw radii from the center of the escape wheel to these positions and draw
tangents from the ends of these radii toward the center line. The point where
these meet will be the bending point of the pendulum spring.

Fig. 48.
This is clearly shown at H, Fig. 47. The points of suspension for the
pallets are planted on the line of these tangents and a little below the point
H, where the tangents meet on the line of centers. This is done to avoid the
mechanical difficulty of having the studs for the two pallets occupy the
same place at the same time. The arms of the pallets below the stops may be
of any length, but they are generally constructed of the same angle as the
upper arms and will be all right if drawn parallel to these upper arms. They
are in some instances continued further down, but this is largely a matter of
taste and the lower portion of the escapement is generally drawn so as to be
symmetrical.

The impulse of the pendulum is given by having pins projecting from
the pallet arms and bearing upon the pendulum rod, which pins may be of
brass, steel or ivory. In the heavier escapements they are made of ivory in
order to avoid any chatter from contact with the pendulum rod of a heavy
pendulum. These pallets should be as light as it is possible to make them
without having them chatter under the impact of the escape wheel arms on
the stops. They have only to counteract the force of the pendulum spring
and the resistance of the air and for light pendulums this force is much less
than is generally understood. Two ounces of impulse will maintain a 250-
pound pendulum, but two pennyweights is more than sufficient for a fifty-
pound pendulum. The reader can see that in the case of a pendulum
weighing but eight to fourteen pounds, there will be a still greater
proportionate drop, as the spring itself is thinner, the rod is thinner, the
pendulum ball offers little resistance to the air and the consequence is that it
is difficult to get the pallet arms light enough for an ordinary clock.
Watchmakers who make this escapement for themselves, to drive an
eight to fourteen pound pendulum, generally make the escape wheel three
inches diameter and make the escape wheel and pallet arms all from the
steel obtained by buying an ordinary carpenter’s saw. The lifting planes
should not be more than one-eighth its diameter from the center of the
escape wheel, as where this is the case the circular motion of the center pins
will be so great that the pallet in action will be thrown out too rapidly and
will chatter when striking the pendulum rod. On the other hand it should not
be less than one-twelfth of the diameter of the escape wheel, or the
pendulum will not be given sufficiently free swing and the motion will be
so slow that while such a clock will work under favorable conditions,
jarring, shaking in wind storms, etc., will have a tendency to make the
pendulum wabble and stop the clock. From what has been said above, it
will also be seen that the necessity for slow motion of the pallet arms unfits
this escapement for use with short pendulums.
The action of the escapement is as follows: The pendulum traveling to
the right, when it has thrown the right pallet arm sufficiently far, will
liberate the escape wheel tooth from the stop G and the pinion, acting on the
lifting plane, will raise the pallet arm, allowing the pendulum to continue its
course without doing any further work until it has reached nearly its
extreme point of excursion, when the weight of the pallet will be dropped

upon the pendulum rod and remain there, acting upon the pendulum until it
has passed the center when the pallet arm will be stopped by the banking
pin M¹; exactly the same procedure takes place on the left side of the
escapement during the swing of the pendulum to the left. The beat pins M
and M¹ should be set so that the impulse pins e¹ and e² will just touch the
pendulum when the latter is hanging at rest and the escapement will then be
in beat. The stops should be cut from sheet steel and the locking faces of the
escape wheel arms, stops on the pallets, lifting planes of the pallets and the
lifting pins should all be hardened. In some of the very fine escapements the
faces of the blocks are jeweled. The arms of the inner part of the escape
wheel are usually set at equal angular distances between those of the outer,
although this is not absolutely necessary, and the lifting pins are set on radii
to the acting faces of the arms of one of the wheels, so as to cross the line of
centers at the distance from the center, not exceeding one-eighth of the
radius of the wheel, for the reasons explained above.

Fig. 49.

From the comparatively great angle at which the arms are placed, the
distance through which they have to be lifted to give sufficient impulse is
less in this escapement than in one with a larger number of teeth acting in
the same plane, as the pallets would then hang more nearly upright. This is
a great advantage, as the contact is shorter. The unlocking is also easier for
the same reason, and from the greater diameter of the wheel in proportion to
other parts of the escapement, the pressure on the stops is considerably less.
The two wheels must be squared on the arbor, so there will be no possibility
of slipping. The lifting pins D are shouldered between them like a three-
tooth lantern pinion. In small escapements the lifting pins are not worked
out of the solid arbor, but are made as hardened screws to connect the two
portions of the wheel. In tower clocks the pinion is generally made solid on
the shaft J, Fig. 48. The wheel, A, B, C, is made to pass over the pinion D
and is fitted to a triangular seat, the size of the triangle of the leaves, D,
against the collar on the shaft. The other wheel, a, b, c, is fitted to the inside
triangle of the pinion, so that the leaves, D, form a shoulder against which it
fits. The pallets, E and E¹, also lie in one plane between the wheels, but one
stop, F, points forward to receive the A, B, C, teeth and the other, G, points
backward to receive the a, b, c teeth alternately. The distance of the
pendulum top, H, or cheeks from the center of the escape wheel, J equals
the diameter of the escape wheel. The lifting pins should be so placed that
the one which is holding up a pallet and the one which is to lift next will be
vertical over each other, on the line of centers, the third pin being on the
level with the center, and to one side of it, see Fig. 48, enlarged view.
The fly is a very essential part of this escapement, as the angular motion
of the escape wheel is such that unless it were checked it would be apt to
rebound and unlock; consequently, a large fly is always a feature of this
escapement and is mounted upon the scape wheel arbor with spring friction
in such a way that the fly can continue motion after the scape wheel has
been stopped. This is provided for by a spring pressure, either like the
ordinary spring attachment of the fly of striking trains of small clocks, or as
shown in Fig. 49 for tower clocks. This fly is effective in proportion to its
length and hence a long narrow fly will be better than a shorter and wider
one, as the resistance of the air striking against the ends of the fly is much
greater the further you get from the center.

Fig. 50.
The pallet stud pins and the impulse pins should on no account be
touched with oil or other grease of any kind, but be left dry whatever they
are made of, because the slightest adhesion between the impulse pins and
the pendulum rod is fatal to the whole action of the escapement. Care must
also be taken that one pallet begins to lift simultaneously with the resting of
the other, neither before nor after.

The gravity escapement requires a heavier weight or force to operate the
train than a dead beat escapement, because it must be strong enough to be
sure of lifting the pallets quickly and firmly, and also because the escape
wheel having but six teeth necessitates the use of another wheel and pinion
between the escape and center and consequently the train is geared back
more than it would be for a dead beat escapement, with the seconds hand
mounted on the escape wheel arbor. But with this form of escapement the
superfluous force does not work the pendulum and it does no harm if the
train is good enough not to waste power in getting over rough places left in
cutting the teeth of the wheels or any jamming from those which have
unequal widths or spaces. For this reason a high numbered train is better
than a low numbered one, as these defects are greater on the teeth of a low
numbered train and any defect in such cases will show itself.
In the gravity escapement the escape wheel must have a little run at the
pallets before it begins to lift them and in order to do this the banking pins,
M, M¹ for the pallet arms to rest on, should hold them just clear of the
lifting pins or leaves of the escape wheel. The escape wheel should be as
light as possible, for every blow heard in the machine means a loss of
power and wear of parts. Of course, in an escapement a sudden stop is
expected, but the light wheel will reduce it to a minimum if the fan is large
enough. Particular attention should therefore be given to the length of this
fan and if the stop of the escape wheel seems too abrupt, the fan should be
lengthened.

Fig. 51.
Figs. 50 and 51 show the same escapement with a four-legged wheel
instead of the double three-legged. In this case, where there is but one
wheel, the pallets must of necessity work on opposite sides of the wheel and
hence they are not planted in the same plane with each other, but are placed
as close to each side of the wheel as is practicable.

To lay out this escapement, draw the circle of the escape wheel as
before, make your line of centers and mark off on the circle 67½° on each
side of the line of centers and draw radii to these points, which will indicate
the approximate position of the stops. Tangents to these radii, meeting
above the wheel on the line of centers will give the theoretical point of the
suspension. One set of the lifting pins is planted on radii to the acting faces
of the teeth of the escape wheel. The opposite set, on the other side of the
wheel, is placed midway between the first set. This secures the lifting at the
line of centers. The wheel turns 45° at each beat and its arbor likewise
carries a fly.
In case the locking is not secure, the stops may be shifted a little up or
down, care being taken to keep them 135° apart. In this way a draw may be
given to the locking of the scape wheel arms similar to the draw of the
pallets in a detached lever escapement and thus any desired resistance to
unlocking may be secured. The stops in either escapement are generally
made of steel and it is of the utmost importance that the arms of the escape
wheel should leave them without imparting the least suspension of an
impulse. Therefore, the stops and the ends of the arms should be cut away
(backed off) to rather a sharp angle to insure clearance when the arms are
leaving the stops. It is also of equal importance that the legs of the wheels
should fall on the stops dead true. The fit of each of the legs should be
examined on both stops with a powerful eye-glass, so that they should be
correct and also see that when the unlocking takes place the wheel is
absolutely free to turn.

CHAPTER XII.
THE CYLINDER ESCAPEMENT AS APPLIED TO CLOCKS.

We remarked in a previous chapter that the lifting planes were
sometimes on the wheel and sometimes on the anchor. In another chapter
we pointed out clearly that the run on the locking surface of the pallets had
an important bearing on the freedom of the escapement and hence on the
rate of the dead beat escapement. In considering the cylinder escapement,
so common in carriage clocks, we shall find that the lift is almost entirely
on the curved planes of the escape wheel, and that the locking planes are
greatly extended, so that they form the outer and inner surfaces of the
cylinder walls. Thus we have here a form of the dead beat escapement,
which embraces but one tooth of the escape wheel and is adapted to operate
a balance instead of a pendulum. Therefore the points for us to consider are
as before, the amount of lift, lock, drop and run, and the shapes of our
escape wheel teeth to secure the least friction, as our locking surfaces (the
run) being so greatly extended this matter becomes important.
Action of the Escapement.—Fig. 52 is a plan of the cylinder
escapement, in which the point of a tooth of the escape wheel is pressing
against the outside of the shell of the cylinder. As the cylinder, on which the
balance is mounted, is moved around in the direction of the arrow, the
wedge-shaped tooth of the escape wheel pushes into the cylinder, thereby
giving it impulse. The tooth cannot escape at the other side of the cylinder,
for the shell of the cylinder at this point is rather more than half a circle; but
its point locks against the inner side of the shell and runs there till the
balance completes its vibration and returns, when the tooth which was
inside the cylinder escapes, giving an impulse as it does so, and the point of
the succeeding tooth is caught on the outside of the shell. The teeth rise on
stalks from the body of the escape wheel, and the cylinder is cut away just
below the acting part of the exit side, leaving for support of the balance
only one-fourth of a circle, in order to allow as much vibration as possible.
This will be seen very plainly on examining Fig. 53, which is an elevation
of the cylinder to an enlarged scale.

Fig. 52. a, wheel; b, cylinder; f, stalk on which teeth are mounted.
Proportion of the Escapement.—The escape wheel has fifteen teeth,
formed to give impulse to the cylinder during from 20° to 40° of its
vibration each way. Lower angles are as a rule used with large than with
small-sized escapements; but to secure the best result either extreme must
be avoided. In the escapement with very slight inclines to the wheel teeth,
the first part of the tooth does no work, as the tooth drops on to the lip of
the cylinder some distance up the plane. On the other hand, a very steep
tooth is almost sure to set in action as the oil thickens. The diameter of the
cylinder, its thickness and the length of the wheel teeth are all co-related.
The size of the cylinder with relation to the wheel also varies somewhat
with the angle of impulse, a very high angle requiring a slightly larger
cylinder than a low one. If a cylinder of average thickness is desired for an
escapement with medium impulse, its external diameter may be made equal
to the extreme diameter of the escape wheel multiplied by 0.115.

Fig. 53.

Fig. 54.
Then to set out the escapement, if a lift of say 30° be decided on, a
circle on which the points of the teeth will fall is drawn within one
representing the extreme diameter of the escape wheel, at a distance from it
equal to 30° of the circumference of the cylinder. Midway between these
two circles the cylinder is planted (see Fig. 54). If the point of one tooth is
shown resting on the cylinder, a space of half a degree should be allowed
for freedom between the opposite side of the cylinder and the heel of the
next tooth. From the heel of one tooth to the heel of the next equal 24° of
the circumference of the wheel, 360 ÷ 15 = 24°, and from the point of one
tooth to the point of the next also equals 24° so that the teeth may now be
drawn. They are extended within the innermost dotted circle to give them a
little more strength, and their tips are rounded a little, having the points of
the impulse planes on the inner or basing circle. The backs of the teeth
diverge from a radial line from 12° to 30°, in order to give the cylinder
clearance, a high angled tooth requiring to be cut back more than a low one.
A curve whose radius is about two-thirds that of the wheel is suitable for

rounding the impulse planes of the teeth. The internal diameter of the
cylinder should be such as to allow a little freedom for the tooth. The rule in
fitting cylinders is to have equal clearance inside and outside, so as to
equalize the drop. The acting part of the shell of the cylinder (where the lips
are placed) should be a trifle less than seven-twelfths of a whole circle, with
the entering and exit lips which are really the pallets, rounded as shown in
the enlarged plan, Fig. 55, the entering lip or pallet rounded both ways and
the exit pallet rounded from the inside only. This rounding of the lips of the
cylinder adds a little to the impulse beyond what would be given by the
angle on the wheel teeth alone. The diameter of the escape wheel is usually
half that of the balance, rather under than over.
Size of Cylinder Pivot.—To establish the size of the pivot with relation
to its hole is apparently an easy thing to do correctly, but to an
inexperienced workman it is not so. The side shake in cylinder pivot holes
should be greater than that for ordinary train holes; one-sixth is the amount
prescribed by Saunier; the size of the pivot relatively to the cylinder about
one-eighth the diameter of the body of the cylinder. It is very necessary that
this amount of side shake should be correctly recognized; if less than the
amount stated, the escapement, though performing well while the oil is
fresh, fails to do so when it commences to thicken.

Fig. 55.

When the balance spring is at rest, the balance should have to be moved
an equal amount each way before a tooth escapes. By gently pressing
against the fourth wheel with a peg this may be tried. There is generally a
dot on the balance and three dots on the plate to assist in estimating the
amount of lift. When the balance spring is at rest, the dot on the balance
should be opposite to the center dot on the plate. The escapement will then
be in beat, that is, provided the dots are properly placed, which should be
tested. Turn the balance from its point of rest till a tooth just drops, and note
the position of the dot on the balance with reference to one of the outer dots
on the plate. Turn the balance in the opposite direction till a tooth drops
again, and if the dot on the balance is then in the same position with
reference to the other outer dot, the escapement will be in beat. The two
outer dots should mark the extent of the lifting, and the dot on the balance
would then be coincident with them as the teeth dropped when tried in this
way; but the dots may be a little too wide or too close, and it will therefore
be sufficient if the dot on the balance bears the same relative position to
them as just explained; but if it is found that the lift is unequal from the
point of rest, the balance spring collet must be shifted in the direction of the
least lift till the lift is equal. A new mark should then be made on the
balance opposite to the central dot on the plate.
When the balance is at rest, the banking pin in the balance should be
opposite to the banking stud in the cock, so as to give equal vibration on
both sides. This is important for the following reason. The banking pin
allows nearly a turn of vibration and the shell of the cylinder is but little
over half a turn, so that as the outside of the shell gets round towards the
center of the escape wheel, the point of a tooth may escape and jam the
cylinder unless the vibration is pretty equally divided. When the banking is
properly adjusted, bring the balance round till the banking pin is against the
stud; there should then be perceptible shake between the cylinder and the
plane of the escape wheel. Try this with the banking pin, first against one
and then against the other side of the stud. If there is no shake, the wheel
may be freed by taking a little off the edge of the passage of the cylinder
where it fouls the wheel, by means of a sapphire file, or a larger banking pin
may be substituted at the judgment of the operator. See that the banking pin
and stud are perfectly dry and clean before leaving them: a sticky banking
often stops a clock when nearly run down. Cylinder timepieces, after going
for a few months, sometimes increase their vibration so much as to

persistently bank. To meet this fault a weaker mainspring may be used, or a
larger balance, or a wheel with a smaller angle of impulse. By far the
quickest and best way is to very slightly lap the wheel by holding a piece of
Arkansas stone against the teeth, afterwards polishing with boxwood and
red stuff. So little taken off the wheel in this way as to be hardly perceptible
will have great effect.
Sometimes the escape wheel has too much end shake. We must notice in
the first place how the teeth are acting in the cylinder slot. Suppose, when
the escape wheel is resting upon its bottom shoulder, the cylinder will ride
upon the plane of the wheel, which will cause it to kick or give the wheel a
trembling motion, then we know that the cylinder is too low for the wheel;
therefore, we have not only to lower the escape top cock in order to correct
the end shake, but we must also drive the bottom cylinder plug out a little in
order to raise the cylinder sufficient to free it from the plane of the wheel.
Now, if the end shake of the cylinder is correct previous to this, we shall
now either have to raise the cock or drive the top plug in a little. But
suppose the end shake of the escape pinion is excessive, and is, when the
bottom shoulder is resting on the jewel, a little too low so that the bottom of
the escape wheel runs foul of the cylinder shell; in this case we simply drive
out the steady pins from the bottom escape wheel cock and file a piece off
the cock, leaving it perfectly flat when we have enough off. We then insert
the steady pins again, screw it down, and if the end shake is right, the
escapement is mostly free and right also.
Now let us consider the frictions; there is the resistance of the pivots,
which depends on their radius, on the weight of the balance, the balance
spring, the collet, and the weight of the cylinder; these are called locking
frictions. Then there are those of the planes, of the teeth of the wheel, of the
lips of the cylinder. It is on these that the change and destruction of the
cylinder are produced. To prevent this destruction, it is necessary to render
the working parts of the cylinder very hard and well polished, as well as the
teeth of the escape wheel.
The oil introduced in the cylinder is also a cause as in the dead beat. It
may thicken; the dust proceeding from the impact of the escapement forms
with the oil an amalgam which wears the cylinder. The firmness and
constancy of the cylinder depend on the preservation and fluidity of the oil.

Then there are the accidental frictions; the too close opening of the
cylinder, the play of the balance and of the wheel, with the thickening of the
oil, changes the arc of vibration a good deal; the teeth of the wheel may not
be sufficiently hollowed, so that the cylinder can revolve in the remaining
space, for the oil with the dust forms a thickness which also changes the
vibration. The drop should not be too great, for it is increased by the
thickening of the oil and impedes the vibration.
Examination of Clocks.—In this particular escapement, when used for
larger timepieces than watches, it is astonishing the variety of methods
which are employed, yet the same results are expected. In examining such
clocks we will first notice that the chariot, cock, etc., are so placed, many of
them, that the last wheel in the train is a crown wheel, hence it is made to
work at 90° with the escape wheel pinion which is set at right angles with
the crown wheel pinion, and, as a matter of course, the cylinder is also set
the same way. Now, this arrangement needs especial care, for it is quite
natural that when the entire friction of the cylinder is only on the bottom
part of the bottom pivot, the clock is sure to go faster than when the whole
length of both pivots are more in contact with their jewel holes, which is
always the case when the cylinder is parallel with all the pinions, instead of
standing upon one pivot only. Now, although there must of necessity be a
very great difference in timing the clock in the two different positions, yet
we find no difference in the strength of mainspring or any part of the train,
which is a mistake, for the result is simply this: the clock will gain time for
the first few days after winding, and will then gradually go slower and
slower until the mainspring is entirely exhausted. It is not very difficult to
ascertain why it goes so fast after winding, for then the whole tension of the
spring is on, and as there is not sufficient friction on the point of one pivot
to counteract this, the banking pin is almost sure to knock, and will continue
to knock for the first few days until a part of the spring’s pressure is
exhausted. Now, in this case the knocking of the banking pin alone would
cause the clock to gain time, even if the extra tension of the mainspring did
not assist it to do so. Hence, on the whole, the result is anything but
satisfactory, for such a clock can never be properly brought to time.
Having said this much about the fault (which is entirely through the
want of a little forethought with the manufacturer), I will give as good a
remedy as I can suggest to give the reader an idea of how these faults may

be put to right, if he is willing to spend the time upon them. In the first
place take out the cylinder and make the bottom pivot perfectly flat instead
of leaving it with a round end, as they are mostly left, which only allows
just one part of the pivot to be in contact with the endstone. By leaving this
pivot flat on the bottom, there is more surface in contact; hence, in a sense,
more friction.
In some cases the whole pivot left flat would not be sufficient to retard
the mainspring’s force; then we must resort to other methods to effect a
cure.
Well, our next method in order to try and get the clock to be a uniform
timekeeper, is to change the mainspring for one well finished and not quite
so strong as the original one. Perhaps some will say “why not do this before
we go to the trouble of flattening the bottom pivot?” Just this; when a pivot
is working only upon the bottom it is best to have a flat surface to work
upon, as the balance is then oscillated with more uniformity, even when the
mainspring is not exactly uniform in its pressure; therefore we do no harm
—but good—by making the bottom pivot flat, and this alone will
sometimes be sufficient to cure the fault of the banking knocking if nothing
else.
To my mind, when such strong mainsprings are used as we generally
see in this class of timepiece, neither of the jewel holes or pivots should be
so small as they usually are. Fancy such small pivots as are mostly seen
upon the escape wheel pinion being driven by such a strong mainspring. If
we allow the clock to run down while the escape wheel is in place, we are
very liable to find one or both pivots broken off before it gets run down. I
think all such pivots ought to be sufficiently strong to stand the pressure of
the mainspring through the train of wheels without coming to grief. But
there is another reason why these pivots are liable to get broken off while
letting the train run down: that is, the badly pitched depth we often find in
the crown wheel and escape wheel pinion. We frequently find too much end
shake to the crown wheel which, while resting one shoulder of the arbor
against the plate puts the depth too deep, and on the other shoulder the
depth is too shallow. Now, when the train is running rapidly this crown
wheel is jumping about in the escape wheel pinion, so that the roughness of
the running all helps to break off the escape wheel pivots. The best way to
correct this depth is to notice how the screws fit in the cylinder plate—for

these screws have to act as steady pins as well. If the holes where the
screws go through are at all large, we then notice which would be the most
convenient side to screw it securely in order to put a collet upon the
shoulder of the crown wheel so that the depth will be right by making the
end shake right with only fixing a collet to one shoulder. This depth, when
correct, will also cause a more uniform pressure upon the escapement, and
help to make the clock keep better time. We are supposing that this crown
wheel is perfectly true, or it is not much use trying to correct the depth as
mentioned above, for even if the end shake be ever so exact and the wheel
teeth are out of true, we shall never get the depth to act as it ought, neither
can the clock be depended upon for keeping going, regardless of keeping
time. When this crown wheel is out of true it is best to rivet it true, not do as
I have seen it done, placed in the lathe and topped true, and then the teeth
rounded-up by hand. This method simply means a faulty depth after all, for
in topping the teeth, those teeth which require the most topping will, when
they are finished, be shorter from the top to the base than those which do
not get topped so much; therefore, some of the teeth are longer than the
others, while the shorter ones are thicker; for when the wheel was originally
cut the teeth were all cut alike. These remarks will apply to several kinds of
wheels; for whenever a wheel is topped to put it true, we may depend we
are making a very faulty wheel of it unless we have a proper wheel cutting
machine.
The crown wheel must not be too thick because we will find the tooth to
act with the inner edge, and what is left outside only endangers touching the
pinion leaf which is next to come into action. Make sure the escape pinion
is not too large, which sometimes happens. If it is, it must be reduced in
size, or better, put in a new one. The crown wheel holes must fit nicely and
the end shake be well adjusted. Do not spare any trouble in making this
depth as perfect as you are able, as most stoppages happen through the
faults in this place. It would be advisable, when sure the depth is correct, to
drill two steady pin holes through the escapement plateau into the edge of
the plates. When steady pins are inserted this will always ensure the depth
being right when put together.
In some of these clocks it is not only the crown wheel, but frequently
the escape wheel has too much end shake. The former, as I have said, can
be corrected by making a small collet that will just fit over pivot, fasten it

on friction-tight, place the wheel in the lathe and turn the collet down until
it is the same size as the other part of the arbor, then run off the end to the
exact place for the end shake to be right. If it is properly done and a steel
collet is used, it will not be detected that a collet has been put on. Now,
when the escape wheel end shake is wrong we have to proceed differently
under different circumstances for we must notice in the first place how the
teeth are acting in the cylinder slot.
See that the cylinder and wheel are perfectly upright. Suppose, when the
escape wheel is resting upon its bottom shoulder, the cylinder will ride upon
the plane of the wheel, which will cause it to kick or give the wheel a
trembling motion, then we know that the cylinder is too low for the wheel;
therefore, we have not only to lower the escape top cock in order to correct
the end shake, but we must also drive the bottom cylinder plug out a little in
order to raise the cylinder sufficient to free it from the plane of the wheel.
Now, if the end shake of the cylinder is correct previous to this, we shall
either have to raise the cock or drive the top plug in a little. But suppose the
end shake of the escape pinion is excessive, and is, when the bottom
shoulder is resting on the jewel, a little too low so that the bottom of the
escape wheel runs foul of the cylinder shell; in this case we simply drive
out the steady pins from bottom escape wheel cock and file a piece off the
cock, leaving it perfectly flat when we have got enough off. We then insert
the steady pins again, screw it down, and, if the end shake is right, the
escapement is mostly free and right also. It sometimes happens that the
wheel is free of neither the top nor bottom plug, but should this be the case,
sufficient clearance may be obtained by deepening the opening with a steel
polisher and oilstone dust or with a sapphire file. A cylinder with too high
an opening is bad, for the oil is drawn away from the teeth by the escape
wheel.
If a cylinder pivot is bent, it may very readily be straightened by placing
a bushing of a proper size over it.
These clocks are very good for the novice to exercise his skill in order
to thoroughly understand the workings of the horizontal escapement. He is
better able to see how the different parts act with each other than he is in the
small watch. When the escape is correct he will find that the plane of the
escape wheel will work just in the center of the small slot in the cylinder.

If he will notice how the teeth stand in the cylinder when the banking
pin is held firmly upon the fixed banking pin, it will give him an idea of
how this should be. At one side the lip of the cylinder is just about to touch
the inside of the escape tooth, but the banking pin just prevents it from
doing so, while on the other side the cylinder goes round just far enough to
let the point of the next tooth just get on the edge of the slot, but it cannot
get in owing to the intervention of the banking pin. If this is allowed to get
in the slot just here, we then have what is called “a locking,” which is, in
reality, an overturned banking. If the other side is so that the banking pin
does not stop it soon enough, the edge of the slot knocks upon the inside of
the teeth and causes a trembling of the escape wheel, and the clock left in
this form will never keep very good time. We may easily remedy this by
taking off the hair spring collet; holding the cylinder firmly in the plyers,
and with the left hand turn the balance a little outwards; this will bring the
banking pins in contact before the cylinder touches the inside of the wheel
teeth, and all is right, providing we are careful in not doing it too much; if
so, we shall find the banking knock—a fault which is quite as bad, if not
worse, than the one we are trying to remedy. Those particulars are the most
important of anything in connection with the cylinder escapement. Yet, as
this kind of clock is now being made up at such a low price, these seeming
little items are frequently overlooked; hence, when they get into the hands
of the inexperienced, there is often more trouble with them than there need
be if they knew where to look for some of the faults which I have been
endeavoring to bring to light. There are several other things in connection
with this particular clock, but we will not comment further just now, but
take them up when we are considering the trains, etc.

Fig. 56.

In the meantime we will resume our study of the cylinder escapement
with particular reference to badly worn or otherwise ill fitting escape
wheels, as many times, the other points being right, the wheel and cylinder
may be such as to give either too great or too small a balance vibration.
A poor motion can also be due to a rough or a badly polished cylinder,
but such a cylinder we rarely find. That with a wrong shape of the cylinder
lips the motion is not much lessened can be seen in quite ordinary
movements, where the quality is certainly not of the best neither are the lips
correctly formed, nevertheless they have rather an excessive motion. To
cover up these defects in such movements the cylinder wheel teeth are
purposely given the shape as shown at B in Fig. 56, and to give sufficient
power a strong mainspring is inserted.
With an excessive balance vibration we can usually conclude that it is
an intentional deception on the part of the manufacturer, while a poor
motion can generally be ascribed to careless methods in making. The
continued efforts in making improvements to quicken and cheapen
manufacturing processes very frequently result in the introduction of
defects which are only found by the experienced and practical watchmaker.
As to the causes which induce excessive balance vibrations? As this
defect is generally found in the cheaper grades of cylinder escapements,
having usually rather small, heavy, and often clumsy balances, those which
have balances whose weight is probably less than they ought to be, need not
here be further considered, and it only remains for us to look to the cylinder
or the escape wheel for the causes which produce these excessive
vibrations. It will be found that the cylinder is smaller in diameter than
usually employed in such a size of clock; the escape wheel is naturally also
smaller, and its teeth generally resemble B, Fig. 56, while A shows the
correct shape of a tooth for a wheel of that diameter.
In using small cylinders we can give the escape wheel teeth a somewhat
greater angle of inclination than generally used, but that the proper amount
of incline is exceeded is proved by the fact that the balance vibrates more
than two-thirds of a turn. It can also be readily seen that with a tooth like B
a greater impulse must be imparted than one with an easy curve like A, and
the impulse is still further increased as the working width of the tooth B

(the lift) is greater, indicated by line b, while the same line in a correct
width of tooth, as shown at a, is considerably shorter.
In addition to what has been said of these escapements, we also find
them provided with very strong mainsprings to give the necessary power to
a tooth like B with its steeply inclined lifting face or impulse angle.
To decrease the great amplitude of the balance vibrations many
watchmakers simply replace the strong mainspring with a weaker one. But
this procedure is not advantageous as the power of the escape wheel tooth is
insufficient to start the balance going and this is due to two causes. First, the
great angle of the escape wheel tooth, and secondly, the inertia of the
balance. It is only by violently shaking such a clock that, we are enabled to
start it going. And the owner soon becomes dissatisfied from its frequent
stoppage due to setting of the hands and other causes so that he will be
often obliged to shake it until it starts going once more.

Fig. 57. Fig. 58.
For properly correcting these defects the best method to pursue is to
replace the cylinder wheel with another one, whose teeth are of the shape as
shown at Fig. 55 and without question a good workman will always replace
the escape wheel if the clock is of fair quality. But if a low grade one, we
would hardly be justified in going to the expense of putting in new wheels,
as the low prices for which these clocks are sold preclude such an
alteration. As we must improve the wheel some way to get a fair
escapement action we can place it in a lathe and while turning, hold an oil
stone slip against it, we can remove the point S, Fig. 56. After removing the

point the tooth will now have the form as shown at tooth C, Fig. 57. We
now take a thin and rather broad watch mainspring, bending a part straight
and holding it in the line f f, and revolving the wheel in the direction as
shown by the arrow, its action being indicated by figures 1 to 8; beginning
at the point of the tooth at 1, at 2 it comes in contact with the whole of the
lifting face, and from 3 to 8 only on the projecting corner which was left by
the oil stone slip in removing the heel of the tooth. In this way all the teeth
are acted upon until the corner is entirely removed. Of course oil stone dust
and oil is first used upon the spring for grinding, after which the teeth are
polished with diamantine. Care must be observed in using the spring so as
not to get the end f too far into the tooth circle, as it would catch on the heel
of the preceding tooth.
After the foregoing operation has been completed any feather edge
remaining on the points of the teeth must be removed with a sapphire file
and polished; we will now have a tooth as indicated by D, Fig. 57. This
shape of tooth can hardly be said to be theoretically correct, nevertheless it
is a close approximation of the proper form of tooth, which is shown by the
dotted lines, and will then perform its functions much better than in its
original condition.
Fig. 58 also shows how the spring must be moved from side to side—
indicated by dotted lines—so that the lifting face will have a gentle curve
instead of being flat; R represents the tooth.
After the wheel has been finished, as described, and again placed in the
clock, it will be found that the balance makes only two-thirds of a turn, and
as a result the movement can be easier brought to time and closely
regulated.
In the above I have described the cause of excessive balance vibration,
the method by which it can be corrected, and in what follows I shall
endeavor to make clear the reasons for a diminished balance vibration or
poor motion. It has been probably the experience of most watchmakers to
repair small cylinders of a low grade, having a poor motion or no motion at
all, and it would hardly be profitable to expend much time in repairing
them. But considerable time is often wasted in improving the motion by
polishing pivots and escape wheel teeth, possibly replacing the cap jewels,
or even the hole jewels, increasing the escapement depth or making it

shallower, examining the cylinder and finding nothing defective, and as a
last effort putting in a stronger mainspring. But all in vain, the balance
seems tired and with a slight pressure upon an arm of the center wheel it
stops entirely.

Fig. 59.
In this case, as in a former one, in fact, it is necessary at all times to
carefully examine the cylinder wheel. My reason for not considering the
cylinder itself so much as the wheel is that the makers of them have made a
considerable advance in their methods of manufacture, so we find the
cylinders fairly well made and generally of the correct size. Even if the
cylinder is incorrectly sized, either too large or small, it does not necessarily
follow that the watch would have a bad motion, as I have frequently had old
movements where the cylinder was incorrectly proportioned and yet the
motion was often a good, satisfactory one. Generally speaking, the cylinder
escapement is one which admits of the worst possible constructive
proportions and treatment, as we have often examined such clocks when
left for repairs, that, notwithstanding their being full of dirt, worn cylinder,
broken jewel holes, etc., they have been running until one of the cylinder
pivots has been completely worn away.
It only remains to look for the source of the trouble in the escape wheel.
If we examine the wheel teeth carefully, we shall find them resembling
those in Fig. 59, the dotted lines representing the correct shape of the teeth
for a wheel of that diameter.
Why do we find wheels having such defective teeth? This is probably
due to their rapid manufacture, as they very likely had the correct shape

when first cut, but by careless grinding and polishing they were given
improper forms, careless treatment being very evident at tooth F, which we
find on examination has a feather edge at the point as well as at the heel of
the tooth. If we grind these edges of the tooth with a ruby file, by placing it
in the position as indicated by dotted lines h and h¹, and afterwards
polishing the tooth point, we will find that the balance makes a better
vibration. A wheel, having teeth like E, can still be used, but the balance
will have a very poor motion, due to the fact that the impulse angle of the
wheel tooth is too small; the impulse faces of the teeth having so small an
angle, are nearly incapable of any action. With a tooth like G, if we should
remove its bent point at the dotted line d, then the tooth would be too short,
and as the inclination of the impulse face is incapable to produce a proper
action, a new wheel must be used, having teeth as shown at Fig. 55.
The reasons why a tooth, having the shape as shown at F and G (Fig.
59), will cause a bad action of the escapement and also why in such cases
with a greater force acting on the wheel, causes a stopping of the clock, I
will endeavor to explain with the aid of the illustration Fig. 60. Here we
clearly see the curved points of the teeth resting against the outer and inner
walls of the cylinder while the escapement is in action.
Teeth H and H¹ represent the defective tooth, while K and K¹ shows a
correctly formed tooth for a wheel of the same size, the correct depth and
positions where the tooth strikes the inner and outer walls of the cylinder. It
will be readily seen that the position of the tooth point upon the cylinder (at
c) is most favorable in reducing the resistance to the least possible amount.
But in the case of the teeth H and H¹ the condition is entirely different. We
find that it was necessary to set the escapement very deeply in order that it
could perform its functions at all, and, as a consequence, we have a false
proportion; the effects being considerably increased by the worst possible
position of the teeth H and H¹, where they touch the cylinder. While the
cylinder c is turning in the direction shown by the arrows i i¹, the tooth does
not affect the cylinder to any extent; but during the reverse movement of the
cylinder, in the direction of o o¹, an excessive amount of engaging friction
must take place. A close inspection of the drawing will enable us to see that
there is a great tendency of the cylinder to drag the tooth along with it
during each of these motions. It is evident that in such a case the friction
will eventually become so great as to lock the escapement, and if greater

pressure is applied by any means to teeth H and H¹, it is easily seen that this
effect will take place much more rapidly. Replacing the escape wheel with
one of correctly formed teeth and size is the best means at our disposal.

Fig. 60.

CHAPTER XIII.
THE DETACHED LEVER ESCAPEMENT
AS APPLIED TO CLOCKS.

As the clock repairer is almost of necessity a watchmaker, or hopes to
become one, and as he must enter deeply into the study of all questions
pertaining to the detached lever in its various forms before he can make any
progress at all in watchmaking, it would seem unnecessary to repeat in
these pages that which has already been so well said and so perfectly
drawn, described and illustrated by such authorities as Moritz Grossman,
Britten, Playtner and the various teachers in the horological schools, to say
nothing of an equally brilliant and more numerous coterie of writers among
the French, Germans and Swiss, so that the reader is referred to these
writers for the mathematics and drawings which already so fully cover the
technical and theoretical properties of the detached lever escapement. A few
words as to its adaptation to clocks may, however, not be out of place.
Anyone who sees the clocks of to-day would be inclined to suppose that
the first clocks were constructed with pendulums, because this is evidently
the most simple and reliable system for clocks, and that the employment of
the balance has been suggested by the necessity for portable time pieces.
This is, however, not the case, for the first clocks had a verge escapement
with a crude balance consisting of two arms, carrying shifting weights for
regulation. The pendulum was not used until about three hundred years after
the invention of the first clock.
After the invention of the dead beat escapement, with its great gain in
accuracy by the reduction of the arc of pendulum oscillation, attempts were
made to combine its many virtues with the necessarily large vibrations of a
balance and thus get all the advantages of both systems. By placing the
lever on the arbor of the anchor, it was possible to multiply the small angle
of impulse on the pallets very considerably at the balance, and to make all
connection between them cease immediately after the impulse had been
given. The dead beat escapement was thus converted into the detached lever

escapement and the latter made available for both watches and clocks.
Another important feature of this escapement is that when properly
proportioned it will not set on the locking or lifting, but will start to go as
soon as power is applied to the escape wheel through the train. This cannot
be said of the cylinder, duplex, or detent escapements, and it will be seen at
once that this has an important influence upon the cost of construction,
which must always be considered in the manufacture of cheap clocks in
enormous quantities.

Fig. 61. Pin Escapement for Clocks.
The lever escapement with pins for pallets and the lifting planes on the
teeth of the escape wheel, which is the one usually put into cheap clocks, is
from the theoretical point of view a very perfect form, because its lifting
and locking take place at exactly the same center distance and at the same
angles, which again allows for greater latitude in cheap construction, while

still maintaining a reasonably accurate rate of performance. These are the
main reasons why the pin anchor has such universal use in cheap clocks.
As this escapement is generally centered between the plates, banking
pins are dispensed with by extending the counterpoise end of the lever far
enough so that its crescent shaped sides will perform that office by banking
against the scape wheel arbor; see Fig. 61. The fork end of the lever
engages with an impulse pin carried in the balance and the balance arbor is
cut away to pass the guard point or dart, thus doing away with the roller
table. In other constructions the roller table is supplied in the shape of a
small brass collet which carries the pin and has a notch for the guard point,
thus making a single roller escapement.
The diameter of the lifting pins is generally made equal to 2½ degrees
of the scape wheel, which gives a lift of 2 degrees on the pallet arms, and
the remainder of the lift, 6½ degrees, must be performed by the lifting
planes of the wheel teeth. The front sides of the wheel teeth are generally
made with 15 degrees of draw and the lever should bank when the center of
the pin is just a little past the locking corner of the tooth. Other details of
the pin anchor escapement coincide with the ordinary pallet form, as used in
watches, and the reader is referred for them to the works of the various
authors mentioned previously.
The trouble with the majority of these clocks is in the escapement and
balance pivots, and to these parts are we going to direct particular attention,
for often, be it ever so clean, the balance gets up a sort of “caterpillar
motion” that is truly distressing, and if no more is done we may expect a
“come back” job in a very short time. In taking down the movement the
face wheels are left in place, but sometimes it may be necessary to remove
the “set wheel” of the alarm in order to proceed as we do. Remove the
screws or pins that hold the plates together in the vicinity of the
escapement, leaving the others, though if screws they may be loosened
slightly; pry up the corner of the plate over the lever to loosen one pivot of
same and let it drop away from the scape wheel sufficiently to let the wheel
revolve until it is locked by a wire or pegwood previously inserted in the
train, after which the plates can be pried apart more conveniently to permit
the lever being removed entirely, also the scape wheel and the one next
following. As nickel clocks differ in make-up, the operator must, of course,
exercise judgment as to the work in hand to accomplish this.

Have ready a straight-sided tin pail, with cover, that will hold at least
one-half gallon of gasoline and of diameter large enough to receive the
largest brass clock; remove the wire or pegwood and immerse the clock into
the fluid and allow it to run down; this will loosen all the dirt and gummy
oil and clean the clock very effectually. Let it remain long enough for all the
dirt to settle to the bottom of the pail; then remove and wipe as dry as
possible with a soft rag; by having no binder on the spring it is permitted to
uncoil to its full, and thereby remove all gummy oil between its coils. Now
peg out the holes of the wheels removed and of the lever and that portion of
our work is complete.
Polish or burnish the pivots of wheels either in a split chuck in the lathe,
or by holding in a pin vise, resting the pivot on a filing block (an ivory one
is best), and revolving between the fingers, using a smooth back file for
burnishing, after the manner of pointing up a pin tongue, only let the file be
held flat, so as to maintain a cylindrical pivot as nearly as possible. The
scape wheel is now polished, i. e., the teeth, with a revolving bristle wheel
on a polishing lathe, charged with kerosene oil and tripoli. This will smooth
up the teeth in fine form, especially those wheels that work into a lever with
pin pallets. Clean the scape wheel by dipping into gasoline to remove all the
oil and tripoli. The other wheel may simply be brushed in the gasoline or
dipped and then brushed dry.
We now turn our attention to the lever and closely examine the pallets
with a glass; if there are the least signs of wear upon them they must be
removed. Of the lever with pin pallets it is better to remove the steel pins
and insert new ones. See if the holes in the anchor where they are inserted
will admit a punch to drive them out from the back; if not, open these holes
with a drill until the ends of the pins are reached. Put a hollow stump with a
sufficiently large hole in the staking tool, and by placing the pins in the
stump they can be driven out successively, being sure that the driving punch
is no larger than the pins; drive or insert into their places a couple of
needles of the proper size, and then break off at correct lengths; this
completes the job in this particular style of lever.
With the other style the job is not quite so easy; with a pair of small
round-nose pliers grasp the brass fork close up to the staff and bend it back
from the pallets till it lays parallel with the staff; treat the counter poise of
the fork in like manner; place a thin zinc lap into the lathe, charged with

flour of emery, and with the fingers holding the pallets grind off all wheel
teeth marks on both the impulse and locking faces of the pallets. Then
polish with a boxwood lap charged with diamantine. It is surprising how
speedily this can be done if laps are at hand. The only care necessary is not
to round off the corners of the pallets, and as they are so large they can be
easily held flat against the laps with the thumb and finger as before stated.
Bend back the fork and counterpoise to their original position. The fork
must now be attended to; see that no notches are worn in the horns of the
fork by the steel impulse pin in the balance; if they appear they must be
dressed out and polished, also examine and smooth if necessary the ends of
the horns that bank against the balance staff. These may seem small matters,
but they are often what cause all the trouble.
We now come to the balance staff and the hardened screws in which the
staff vibrates; their irregularities are often the source of much vexation, and
there is only one way to go at it and that is with a will and determination to
make it right. Examine the points of the staff and see if they are in their
normal shapes and are sharp and bright; if so they will probably do their
work. But we will suppose we have a bad case in hand and will therefore
treat it thoroughly according to our method. We find the staff is large in
diameter and the ends are very blunt; the notch in the center has a burr on
each side as hard as glass, making an admirable cause for catching the
horns of the fork in some of the vibrations or in a certain position; also the
round part of the staff back of the notch is rough and looks as if it never had
been finished, and, in fact, it has not, for it truly appears as if half, if not all,
the nickel clocks are made to be finished by the watchmaker. Remove the
hairspring and place the staff between the jaws of your bench vise, with the
jaws close up to the staff, but not gripping it, the balance “hub” resting on
the jaws with the impulse pin also down between the jaws. Have a block of
brass about one-fourth inch square; rest it on top of the staff, or on its pivot
end, if it may so be called, holding it with the thumb and finger of the left
hand. Strike this block with a hammer and drive out the staff; a hollow
punch is apt to be split in doing this, and as the pivot is to be re-pointed no
harm will be done to the pivot or to the end of the staff. Draw the temper so
it will work easily, insert into a split chuck and turn up new points; have
them long and tapering, that is, turn the points to a long slant from the end
of the staff to the body of same, or at least twice as much taper as they
generally have; polish off the back of the notch or round part of the staff

with an oil stone slip. Remove from the chuck, smear all over with
powdered boracic acid by first wetting the staff in water, and then heat to a
bright red and plunge straight into water; it will now be white and hard;
draw the temper from the staff in the vicinity of the notch, leaving the pivot
points hard as before; re-insert into the chuck and with diamantine polish
the points and also around the staff in the vicinity of the notch. The drawing
of the temper from the center of the staff to a spring temper is to make it
less liable to breakage while driving on the balance. Fasten the staff tight in
the vise and with a rather stout brass tube, large enough to step over the
largest staff, drive on the balance to its former position.
If the workman has a pivot polisher with a large lap, the job may be
done, without softening the staff or removing the balance, by grinding the
pivots. In turning the staff we often find it almost impossible to hold true.
We straighten the best we can and then turn up our pivots, and as long as
the untruth of the staff will not cause the balance to wabble to such an
extent as to give us a headache or cause us to look cross-eyed it will do. We
do not wish to be misunderstood or to give the impression that we go on the
principle of “good enough”; but as gold dollars cannot be bought for
seventy-five cents, neither can a workman devote the time to have
everything perfect for fifty cents; and for this very reason do they come in
such an unfinished state from the manufacturers.
Next see if the two screws in which the balance vibrates have properly
cut countersinks; if rough or irregular, better at once draw the temper, re-
drill with a sharp-angled drill and again harden.
Occasionally a bunch of these clocks will come in with both pivots and
cones badly rusted. This has generally been caused by acid pickling, or
some sort of chemical hardening at the factory; the acid or alkali gets into
the pores of the steel and comes out after the clock has been shipped. They
are generally made in such quantities that fifty or a hundred thousand of
them have been distributed before finding out that they were not right and
then it is a matter of two or three years before the factory hears the last of it.
The trouble is attributed to bad oil, or to anything else but the hardening,
which is the real cause, and the expense of taking back and refitting the
balance arbors and cones, paying freight both ways and standing the abuse
of disgruntled jewelers, goes on until life becomes anything but a bed of
roses. Every jeweler should warn the factory immediately on finding rust in

the cones of a shipment of new clocks and not attempt to fix them himself,
as such a fault cannot be discovered at the factory and every day it
continues means more thousands of clocks distributed that will give trouble.
Our clock is now ready to be put together. Wind up the spring and slip
on the binder; then put in the wheels and lever; then adjust the balance and
hairspring to their proper places, slightly wind the mainspring and then see
(by bringing either horn against the staff) whether it sticks and holds the
balance; if so, shorten the fork slightly by bending; try this until the balance
and fork act perfectly free and safe. Slightly oil the balance pivots; an
excess will only gather dust and prove detrimental, as the countersinks form
an admirable place for holding the dust. Now oil the remaining parts and we
are sadly mistaken if our clock does not make a motion that will be
gratifying.
The foregoing process may seem tedious and uncalled for and too close
mention made of the lesser portions of the work, but we must not “despise
the day of small things,” and as we are watchmakers, we are expected to do
this work, even though troublesome and the pay small; we should also bear
in mind that if we only make a nickel clock run and keep fair time, it will be
a large advertisement, and possibly repay tenfold. It takes only an hour to
do this job complete, while in many cases only the balance staff needs
attention.
Sometimes such a clock will be apparently all right mechanically but
will continue to lose time; then it is probable that the balance does not make
the proper number of vibrations, which causes the clock to lose time. There
is one way to tell this, which will soon locate the trouble: count the train to
ascertain the number of vibrations the balance should make in one minute.
You do this by counting the number of teeth in the center wheel, which we
will say is 48; third wheel 48; fourth wheel, 45; escape, 15. Multiply all
teeth together, which give us 48 × 48 × 45 × 15 = 1,555,200. Now count the
leaves in the third wheel pinion, which is 6; fourth, 6; escape, 6. Multiply
these together, 6 × 6 × 6 = 216; now divide the leaves into the teeth,
1,555,200 ÷ 216 = 7,200, which is the number of whole vibrations some
Ansonia alarm clocks make in one hour. Dividing 7,200 by 60 gives us 120,
the number of vibrations per minute. Now the balance must make 120
vibrations in one minute, counting the balance going one way. If the
balance only vibrates 118, the clock will lose time and the hairspring must

be taken up or made shorter, until it makes the required number of
vibrations. If it should vibrate 122 the clock would gain and the hairspring
should be let out.
Find out the number of vibrations your balance should make and work
accordingly; and if you find that the balance makes the proper number of
vibrations in one minute, then the trouble must lie in the center post, which
has not enough friction to carry the hands and dial wheels, or the wheel that
gears into the hour wheel and regulates the alarm hand is too tight and holds
back the hands. You should find some trouble about these wheels or center
post, for where a balance makes the proper number of vibrations in one
minute, the minute hand cannot help going around if everything else is
correct.
Fig. 62 illustrates the escapement of the Western Clock Manufacturing
Company for their cheap levers. It has hardened steel pallets placed in a
mould and the fork cast around them, thus insuring exact placing of the
pallets, and the company claim that they thus secure a detached lever
escapement with all the advantages of hardened and polished pallets at a
minimum cost.

Fig. 62.
Mr. F. Dauphin, of Cassel, Germany, on page 387 of Der Deutsche
Uhrmacher Zeitung, 1905, has described a serious fault of some of the
cheap American alarm clocks in the depthings of the escapements and how
he remedied it by changing the position of the pins. It is to be regretted that
Mr. Dauphin did not state the measurements of the parts as nearly as

possible in this article and also give the manufacturer’s name, simply to
enable others not as skilled as he is to do what I would do in such a case;
namely, to return it to the jobber and get a new and correct movement in its
stead free of charge. The American clock manufacturers are very liberal in
this respect and never hesitate to take back a movement that was not correct
when it left the factory, even when the customer, in the attempt to correct it,
has spoiled it; spoiled or not, it goes to the waste pile anyway, when it
reaches the factory. I seriously doubt the ability of the average watch
repairer to correctly change the position of the pins as suggested; and to
change the center of action of the lever is certainly a desperate job. I
herewith give a correct drawing of an escape wheel and lever, such as are
used in the above cited clocks, made from measurements of the parts of a
clock. The drawing is, of course, enlarged. The measurements are: Escape
wheel, actual diameter, 18.11 mm.; original diameter, 17 mm.; lever, from
pin to pin, outside, 9.3 mm.; distance of centers of wheel and lever, 10.0
mm. I found that all these measurements almost exactly agree with
Grossmann’s tables, and I do not doubt at all that they were taken from
them. There is only one mistake visible, which is in the shape of the escape
teeth, and I fail to see why this was overlooked by those in charge at the
factory; the draw is insufficient. It is only from seven to eight degrees, when
it should be fifteen degrees. I show this at tooth A, in the drawing, where
you can see both dotted lines, measuring the angle of draw; line C as it is
and line B as it should be.

Fig. 63.
Notwithstanding the deficient draw, this escapement will work safely as
long as the pivot holes are not too large, or worn sideways; but if you want
to make it safe you should file the locking faces of teeth slightly under;
even if you do not make a model job, you have remedied the fault. Make a
disk of 18.11 mm. diameter, put it on the arbor of the wheel and lay a
straight edge from the point of the tooth to the center of the disk, so as to
see how much it needs to be filed away. Even if this undercutting is not
very true it will go.
To Measure Wheels with Odd Numbers of Teeth.—This is a job that
so frequently comes to the watchmaker who has to replace wheels or
pinions that the following simple method should be generally appreciated. It
depends upon the fact that the radius of a circle, R, Fig. 64, equals the
versed sine E (dotted) plus the cosine B. If we stand such a wheel on the
points of the teeth, A C, and measure it we shall get the length of the line T
B only, when what we really need is the length of the lines T B E, to give us
the real diameter for our wheel, and E we find has been cut away, so that we
cannot measure it. Say it is a 15-tooth escape wheel, then by standing the

old wheel up on the anvil of a vertical micrometer, resting it on two of its
teeth, as shown in Fig. 64, the measuring screw can be brought in contact
with the tooth diametrically opposite the space between the two teeth on the
anvil, and a measurement taken, which will be less than the full diameter by
the versed sine of 12 degrees (half the angle included between two
adjoining teeth). By bringing each tooth in succession to the top, such a
wheel could be measured in fifteen different directions, which would vary
slightly, owing to the fact that some of the teeth may be bent a little, but the
mean of these measures should be what the wheel would measure were the
teeth in their original shape. If a tooth was badly bent the three measures in
which it was involved could be rejected, and the mean of the other twelve
measures taken as the correct value and found to be, we will say, 0.732
inch. Consulting a table of natural sines the cosine of 12 degrees is found to
be 0.97815, which subtracted from 1 gives 0.02185 as the versed sine.
Multiplying this by 0.36 inch (practically one-half of our measured 0.732)
to get the approximate radius of the wheel, we get 0.008 inch, the amount to
be added to the micrometer measurement in order to get the diameter of the
blank.
At first sight it may appear like a vicious principle that we must know
the radius of the wheel before we can determine the value of the correction
in question, but we only need to know the radius approximately in order to
determine the correction very closely, an error of ¹⁄₂₀ inch in the assumed
value of the radius producing an error of only 0.001 inch in the value of the
correction.

Fig. 64. Getting the full diameter.
This method can of course be applied to all wheels and pinions to get
the size of the blank; with other wheels than escape wheels, where the pitch
line and the full diameter do not coincide, the addendum may be subtracted
from the full diameter to get the pitch line.
Cutters for Clock Trains.—In cutting escape wheels or others with
wide space between the teeth, it is a matter of some difficulty with many
people to enable them to set the cutter properly.
Mr. E. A. Sweet calls attention to the fact that if a cutter be set so that its
center touches the circumference of the wheel to be cut, said cutter will be
in the proper position for work. For instance, if an escape wheel is to be cut,
it is sufficient to set the cutter in such a manner that that portion of the
cutter forming the bottom of the cut touch the circumference of the blank at
the center of the cutter. It may then be backed off and fed in with the
certainty of being properly placed.

CHAPTER XIV.
PLATES, PIVOTS AND TIME TRAINS.

Before going further with the mechanism of our clocks we will now
consider the means by which the various members are held in their
positions, namely, the plates. Like most other parts of the clock these have
undergone various changes. They have been made of wood, iron and brass
and have varied in shapes and sizes so much that a great deal may be told
concerning the age of a clock by examining the plates.
Most of the wooden clocks had wooden plates. The English and
American movements were simply boards of oak, maple or pear with the
holes drilled and bushed with brass tubes—full plates. The Schwarzwald
movements were generally made with top and bottom boards and
stanchions, mortised in between them to carry the trains, which were always
straight-line trains. The rear stanchions were glued in position and the front
ones fitted friction-tight, so that they could be removed in taking down the
clock. This gave a certain convenience in repairing, as, for instance, the
center (time) train could be taken down without disturbing the hour or
quarter trains, or vice versa. Various attempts have been made since to
retain their convenience with brass plates, but it has always added so much
to the cost of manufacture that it had to be abandoned.
The older plates were cast, smoothed and then hammered to compact
the metal. The modern plate is rolled much harder and stiffer and it may
consequently be much thinner than was formerly necessary. The proper
thickness of a plate depends entirely upon its use. Where the movement
rests upon a seat board in the case and carries the weight of a heavy
pendulum attached to one of the plates they must be made stiff enough to
furnish a rigid support for the pendulum, and we find them thick, heavy and
with large pillars, well supported at the corners, so as to be very stiff and
solid. An example of this may be seen in that class of regulators which carry
the pendulum on the movement. Where the pendulum is light the plates
may therefore be thin, as the only other reason necessary for thickness is

that they may provide a proper length of bearing for the pivots, plus the
necessary countersinking to retain the oil.
In heavy machinery it is unusual to provide a length of box or journal
bearing of more than three times the diameter of the journal. In most cases a
length of twice the diameter is more than sufficient; in clock and other light
work a “square” bearing is enough; that is one in which the length is equal
to the diameter. In clocks the pivots are of various sizes and so an average
must be found. This is accomplished by using a plate thick enough to
furnish a proper bearing for the larger pivots and countersinking the pivot
holes for the smaller pivots until a square bearing is obtained. This
countersinking is shaped in such a manner as to retain the oil and as more of
it is done on the smaller and faster moving pivots, where there is the
greatest need of lubrication, the arrangement works out very nicely, and it
will be seen that with all the lighter clocks very thin plates may be
employed while still retaining a proper length of bearing in the pivot holes.
The side shake for pivots should be from .002 to .004 of an inch; the
latter figure is seldom exceeded except in cuckoos and other clocks having
exposed weights and pendulums. Here much greater freedom is necessary
as the movement is exposed to dust which enters freely at the holes for
pendulum and weight chains, so that such a clock would stop if given the
ordinary amount of side shake.
We are afraid that many manufacturers of the ordinary American clock
aim to use as thin brass as possible for plates without paying too much
attention to the length of bearing. If a hole is countersunk it will retain the
oil when a flat surface will not. The idea of countersinking to obtain a
shorter bearing will apply better to the fine clocks than to the ordinary. In
ordinary clocks the pivots must be longer than the thickness of the plates for
the reason that freight is handled so roughly that short pivots will pop out of
the plates and cause a lot of damage, provided the springs are wound when
the rough handling occurs.
It will be seen by reference to Chapter VII (the mechanical elements of
gearing), Figs. 21 to 25, that a wheel and pinion are merely a collection of
levers adapted to continuous work, that the teeth may be regarded as
separate levers coming into contact with each other in succession; this
brings up two points. The first is necessarily the relative proportions of

those levers, as upon these will depend the power and speed of the motion
produced by their action. The second is the shapes and sizes of the ends of
our levers so that they shall perform their work with as little friction and
loss of power as possible.
To Get Center Distances.—As the radii and circumferences of circles
are proportional, it follows that the lengths of our radii are merely the
lengths of our levers (See Fig. 24), and that the two combined (the radius of
the wheel, plus that of the pinion) will be the distance at which we must
pivot our levers (our staffs or arbors of our wheels) in order to maintain the
desired proportions of their revolution. Consequently we can work this rule
backwards or forwards.
For instance if we have a wheel and pinion which must work together in
the proportion of 7½ to 1; then 7½ + 1 = 8½ and if we divide the space
between centers into 8½ spaces we will have one of these spaces for the
radius of the pitch circle of the pinion and 7½ for the pitch circle of the
wheel, Fig. 65. This is independent of the number of teeth so long as the
proportions be observed; thus our pinion may have eight teeth and the
wheel sixty, 60 ÷ 8 = 7.5, or 75 ÷ 10 = 7.5, or 90 ÷ 12 = 7.5, or any other
combination of teeth which will make the correct proportion between them
and the center distances. The reason is that the teeth are added to the wheel
to prevent slipping, and if they did not agree with each other and also with
the proportionate distance between centers there would be trouble, because
the desired proportion could not be maintained.
Now we can also work this rule backwards. Say we have a wheel of 80
teeth and the pinion has 10 leaves but they do not work together well in the
clock. Tried in the depthing tool they work smoothly. 80 ÷ 10 = 8,
consequently our center distance must be as 8 and 1. 8 + 1 = 9; the wheel
must have 8 parts and the pinion 1 part of the radius of the pitch circle of
the wheel. Measure carefully the diameter of the pitch circle of the wheel;
half of that is the pitch radius, and nine-eighths of the pitch radius is the
proper center distance for that wheel and pinion.
Say we have lost a wheel; the pinion has 12 teeth and we know the
arbor should go seven and one-half times to one of the missing wheel; we
have our center distances established by the pivot holes which are not worn;
what size should the wheel be and how many teeth should it have?

12 × 7.5 = 90, the number of teeth necessary to contain the teeth of the
pinion 7.5 times. 7.5 + 1 = 8.5, the sum of the center distances; the pitch
radius of the pinion can be closely measured; then 7.5 times that is the pitch
radius of the missing wheel of 90 teeth. Other illustrations with other
proportions could be added indefinitely but we have, we think, said enough
to make this point clear.

Fig. 65. Spacing off center distances; c, center of wheel;
e, pitch circle; d, dedendum; b, addendum; a, center of pinion.
Conversion of Numbers.—There is one other point which sometimes
troubles the student who attempts to follow the expositions of this subject
by learned writers and that is the fact that a mathematician will take a
totally different set of numbers for his examples, without explaining why. If
you don’t know why you get confused and fail to follow him. It is done to
avoid the use of cumbersome fractions. To use a homely illustration: Say

we have one foot, six inches for our wheel radius and 4.5 inches for our
pinion radius. If we turn the foot into inches we have 18 inches.
18 ÷ 4.5 = 4, which is simpler to work with. Now the same thing can be
done with fractions. In the above instance we got rid of our larger unit (the
foot) by turning it into smaller units (inches) so that we had only one kind
of units to work with. The same thing can be done with fractions; for
instance, in the previous example we can get rid of our mixed numbers by
turning everything into fractions. Eighteen inches equals 36 halves and 4.5
equals 9 halves; then 36 ÷ 9 = 4. This is called the conversion of numbers
and is done to simplify operations. For instance in watch work we may find
it convenient to turn all our figures into thousands of a millimeter, if we are
using a millimeter gauge. Say we have the proportions of 7.5 to 1 to
maintain, then turning all into halves, 7½ × 2 = 15 and 1 × 2 = 2.
15 + 2 = 17 parts for our center distance, of which the pitch radius of the
pinion takes 2 parts and that of the wheel 15.
The Shapes of the Teeth.—The second part of our problem, as stated
above, is the shapes of the ends of our levers or the teeth of our wheels, and
here the first consideration which strikes us is that the teeth of the wheels
approach each other until they meet; roll or slide upon each other until they
pass the line of centers and then are drawn apart. A moment’s consideration
will show that as the teeth are longer than the distance between centers and
are securely held from slipping at their centers, the outer ends must either
roll or slide after they come in contact and that this action will be much
more severe while they are being driven towards each other than when they
are being drawn apart after passing the line of centers. This is why the
engaging friction is more damaging than the disengaging friction and it is
this butting action which uses up the power if our teeth are not properly
shaped or the center distances not right. Generally speaking this butting
causes serious loss of power and cutting of the teeth when the pivot holes
are worn or the pivots cut, so that there is a side shake of half the diameter
of the pivots, and bushing or closing the holes, or new and larger pivots are
then necessary. This is for common work. For fine work the center distances
should be restored long before the wear has reached this point.
If we take two circular pieces of any material of different diameters and
arrange them so that each can revolve around its center with their edges in
contact, then apply power to the larger of the two, we find that as it revolves

its motion is imparted to the other, which revolves in the opposite direction,
and, if there is no slipping between the two surfaces, with a velocity as
much greater than that of the larger disc as its diameter is exceeded by that
of the larger one. We have, then, an illustration of the action of a wheel and
pinion as used in timepieces and other mechanisms. It would be impossible,
however, to prevent slipping of these smooth surfaces on each other so that
power (or motion) would be transmitted by them very irregularly. They
simply represent the “pitch” circles or circles of contact of these two
mobiles. If now we divide these two discs into teeth so spaced that the teeth
of one will pass freely into the spaces of the other and add such an amount
to the diameter of the larger that the points of its teeth extend inside the
pitch circle of the smaller, a distance equal to about 1⅛ times the width of
one of its teeth, and to the smaller so that its teeth extend inside the larger
one-half the width of a tooth, the ends of the teeth being rounded so as not
to catch on each other and the centers of revolution being kept the same
distance apart, on applying power to the larger of the two it will be set in
motion and this motion will be imparted to the smaller one. Both will
continue to move with the same relative velocity as long as sufficient power
is applied. Other pairs of mobiles may be added to these to infinity, each
addition requiring the application of increased power to keep it in motion.
These pairs of mobiles as applied to the construction of timepieces are
usually very unequal in size and the larger is designated as a “wheel” while
the smaller, if having less than 20 teeth, is called a “pinion” and its teeth
“leaves.” Now while we have established the principle of a train of wheels
as used in various mechanisms, our gearing is very defective, for while
continuous motion may be transmitted through such a train, we will find
that to do so requires the application of an impelling force far in excess of
what should be required to overcome the inertia of the mobiles, and the
amount of friction unavoidable in a mechanism where some of the parts
move in contact with others.
This excess of power is used in overcoming a friction caused by
improperly shaped teeth, or when formed thus the teeth of the wheel come
in contact with those of the pinion and begin driving at a point in front of
what is known as the “line of centers,” i. e., a line drawn through the centers
of revolution of both mobiles, and as their motion continues the driven
tooth slides on the one impelling it toward the center of the wheel. When

this line is reached the action is reversed and the point of the driving tooth
begins sliding on the pinion leaf in a direction away from the center of the
pinion, which action is continued until a point is reached where the straight
face of the leaf is on a line tangential to the circumference of the wheel at
the point of the tooth. It then slips off the tooth, and the driving is taken up
on another leaf by the next succeeding tooth. The sliding action which takes
place in front of the line of centers is called “engaging,” that after this line
has been passed “disengaging” friction.
Now we know that in the construction of timepieces, friction and
excessive motive power are two of the most potent factors in producing
disturbances in the rate, and that, while some friction is unavoidable in any
mechanism, that which we have just described may be almost entirely done
away with. Let us examine carefully the action of a wheel and pinion, and
we will see that only that part of the wheel tooth is used, which is outside
the pitch circle, while the portion of the pinion leaf on which it acts is the
straight face lying inside this circle, therefore it is to giving a correct shape
to these parts we must devote our attention. If we form our pinion leaves so
that the portion of the leaf inside the pitch circle is a straight line pointing to
the center, and give that portion of the wheel tooth lying outside the pitch
circle (called the addenda, or ogive of the tooth) such a degree of curvature
that during its entire action the straight face of the leaf will form a tangent
to that point of the curve which it touches, no sliding action whatever will
take place after the line of centers is passed, and if our pinion has ten or
more leaves, the “addenda” of the wheel is of proper height, and the leaves
of the pinion are not too thick, there will be no contact in front of the line of
centers. With such a depth the only friction would be from a slight adhesion
of the surfaces in contact, a factor too small to be taken into consideration.

Showing that a hypocycloid of half the pitch circle is a straight line.

Generating an epicycloid curve for a cut pinion. D, generating circle.
Dotted line epicycloid curve. Note how the shape varies with the
thickness of the tooth.
Here, then, we have an ideal depth. How shall we obtain the same
results in practice? It is comparatively an easy matter to so shape our cutters
that the straight faces of our pinion leaves will be straight lines pointing to
the center, but to secure just the proper curve for the addenda of our wheel
teeth requires rather a more complicated manipulation. This curve does not
form a segment of a circle, for it has no two radii of equal length, and if
continued would form, not a circle, but a spiral. To generate this curve, we
will cut from cardboard, wood, or sheet metal, a segment of a circle having
a radius equal to that of our wheel, on the pitch circle, and a smaller circle

whose diameter is equal to the radius of the pinion, on the pitch circle. To
the edge of the small circle we will attach a pencil or metal point so that it
will trace a fine mark. Now we lay our segment flat on a piece of drawing
paper, or sheet metal and cause the small circle to revolve around its edge
without slipping. We find that the point in the edge of the small circle has
traced a series of curves around the edge of the segment.
These curves are called “epicycloids,” and have the peculiar property
that if a line be drawn through the generating point and the point of contact
of the two circles, this will always be at right angles to a tangent of the
curve at its point of intersection. It is this property to which it owes its value
as a shape for the acting surface of a wheel tooth, for it is owing to this that
a tooth whose acting surface is bounded by such a curve can impel a pinion
leaf through the entire lead with little sliding action between the two
surfaces. This, then, is the curve on which we will form the addenda of our
wheel teeth.
In Fig. 66, the wheel has a radius of fifteen inches and the pinion a
radius of one and one-half, and these two measurements are to be added
together to find the distance apart of the two wheels; 16.5 inches is then the
distance that the centers of revolution are apart of the wheels. Now, the
teeth and leaves jointly act on one another to maintain a sure and equable
relative revolution of the pair.
In Fig. 66, the pinion has its leaves radial to the center, inside of the
pitch line D, and the ends of the leaves, or those parts outside of the pitch
line, are a half circle, and serve no purpose until the depthings are changed
by wear, as they never come in contact with the wheel; the wheel teeth only
touch the radial part of the pinion and that occurs wholly within the pitch
line. So in all pinions above 10 leaves in number the addendum or curve is
a thing of no moment, except as it may be too large or too long. In many
large pieces of machinery the pinions, or small driven wheels, have no
addendum or extension beyond their pitch diameter and they serve every
end just as well. In watches there is so much space or shake allowed
between the teeth and pinions that the end of a leaf becomes a necessity to
guard against the pinion’s recoiling out of time and striking its sharp corner
against the wheel teeth and so marring or cutting them. In a similar pair of
wheels in machinery there are very close fits used and the shake between

teeth is very slight and does not allow of recoil, butting, or “running out of
time.”
Running out of time is the sudden stopping and setting back of a pinion
against the opposite tooth from the one just in contact or propelling. This,
with pinions of suppressed ends, is a fault and it is averted by maintaining
the ends.
The wheel tooth drives the pinion by coming in contact with the straight
flank of the leaf at the line of centers, that is a line drawn through the
centers of the two wheels; centers of revolution.
The curve or end of the wheel tooth outside of the pitch line is the only
part of the tooth that ever touches the pinion and it is the part under friction
from pressure and slipping. At the first point of contact the tooth drives the
pinion with the greatest force, as it is then using the shortest leverage it has
and is pressing on the longest lever of the leaf. As this action proceeds, the
tooth is acted on by the pinion leaf farther out on the curve of the wheel
tooth, thus lengthening the lever of the wheel and at the same time the tooth
thus acts nearer to the center of the pinion by touching the leaf nearer its
center of revolution.
By these joint actions it will appear that the wheel first drives with the
greatest force and then as its own leverage lengthens and its force
consequently decreases, it acts on a shorter leverage of the pinion, as the
end of a tooth is nearer to the center of the pinion, or on the shortest pinion
leverage, just as the tooth is about ceasing to act.
The action is thus shown from the above to be a variable one, which
starts with a maximum of force and ends with a minimum. Practically the
variable force in a train is not recognized in the escapement, as the other
wheels and pinions making up the train are also in the same relations of
maximum and minimum forces at the same time, and thus this theoretical
and virtual variability of train force is to a great extent neutralized at the
active or escaping end of the movement.
There is another action between the tooth and leaf that is not easy to
explain without somewhat elaborate sketches of the acting parts, and as this
is not consistent with such an article, we may dismiss it, and merely state

that it is the one of maintaining the relative angular velocities of the two
wheels at all times during their joint revolutions.
In Fig. 66 will be seen the teeth of the wheel, their heights, widths and
spacing, and the epicycloidal curves. Also the same features of the pinion’s
construction. The curve on the end of the wheel teeth is the only curve in
action during the rotation between wheel and pinion. Each flank (both teeth
and leaves) is a straight line to the center of each. A tooth is composed of
two members—the pillar or body of the tooth inside of the pitch line and
the cycloid or curve, wholly outside of this line. The pinion also has two
members, the radial flank wholly inside of the pitch line, and its addendum
or circle outside of this line.

Fig. 66.
In Fig. 66 will be seen a tooth on the line of centers A B, just coming in
action against the pinion’s flank and also one just ceasing action. It will be

seen that the tooth just entering is in contact at the joint pitches, or radii, of
the two wheels, and that when the tooth has run its course and ceased to act,
that it will be represented by tooth 2. Then the exit contact will be at the
dotted line o o. From this may be seen just how far the tooth has, in its
excursion, shoved along the leaf of the pinion and by the distance the line o
o, is from the wheel’s pitch line G, at this tooth. No. 2, is shown the extent
of contact of the wheel tooth. By these dotted lines, then, it may be seen
that the tooth has been under friction for nearly its whole curve’s length,
while the pinion’s flank will have been under friction contact for less than
half this distance. In brief, the tooth has moved about ⁸⁰⁄₁₀₀ of its curved
surface along the straight flank .35 of the surface of the pinion leaf. From
this relative frictional surface may be seen the reason why a pinion is apt to
be pitted by the wheel teeth and cut away. In any case it shows the relation
between the two friction surfaces. In part a wheel tooth rolls as well as
slides along the leaf, but whatever rolling there may be, the pinion is also
equally favored by the same action, which leaves the proportions of
individual friction still the same.
In Fig. 66 may be seen the spaces of the teeth and pinion. The teeth are
apart, equal to their own width and the depths of the spaces are the same
measurement of their width—that is, the tooth (inside of the pitch line) is a
pillar as wide as it is high and a space between two teeth is of like
proportions and extent of surface. The depth of a space between two teeth is
only for clearance and may be made much less, as may be seen by the
pinion leaf, as the end of the circle does not come half way to the bottom of
a space.
The dotted line, o o, shows the point at which the tooth comes out of
action and the pointed end outside of this line might be cut off without
interfering with any function of the tooth. They generally are rounded off in
common clock work.
The pinion is 3 inches diameter and is divided into twelve spaces and
twelve leaves; each leaf is two-fifths of the width of a space and tooth. That
is one-twelfth of the circumference of the pinion is divided into five equal
parts and the leaf occupies two and a space three of these parts. The space
must be greater than the width of a leaf, or the end of a leaf would come in
contact with a tooth before the line of centers and cause a jamming and
butting action. Also the space is needed for dirt clearance. As watch trains

actuated by a spring do not have any reserve force there must be allowance
made for obstructions between the teeth of a train and so a large latitude is
allowed in this respect, more than in any machinery of large caliber. As will
be seen by Fig. 66, the spans between the leaves are deep, much more so
than is really necessary, and a space at O C shows the bottom of a space, cut
on a circle which strengthens a leaf at its root and is the best practice.
Having determined the form of our curve, our next step will be to get
the proper proportions. Saunier recommends that in all cases tooth and
space should be of equal width, but a more modern practice is to make the
space slightly wider, say one-tenth where the curve is epicycloidal. When
the teeth are cut with the ordinary Swiss cutters, which, of course, cannot be
epicycloidal, it is best to make the spaces one-seventh wider than the tooth.
This proportion will be correct except in the case of a ten-leaf pinion, when,
if we wish to be sure the driving will begin on the line of centers, the teeth
must be as wide as the spaces; but in this case the pinion leaf is made
proportionately thinner, so that the requisite freedom is thus obtained.
The height of the addenda of the wheel teeth above the pitch circle is
usually given as one and one-eighth times the width of a tooth. While this is
approximately correct, it is not entirely so, for the reason that as we use a
circle whose diameter is equal to the pitch radius of the pinion for
generating the curve, the height of the addenda would be different on the
same wheel for each different numbered pinion. So that if a wheel of 60
were cut to drive a pinion of 8, the curve of this tooth would be found too
flat if used to drive a pinion of 10. Now, since the pitch diameter of the
pinion is to the pitch diameter of the wheel as the number of leaves in the
pinion are to the number of teeth in the wheel, in order to secure perfect
teeth: we must adopt for the height of the addenda a certain proportion of
the radius or diameter of the pinion it is to drive, this proportion depending
on the number of leaves in the pinion.
A careful study of the experiments on this subject with models of depths
constructed on a large scale, shows that the proportions given below come
the nearest to perfection.
When the pinion has six leaves the spaces should be twice the width of
the leaves and the depth of the space a little more than one-half the total
radius of the pinion. The addenda of the pinion should be rounded, and

should extend outside the pitch circle a distance equal to about one-half the
width of a leaf. The addenda of the wheel teeth should be epicycloidal in
form and should extend outside the pitch circle a distance equal to five-
twelfths of the pitch radius of the pinion.
With these proportions, the tooth will begin driving when one-half the
thickness of a leaf is in front of the line of centers, and there will be
engaging friction from this point until the line of centers is reached.
This cannot be avoided with low numbered pinions without introducing
a train of evils more productive of faulty action than the one we are trying
to overcome. There will be no disengaging friction.
When a pinion of seven is used, the spaces of the pinion should be twice
the width of the leaves, and the depth of a space about three-fifths of the
total radius of the pinion. The addenda of the pinion leaves should be
rounded, and should extend outside the pitch circle about one-half the width
of a leaf. The addenda of the wheel teeth should be epicycloidal, and the
height of each tooth above the pitch circle equal to two-fifths of the pitch
radius of the pinion.
There is less engaging friction when a pinion of seven is used than with
one of six, as the driving does not begin until two-thirds of the leaf is past
the line of centers. There is no disengaging friction.
With an eight-leaf pinion the space should be twice as wide as the leaf,
and the depth of a space about one-half the total radius of the pinion. The
addenda of the pinion leaves should be rounded and about one-half the
width of a leaf outside the pitch circle. The addenda of the wheel teeth
should be epicycloidal, and the height of each tooth above the pitch circle
equal to seven-twentieths of the pitch radius of the pinion.
With a pinion of eight there is still less engaging friction than with one
of seven, as three-quarters of the width of a leaf is past the line of centers
when the driving begins. As there is no disengaging friction, a pinion of this
number makes a very satisfactory depth.
A pinion with nine leaves is sometimes, though seldom, used. It should
have the spaces twice the width of the leaves, and the depth of a space one-
half the total radius. The addenda should be rounded, and its height above
the pitch circle equal to one-half the width of the leaf. The addenda of the

wheel teeth should be epicycloidal, and the height of each tooth above the
pitch circle equal to three-sevenths of the total radius of the pinion. With
this pinion the driving begins very near the line of centers, only about one-
fifth of the width of a leaf being in front of the line.
A pinion of ten leaves is the lowest number with which we can entirely
eliminate engaging friction, and to do so in this case the proper proportions
must be rigidly adhered to. The spaces on the pinion must be a little more
than twice as wide as a leaf; a leaf and space will occupy 36° of arc; of this
11° should be taken for the leaf and 25° for the space. The addenda should
be rounded and should extend about half the width of a leaf outside the
pitch circle. The depth of a space should be equal to about one-half the total
radius. For the wheel, the teeth should be equal in width to the spaces, the
addenda epicycloidal in form, and the height of each tooth above the pitch
circle, equal to two-fifths the pitch radius of the pinion.
A pinion having eleven leaves would give a better depth, theoretically,
than one of ten, as the leaves need not be made quite so thin to ensure its
not coming in action in front of the line of centers. It is seldom seen in
watch or clock work, but if needed the same proportions should be used as
with one of ten, except that the leaves may be made a little thicker in
proportion to the spaces.
A pinion having twelve leaves is the lowest number with which we can
secure a theoretically perfect action, without sacrificing the strength of the
leaves or the requisite freedom in the depths. In this pinion, the leaf should
be to the space as two to three, that is, we divide the arc of the
circumference needed for a leaf and space into five equal parts, and take
two of these parts for the leaf, and three for the space; depth of the space
should be about one-half the total radius. The addenda of the wheel teeth
should be epicycloidal, and the height of each tooth above the pitch line
equal to two-sevenths the pitch radius of the pinion.
As the number of leaves is increased up to twenty, the width of the
space should be decreased, until when this number is reached the space
should be one-seventh wider than the leaf. As these numbers are used
chiefly for winding wheels in watches, where considerable strength is
required, the bottoms of the spaces of both mobiles should be rounded.

Circular Pitch. Diametral Pitch.—In large machinery it is usual to
take the circumference and divide by the number of teeth; this is called the
circular pitch, or distance from point to point of the teeth, and is useful for
describing teeth to be cut out as patterns for casting.
But for all small wheels it is more convenient to take the diameter and
divide by the number of teeth. This is called the diametral pitch, and when
the diameter of a wheel or pinion which is intended to work into it is
desired, such diameter bears the same ratio or proportion as the number
required. Both diameters are for their pitch circles. As the teeth of each
wheel project from the pitch circle and enter into the other, an addition of
corresponding amount is made to each wheel; this is called the addendum.
As the size of a tooth of the wheel and of a tooth of the pinion are the same,
the amount of the addendum is equal for both; consequently the outside
diameter of the smaller wheel or pinion will be greater than the arithmetical
proportion between the pitch circles. As the diameters are measured
presumably in inches or parts of an inch, the number of a wheel of given
size is divided by the diameter, which gives the number of teeth to each
inch of diameter, and is called the diametral pitch. In all newly-designed
machinery a whole number is used and the sizes of the wheels calculated
accordingly, but when, as in repairing, a wheel of any size has any number
of teeth, the diametral number may have an additional fraction, which does
not affect the principle but gives a little more trouble in calculation. Take
for example a clock main wheel and center pinion: Assuming the wheel to
be exactly three inches in diameter at the pitch line, and to have ninety-six
teeth, the result will be 96 ÷ 3 = 32, or 32 teeth to each inch of diameter,
and would be called 32 pitch. A pinion of 8 to gear with this wheel would
have a diameter at the pitch line of 8 of these thirty-seconds of an inch or
⁸⁄₃₂ of an inch. But possibly the wheel might not be of such an easily
manageable size. It might, say, be 3.25 inches, in which case, 96 being the
number of the wheel and 8 of the pinion, the ratio is ⁸⁄₉₆ or ¹⁄₁₂, so ¹⁄₁₂ of
3.25 = 0.270, the pitch diameter of the pinion. These two examples are
given to indicate alternative methods, the most convenient of which may be
used. After arriving at the true pitch diameters the matter of the addendum
arises, and it is for this that the diametral number is specially useful, as in
every case when figuring by this system, whatever the number of a wheel or
pinion, two of the pitch numbers are to be added. Thus with the 32 pitch,
the outside diameter of the wheel will be 3 in. + ²⁄₃₂, and if the pinion

⁸⁄₃₂ + ²⁄₃₂ = ¹⁰⁄₃₂. With the other method the same exactness is more difficult
of attainment, but for practical purposes it will be near enough if we use ²⁄₃₀
of an inch for the addendum, when the result will be 3.25 + ²⁄₃₀ or 3¼ +
²⁄₃₀ = 3⅓; in. nearly and the pinion 0.270 + ²⁄₃₀ = 0.270 + .0666 = 0.3366; or
to work by ⅓ of an inch is near enough, giving the outside diameter of the
pinion a small amount less than the theoretical, which is always advisable
for pinions which are to be driven.
We represent by Figs. 67 to 71 a wheel of sixty teeth gearing with a
pinion of six leaves. The wheel, whose pitch diameter is represented by the
line mm is the same in each figure. The pinion, which has for its pitch
diameter the line kk, is in Fig. 67, of a size proportioned to that of the
wheel, and its center is placed at the proper distance; that is to say, the two
pitch diameters are tangential.
In Fig. 68 the same pinion, of the proper size, has its center too far off;
the depthing is too shallow. In Fig. 69 it is too deep. Figs. 70 and 71
represent gearing in which the pitch circles are in contact, as the theory
requires, but the size of the pinions is incorrect. If the wheels and pinion
actuated each other by simple contact the velocity of the pinion with
reference to that of the wheel would not be absolutely the same; but the
ratio of the teeth being the same, the same ratio of motion obtains in
practice, and there is necessarily bad working of the teeth with the leaves.
We will observe what passes in each of these cases, and refer to the
suitable remedies for obtaining a passable depthing and a comparatively
good rate, without the necessity of repairs at a cost out of all proportion
with the value of the article repaired.

Fig. 67.
Fig. 67 represents gearing of which the wheel and pinion are well
proportioned and at the proper distance from each other. Its movement is
smooth, but it has little drop or none at all. By examining the teeth h, h′, of
the wheel, it is seen that they are larger than the interval between them.
With a cutter FF, introduced between the teeth, they are reduced at d, d′,
which gives the necessary drop without changing the functions, since the
pitch circles mm and kk have not been modified. The drop, the play
between the tooth d′ and the leaf a, is sufficiently increased for the working
of the gearing with safety.
We have the same pair in Fig. 68, but here their pitch circles do not
touch; the depthing is too shallow. The drop is too great and butting is
produced between the tooth h and the leaf r, which can be readily felt. The
remedy is in changing the center distance, by closing the holes, if worn, or
moving one nearer the other. But in an ordinary clock this wheel may be
replaced with a larger one, whose pitch circle reaches to e. The proportions
of the pair are modified, but not sufficiently to produce inconvenience.

Fig. 68.
It may also answer to stretch the wheel, if it is thick enough to be
sufficiently increased in size. A cutter should then be selected for rounding-
up which will allow the full width to the tooth as at p; but if it is not
possible to enlarge the wheel enough, a little of the width of the teeth may
be taken off, as is seen at h, which will diminish the butting with the leaf r.
Too great depthing, Fig. 69, can generally be recognized by the lack of
drop. When the teeth of the wheel are narrow, the drop may appear to be
sufficient. When the train is put in action the depthing that is too great
produces scratching or butting and the ’scape wheel trembles. This results
from the fact that the points of the teeth of the wheel touch the core of the
pinion and cause it to butt against the leaf following the one engaged, as is
visible at r in Fig. 69. It should be noticed that in this figure the pitch circles
mm and kk overlap each other, instead of being tangential.

Fig. 69.

Fig. 70.
To correct this gearing, the cutter should act only on the addenda of the
teeth of the wheel, so as to diminish them and bring the pitch circle mm to
n. The dots in the teeth d, d′, show the corrected gearing. It is seen that there
will be, after this change, the necessary drop, and that the end of the tooth d′
will not touch the leaf r.
In the two preceding cases we have considered wheels and pinions of
accurate proportion, and the defects of the gearing proceeding from the
wrong center distances. We will not speak of the gearing in which the
pinion is too small. The only theoretic remedy in this case, as in that of too
large a pinion, is to replace the defective piece; but in practice, when time
and money are to be saved, advantage must be taken, one way or another, of
what is in existence.
The buzzing produced when the train runs in a gearing with too small a
pinion proceeds from the fact that each tooth has a slight drop before
engaging with the corresponding leaf. If we examine Fig. 70, it will be easy
to see how this drop is produced. The wheel revolving in the direction
indicated by the arrow, it can be seen that when the tooth h leaves the leaf r,
the following tooth, p, does not engage with the corresponding leaf, s; this
tooth will therefore have some drop before reaching the leaf. A friction may
even be produced at the end or addendum of the tooth p against the
following leaf v.
To obtain a fair depthing without replacing the pinion, the wheels can be
passed to the rounding-up machine, having a cutter which will take off only
the points of the teeth, as is indicated in the figure; the result may be
observed by the dotted lines. The tooth h being shorter, it will leave the leaf
r of the pinion when the latter is in the dotted position; that is to say, a little
sooner. At this moment the tooth p is in contact with the leaf s, and there is
no risk of friction against the leaf v. Care must be taken to touch only the
addendum of the tooth so as not to weaken the teeth. The circumference i
will be that of a pinion of accurate size, and if the pinion is replaced, it will
be necessary to diminish the wheel so that its pitch circle shall be tangential
with i.

Fig. 71.
With too small a pinion a passable gearing can generally be produced.
In any case stoppage can be prevented. This is not so easy when the pinion
is too large. In Fig. 71, the pinion has as its pitch circle the line k, instead of
i, which would be nearer the size with reference to that of the wheel. This is
purposely drawn a little small for clearness of illustration. The essential
defect of such a gearing can be seen; the butting produced between the
tooth p and the leaf s will cause stoppage. How shall this defect be
corrected without replacing the pinion?
To remedy the butting as far as possible, some watchmakers slope the
teeth of the wheel by decentering the cutter on the rounding-up machine. At
FF the cutter is seen working between the teeth d and d′. It is evident that
when the wheel becomes smaller it is necessary to stretch it out, and to
make use of the cutter afterwards. However, the most rational method is to
leave the teeth straight, and to give them the slenderest form possible, after
having enlarged the wheel or having replaced it with another. The motive
force of the wheel being sufficiently weak, the size of the teeth may be
reduced without fear. The essential thing is to suppress the butting. Success
will be the easiest when the teeth are thinner.

In conclusion, we recommend verification of all suspected gearings by
the depthing tool, which is easier and surer than by the clock itself. One can
see better by the tool the working of the teeth with the leaves, and can form
a better idea of the defect to be corrected. With the aid of the illustrations
that have been given it can be readily noticed whether the depthing is too
deep or too shallow, or the pinion too large or too small.
The defects mentioned are of less consequence in a pinion of seven
leaves, and they are corrected more readily. With pinions of higher numbers
the depthings will be smoother, provided sufficient care has been taken in
the choice of the rounding-up cutters.
Rounding-Up Wheels.—It is frequently observed that young
watchmakers, and (regretfully be it said) some of the older and more
experienced ones, are rather careless when fitting wheels on pinions. In
many cases the wheel is simply held in the fingers and the hole opened with
a broach, and in doing this no special care is taken to keep the hole truly
central and of correct size to fit the pinion snugly, and should it be opened a
little too large it is riveted on the pinion whether concentric or not. Many
suppose the rounding-up tool will then make it correct without further
trouble and without sufficient thought of the irregularities ensuing when
using the tool.
To make the subject perfectly clear the subjoined but rather exaggerated
sketch is shown, Fig. 72. Of course, it is seldom required to round-up a
wheel of twelve teeth, and the eccentricity of the wheel would be hardly as
great as shown; nevertheless, assuming such a case to occur the drawing
will exactly indicate the imperfections arising from the use of a rounding-up
tool.

Fig. 72.
Presuming from the drawing that the wheel, as shown by dotted lines,
had originally been cut with its center at m, but through careless fitting had
been placed on the pinion at o, and consequently is very much out of round
when tested in the calipers, and to correct this defect it is put in the
rounding-up tool. The cutter commences to remove the metal from tooth 7,
it being the highest, next the neighboring teeth 6 and 8, then 5 and 9, and so
on until tooth 1 comes in contact with the cutter. The wheel is now round.
But how about the size of the teeth and the pitch? The result of the action of
the cutter is shown by the sectionally lined wheel. Many will ask how such,
a result is possible, as the cutter has acted equally upon all the teeth.
Nevertheless, a little study of the action of the rounding-up cutter will soon
make it plain why such faults arise. Naturally the spaces between the teeth
through the action of the cutter will be equal, but as the cutter is compelled
to remove considerable metal from the point of greatest eccentricity, i. e., at
tooth 7 and the adjoining teeth, to make the wheel round, and the pitch
circle being smaller the teeth become thinner, as the space between the teeth
remains the same. At tooth 1 no metal was removed, consequently it
remains in its original condition. The pitch from each side of tooth 1

becomes less and less to tooth 7, and the teeth thinner, and the thickest tooth
is always found opposite the thinnest.
In the case of a wheel having a large number of teeth and the
eccentricity of which is small, such faults as described cannot be readily
seen, from the fact that there are many teeth and the slight change in each is
so gradual that the only way to detect the difference is by comparing
opposite teeth. And this eccentricity becomes a serious matter when there
are but few teeth, as before explained, especially when reducing an escape
wheel. The only proper course to pursue is to cement the wheel on a chuck,
by putting it in a step chuck or in any suitable manner so that it can be trued
by its periphery and then opening the hole truly. This method is followed by
all expert workmen.
A closer examination of the drawing teaches us that an eccentric wheel
with pointed teeth—as cycloidal teeth are mostly left in this condition when
placed in the rounding-up tool, will not be made round, because when the
cutter has just pointed the correct tooth (tooth No. 1 in the drawing) it will
necessarily shorten the thinner teeth. Nos. 6, 7, 8, i. e., the pitch circle will
be smaller in diameter. We can, therefore, understand why the rounding-up
tool does not make the wheel round.
As we have before observed, when rounding-up an eccentrically riveted
wheel, the thickest tooth is always opposite the thinnest, but with a wheel
which has been stretched the case is somewhat different. Most wheels when
stretched become angular, as the arcs between the arms move outward in a
greater or less degree, which can be improved to some extent by carefully
hammering the wheel near the arms, but some inequalities will still remain.
In stretching a wheel with five arms we therefore have five high and as
many depressed parts on its periphery. If this wheel is now rounded-up the
five high parts will contain thinner teeth than the depressed portions.
Notwithstanding that the stretching of wheels, though objectionable, is
often unavoidable on account of the low price of repairs, it certainly ought
not to be overdone. Before placing the wheel in the rounding-up tool it
should be tested in the calipers and the low places carefully stretched so that
the wheel is as nearly round as can be made before the cutter acts upon it.
It is hardly necessary to mention that the rounding-up tool will not
equalize the teeth of a badly cut wheel, and further should there be a burr on

some of the teeth which has not been removed, the action of the guide and
cutter in entering a space will not move the wheel the same distance at each
tooth, thus producing thick and thin teeth. From what has been said it would
be wrong to conclude that the rounding-up tool is a useless one; on the
contrary, it is a practical and indispensable tool, but to render good service
it must be correctly used.
In the use of the rounding-up tool the following rules are to be
observed:
1. In a new wheel enlarge the hole after truing the wheel
from the outside and stake it concentrically on its pinion.
2. In a rivetted but untrue wheel, stretch the deeper
portions until it runs true, then reduce it in the rounding-up
tool. The better method is to remove the wheel from its
pinion, bush the hole, open concentrically with the outside
and rivet, as previously mentioned in a preceding paragraph.
But if the old riveting cannot be turned so that it can be used
again it is best to turn it entirely away, making the pinion
shaft conical towards the pivot, and after having bushed the
wheel, drill a hole the proper size and drive it on the pinion.
The wheel will be then just as secure as when rivetted, as in
doing the latter the wheel is often distorted. With a very thin
wheel allow the bush to project somewhat, so that it has a
secure hold on the pinion shaft and cannot work loose.
3. Should there be a feather edge on the teeth, this should
be removed with a scratch brush before rounding it up, but if
for some reason this cannot well be done, then place the
wheel upon the rest with the feather edge nearest the latter
so that the cutter does not come immediately in contact with
it. If the feather edge is only on one side of the tooth—which
is often the case—place the wheel in the tool so that the
guide will turn it from the opposite side of the tooth; the
guide will now move the wheel the correct distance for the
cutter to act uniformly. Of course, in every case the guide,
cutter and wheel, must be in correct position to ensure good
work.

4. To obtain a smooth surface on the face of the teeth a
high cutter speed is required, and for this reason it is
advantageous to drive the cutter spindle by a foot wheel.
Making Single Pinions.—There are two ways of making clock pinions;
one is to take a solid piece of steel of the length and diameter needed and
turn away the surplus material to leave the arbor and the pinion head of
suitable dimensions; the other way is to make the head and the arbor of
separate pieces; the head drilled and fixed on the arbor by friction. The
latter plan saves a lot of work, and the cutting of the teeth may be easier.
One method is as good as the other, as the force on the train is very slight
and the pinion head may be driven so tightly on the arbor as to be perfectly
safe without any other fastening, provided the arbor is given a very small
taper, .001 inch in four inches. The steel for the arbor may be chosen of
such a size as to require very little turning, and hardened and tempered to a
full or pale blue before commencing turning it, but the piece intended for
the pinion head must be thoroughly annealed, or it may be found impossible
to cut the teeth without destroying a cutter, which, being valuable, is worth
taking care of.
Pinions for ordinary work are not hardened; as they are left soft by the
manufacturers it would be nonsense for the repairer to put in one hardened
pinion in a clock where all the others were soft. Pinions on fine work are
hardened. Turning is done between centers to insure truth.
Before commencing work on the pinion blanks it is advisable to try the
cutters on brass rod, turned to the exact size, and if the rod is soft enough it
will be found that the cutter will make the spaces before it is hardened,
which is a very important advantage, admitting of correction in the form of
the cutter if required; only two or three teeth need be cut in the brass to
enable one to see if they are suitable, and if found so, or after an alteration
of the cutter, the entire number may be cut round and the brass pinion made
use of for testing its accuracy as to size and shape by laying the wheel along
with it on a flat plate, having studs placed at the proper center distance. By
this means the utmost refinement may be made in the diameter of the brass
pinion, which will then serve as a gauge for the diameter of the steel
pinions, it being recollected, as mentioned in a previous paragraph, that a
slight variation in the diameter of a pinion may be made to counterbalance a
slight deviation from mathematical accuracy in the form of the wheel teeth,

such as is liable to occur owing to the smallness of the teeth making it
impracticable to actually draw the true curves, the only way of getting them
being to draw them to an enlarged scale on paper, and copy them on the
cutter as truly as possible by the eye.
Supposing the cutter has been properly shaped, hardened and completed
and the steel pinion heads all turned to the diameter of the brass gauge, the
cutting may be proceeded with without fear of spoiling, or further loss of
time which might be spent in cutting the long pinion leaves; and even what
is of more importance in work which does not allow of any imperfection,
removing the temptation, which might be strong, to let a pinion go,
knowing it to be less perfect than it should be.
Assuming the pinion teeth to be satisfactorily cut, the next operation
will be hardening and tempering. A good way of doing this is to enclose one
at a time in a piece of gas pipe, filling up the space around the pinion with
something to keep the air off the work and prevent any of the products of
combustion attacking the steel and so injuring the surface. Common soap
alone answers the purpose very well, or it may have powdered charcoal
mixed with it; also the addition of common salt helps to keep the steel clean
and white. The heating should be slow, giving time for the pinion and the
outside of the tube to both acquire the same heat. Over-heating should be
carefully avoided, or there will be scaling of the surfaces, injurious to the
steel, and requiring time and labor to polish off. There is no better way of
hardening than by dipping the pipe with the pinion enclosed in plain cold
water, or if the pinion should drop out of the tube into the water it will do
all the same. To be sure the hardening is satisfactory it will be as well not to
trust to the clean white color likely to result from this treatment, but try both
ends and the center with a file. After all this has been successfully
accomplished the pinions will require tempering, the long arbors
straightening, and the teeth polishing.
The drilled pinion heads, if hardened at all by the method last
mentioned, will, on account of their short lengths, be equally hardened all
over, but if the pinion and arbor should be all in one piece care will be
needed to ensure equal heating all over, or one part may be burnt and
another soft. Also, to guard against bending the long arbors, the packing in
the tube will need to be carefully done, so as to produce equal pressure all
over; otherwise, while the steel is red hot, and consequently soft enough to

bend, even by its own weight, it may get distorted before dropping in the
water. A long thin rod like this almost invariably bends if heated on an open
fire unless equally supported all along; if hardened so, a little tin tray may
be bent up, filled with powdered charcoal, and the pinion bedded evenly in
it. Either this way or with a tube the long arbor may get bent before being
quenched; but if the arbor, though kept straight up to this point, should
happen to be dropped sideways into the water the side cooled first would
contract most. To avoid this, the arbor should be dropped endways, as
vertically as possible.
Tempering the Pinions.—For common cheap work the usual and
quickest way is what is called “blazing off.” That is done either by dipping
each piece singly in thick oil and setting the oil on fire, allowing it to burn
away, or placing a number of pieces in a suitably sized pan, covering with
oil, and burning it. The result is the same either way, the method being
simply a matter of convenience regulated by the number of pieces to be
tempered at one time. As the result of blazing off is to some extent
uncertain, and the pinions apt to be too soft, it will be advisable to adopt the
process of bluing, by which the temper desired may be produced with more
accuracy. The first thing to do will be to clean the surface of the arbor all
along on one side; the pinion head may be left alone. As the pinion head
would get overheated before the arbor had reached the blue color, if the
piece were simply placed on a bluing pan or a lump of hot iron, it will be
necessary to provide a layer of some soft substance to bed the pinion on;
iron, steel or brass filings answer well because the heat is soon uniformly
distributed through the mass, and by judiciously moving the lamp an
equable temper may be got all along, as determined by the color. There is
another and very sure way of getting a uniform temper, in using which there
is no need to polish the arbors. The heat of lead at the point of fusion
happens to be just about the same as that required for the tempering of this
work; so if a ladle full of lead is available each pinion may be buried in it
for a few seconds, holding it down beneath the molten surface with hot
pliers. The temper suitable is indicated by a pale blue, a little softer than for
springs, and a piece of polished steel set floating on the lead will indicate
whether the heat is suitable; if found too great some tin may be added,
which will cause the metal to melt at a lower temperature. Over-heating the
metal must be avoided: it should go no higher than the bare melting point.

Straightening Bent Arbors.—When all care has been taken in the
hardening, the long pieces of wire are still apt to become bent more or less,
and this is especially the case with solid pinions; so before proceeding
further the pieces must be got true, or as nearly so as possible, and it will be
found impracticable to do this by simple bending when the steel is
tempered. If the piece is placed between centers in the lathe and rotated
slowly, the hollow side will be found; this side must be kept uppermost
while the steel is held on a smooth anvil, and the pene, or chisel-shaped,
end of a small hammer applied crossways with gentle blows, stepping
evenly along so that each portion of the steel is struck all along the part
which is hollow; this will stretch the hollow side, and, by careful working,
trying the truth from time to time, the piece can be got as true as may be
wished, and probably keep so during the subsequent turning and finishing,
though it is advisable to keep watch on it, and if it shows any tendency to
spring out of truth again, repeat the striking process, which should always
be done gently and in such a way as to show no hammer marks. Having got
the pieces sufficiently true in this way, each arbor may have a collet of
suitable size driven on to it for permanency, and as the collets will probably
be a little out of truth they may have a finishing cut taken all over them and
receive a final polish.
Polishing.—To polish the steel arbors after turning, a flat metal
polisher, iron or steel, is used; this with emery or oilstone dust and oil
produces a true surface, with a sharp corner at the shoulder; the polisher
will require frequent filing on the flat and the edge to keep it in shape with a
sharp corner, and a grain crossing like the cuts on a file to hold the grinding
material. The polishing of arbors is not done with the object of making them
shine, but to get them smooth and true, so there is no need of using any
finer stuff than emery or oilstone dust.
An old way to polish the leaves was to use a simple metal polisher of a
suitable thickness, placing the pinion on a cork or piece of wood, or even
holding it in the fingers; working away at a tooth at a time until a good
enough polish was obtained; but this method, while being satisfactory as to
results, was also tedious and very slow. It was in some cases assisted by
having guide pinions fitted tight on one or both ends of the arbors to
prevent rounding of the teeth, the polisher resting in the guide and the tooth
to be polished. On the American lathes an accessory is provided called a

“wig wag.” This is a rod fastened at one end to a pulley by a crank pin near
its circumference; the pulley being rotated by a belt from the counter shaft
pulleys causes the rod to move rapidly backwards and forwards. On the
other end of the rod a long narrow piece of lead or tin is fixed, the pinion
being fitted by its centres into a simple frame held in the slide rest so that it
can be rotated tooth by tooth; the lead soon gets cut to the form of the teeth,
and the polishing is quickly effected. Another way is to take soft pine or
basswood, shape it roughly to about the form of space between two teeth
and use it as a file, with emery and oil or oilstone dust. The wood is soon
cut to the exact shape of the teeth, and then makes a quick and perfect job.
The pinion is held in the jaws of the vise and the wooden polisher used as a
file with both hands.
Where there is much polishing to do a simple tool, which a workman
can form for himself, produces a result which is all that can be desired. It
consists of an arbor to work between the lathe centres, or a screw chuck for
wood, with a round block of soft wood, of a good diameter, fixed on it, and
turned true and square across; this will get a spiral groove cut in it by the
corners of the pinion leaves. The pinion is set between centres in a holder in
the slide rest, with the holder set at a slight angle, so that, instead of circular
grooves being cut in the wood a screw will be formed, the angle being
found by trial. On the wood block being rotated and supplied with fine
emery the pinion will be found to rotate, and, being drawn backwards and
forwards by the slide rest, can be polished straight, while the circular action
of the polisher will cause the sides of the pinion leaves to be made quite
smooth and entirely free from ridges.
If it should be desired to face the pinions, like watch pinions, it may be
done in the same way, by cutting hollows so as to leave only a fine ring
round the bottoms of the teeth, and using a hollow polisher with a flat end
held in the fingers while the pinion is rotating. A common cartridge shell
with a hole larger than the arbor drilled in the center of the head makes a
fine polisher for square facing on the ends of pinions, while a stick of soft
wood will readily adapt itself to moulded ends.
The pinion heads being finished and got quite true, the arbors may be
turned true and polished. It is not advisable to turn the arbors small; they
will be better left thick so as to be stiff and solid, as the weight so near the
center is of no importance, the velocity on the small circumference in

starting and stopping being also inappreciable. The thickness of the arbors
when the pinion heads are drilled is determined by the necessity of having
sufficient body inside the bottoms of the teeth; but when solid they may
with advantage be left thicker; however, there is no absolute size. The ends
on which the collets for holding the wheels are to be fixed may be turned to
the same taper as the broach which will be used for opening the collet holes,
while the other ends may be straight.
None of the wheels in a fine clock should be riveted to the pinion heads;
even the center wheel, which goes quite up to the pinion head, is generally
fixed on a collet. The collets are made from brass cut off a round rod, the
outside diameters being just inside the edges of the wheel hubs, and a
shoulder turned to fit accurately into the center hole of each wheel. These
collets should first have their holes broached to fit their arbors, allowing a
little for driving on, as they may be made tight enough in this way without
soldering. Be careful to keep the broach oiled to prevent sticking if you
want a smooth round hole.
The holes in the wheels being made, each collet may be turned to a little
over its final size all over, and then driven on to its place on the pinion, so
that a final turning may be made to ensure exact truth from the arbors’ own
centers. When the collets are thus finished in their places on the arbors, and
the wheels fitted to them, if it is a fine clock, such as a regulator, a hole may
be drilled through each wheel and its collet to take a screw, the holes in the
collet tapped, the holes in the wheels enlarged to allow the screw to pass
freely through, and a countersink made to each, so that the screws, when
finished, may be flush with the wheels. One hole having been thus made
and the wheel fixed with a screw, the other two holes can be made so as to
be true, which would not be so well accomplished if all the holes were
attempted at once. The spacing of the three screws will be accurate enough
if the wheel arms be taken as a guide. If all this has been correctly done, the
wheels will go to their places quite true, both in the round and the flat, and
may be taken off for polishing, and replaced true with certainty, any number
of times.
The polishing of the pivots should be as fine as possible; all should be
well burnished, to harden them and make them as smooth as possible if it is
a common job; if a fine one with hardened arbors the pivots may be ground
and polished as in watch work; if the workman has a pivot polisher and

some thin square edged laps this is a short job and should be done before
cutting off the centers and rounding the ends of the pivots. During all this
work the wheels, as a matter of course, will be removed from the pinions,
and may now be again temporarily screwed on, the polishing of them being
deferred till the last, as otherwise they would be liable to be scratched.
Lantern Pinions.—The lantern pinion is little understood outside of
clock factories and hence it is generally underrated, especially by
watchmakers and those working generally in the finer branches of
mechanics. It will never be displaced in clock work, however, on account of
the following specific advantages:
1. It offers the greatest possible freedom from stoppage
owing to dirt getting into the pinions, as if a piece large
enough to jam and stop a clock with cut pinions, gets into
the lantern pinion, it will either fall through at once or be
pushed through between the rounds of the pinion by the
tooth of the wheel and hence will not interfere with its
operation. It is therefore excellently adapted to run under
adverse circumstances, such as the majority of common
clocks are subjected to.
2. Without giving the reasons it is demonstrable that as
smooth a motion may be got by a lantern pinion as by a solid
radial pinion of twice the number, and that the force required
to overcome the friction of the lantern is therefore much less
than with the other. It follows that such pinions can be used
with advantage in the construction of all cheap and roughly
constructed clocks which are daily turned out in thousands
to sell at a low price.
3. We have before pointed out the enormous advantages
of small savings per movement in clock factories which are
turning out an annual product of millions of clocks, and
without going into details, it is sufficient to refer to the fact
that where eight or ten millions of clocks are to be made
annually the difference in the cost of keeping up the drills
and other tools for lantern pinions over the cost of similar
work on the cutters for solid pinions is sufficient to have a

marked influence upon the cost of the goods. Then the
rapidity with which they can be made and the consequent
smallness of the plant as compared with that which must be
provided for turning out an equal number of cut pinions is
also a factor. There are other features, but the above will be
sufficient to show that it is unlikely that the lantern pinion
will ever be displaced in the majority of common clocks.
From seventy-five to ninety per cent of the clocks now made
have lantern pinions.
The main difference between lantern and cut pinions mechanically is
that as there is no radial flank for the curve of the wheel tooth to press
against in the lantern pinion the driving is all done on or after the line of
centers, except in the smaller numbers, and hence the engaging or butting
friction is entirely eliminated when the pinion is driven, as is always the
case in clock work. Where the pinion is the driver, however, this condition
is reversed and the driving is all before the line of centers, so that it makes a
very bad driver and this is the reason why it is never used as a driving
pinion. This, of course, bars it from use in a large class of machinery.
The actual making of lantern pinions will be found to offer no
difficulties to those who possess a lathe with dividing arrangements, a slide
rest, and a drill holder or pivot polisher to be fixed on it. The pitch circle,
being through the centers of the pins, can be got with great accuracy by
setting the drill point first to the center of the lathe, reading the division on
the graduated head of the slide rest screw, and moving the drill point
outwards to the exact amount of the semi-diameter of the pitch circle. This
presupposes the slide rest screw being cut to a definite standard, as the inch
or the meter, and all measurements of wheels and pinions being worked out
to the same standard, the choice of the standard being immaterial. If the
slide rest screw is not standardized the pitch circle may be traced with a
graver and the drill set to center on the line so traced.
The heads of the pinions may be made either of two separate discs, each
drilled separately, and carefully fitted on the arbor so that the pins may be
exactly parallel with the arbor; or, of one solid piece bored through the
center, turned down deep enough in the middle, and the drill sent right
through the pin holes for both sides at one operation. The former way will
be necessary when the number of pins is small, but the latter is better when

the numbers are large enough to allow of considerable body in the center. In
either case it is advisable to drill only part way through one shroud and to
close the holes in the other with a thin brass washer pressed on the arbor
and turned up to look like part of the shroud after the pins are fitted in the
holes. This makes a much neater way of closing the holes than riveting and
takes but a moment where only one or two pinions are being made.
There is no essential proportion for the thickness of the pins or rounds.
In mathematical investigations these are always taken at first as mere points
of no thickness at all; then the diameters are increased to workable
proportions, and the width of the wheel tooth correspondingly reduced until
there is a freedom or a little shake. If much power has to be transmitted, the
pins, or “staves,” as they are called in large work, have to be strong enough
to stand the strain, but, as the strain in clockwork is very small, the pins
need not be nearly as thick as the breadth of a wheel tooth. In modern
factory practice the custom is to have the diameter of the rounds equal to
the thickness of the leaf of a cut pinion of similar size, the measurement
being taken at the pitch circle of the cut pinion. As we have already given
the proportions observed in good practice on cut pinions they need not be
repeated here. Another practice is to have wheel teeth and spaces equal;
when this is done the spacing of all pinions above six leaf is to have the
rounds occupy three parts and the space five parts.
In some old church clocks, lantern pinions were much used, in many
cases with the pins pivoted and working freely in the ends, or, as they called
them, “shrouds,” but this was a mistake, and they are never made so now. A
simple way for clock repair work is to get some of the tempered steel drill
rod of exactly the thickness desired, hold one end by a split chuck in the
lathe, let the other end run free, and polish with a bit of fine emery paper
clipped round it with the fingers, when the wire will be ready for driving
through the pinion heads, the holes being made small enough to provide for
the rounds being firmly held. The drill may be made of the same wire. The
shrouds may be made either of brass or steel; the latter need not be
hardened, and, when the rounds are all in place and cut off, the ends may be
polished as desired. In the case of a center wheel, where the pinion is close
up to the wheel, and space cannot be spared, the collet on which the wheel
is mounted may form one end of the pinion head.

Fig. 73. Lantern pinion showing pitch circle.

Fig. 74. Generating epicycloid curve for lantern pinion above; compare
with curve for cut pinion of same size pitch circle, page 206.
The Wheel Teeth.—The same principles of calculation belong to these
and solid-cut pinions, the only difference being that the round pins require
wheel teeth of a different shape from those suited to pinion leaves with
radial sides. Both are derived from epicycloidal curves; the curve used for
lantern pinions is derived from a circle of the same size as the pitch circle of
the pinion, while the curve for wheel teeth to drive radial-sided leaves is
derived from a circle of half that diameter, so that the wheel teeth in the
former are more pointed than in the latter. There also is a farther difference;
as was explained in detail when treating of cut pinions, the curve of the
wheel tooth presses upon the radial flank of the leaf inside its pitch circle.
Now there is no radial flank in the lantern and the curve is generated from a
circle of twice the diameter, so that it is twice as long—long enough to
interfere—so it is cut off (rounded) just beyond the useful portion of the
working curve of the wheel tooth.
Pillars and arbors are simple parts, yet much costly machinery is used in
making them. The wire from which they are made is brought to the factories
in large coils, and is straightened and cut into lengths by machines. The
principle on which wire is straightened in a machine is exactly the same as
a slightly curved piece of wire is made straight in the lathe by holding the
side of a turning tool between the revolving wire and the lathe rest, which is
an operation most of our readers must have practiced. The rapid revolution
of the wire against the turning tool causes its highest side to yield, till
finally it presses on the turning tool equally all round, and is consequently
straight. However, in straightening wire by machines the wire is not made
to revolve, but remains stationary while the straightening apparatus
revolves around it. Wire-straightening machines are usually made in the
form of a hollow cylinder, having arms projecting from the inside towards
the center. The cylinder is open at both ends, and the arms are adjustable to
suit the different thicknesses of wire. The wire is passed through the ends of
the cylinder, and comes in contact with the arms inside. A rapid rotary
motion is then given to the cylinder, which straightens the wire in the most
perfect manner, as it is drawn through, without leaving any marks on it
when the machine is properly adjusted. The long spiral lines that are
sometimes seen on the wire work of clocks is caused by this want of

adjustment; and they are produced in the same way as broad circular marks
would be made in soft iron wire if the side of the turning tool was held too
hard against it when straightening it in the lathe.

Fig. 75. A Slide Gauge Lathe.
After the wire has been straightened it is cut off into the required
lengths, and this operation is worthy of notice. If the thick sizes of wire that
are used were to be cut by the aid of a file or a chisel, the ends would not be
square, and some time and material would be lost in the operation of
squaring them; and as economy of material as well as economy of labor is a
feature in American clock manufacture, wire of all sizes is sheared or
broken off into lengths, by being fed through round holes in the shears,
which act the same as when a steady pin is broken when a cock or bridge
gets a sudden blow on the side, or in the same manner as patent cutting
plyers work. The wire is not bent in the operation, and both ends of it are
smooth and flat. The wire for the pillars is then taken to a machine to have
the points made and the shoulders formed for the frames to rest against.
This machine is constructed like a machinist’s bench lathe, with two
headstocks. There is a live spindle running in both heads. In the ends of
these spindles, that point towards the center of the lathe, cutters are
fastened, and the one is shaped so that it will form the end and shoulder of
the pillar that is to be riveted, while the other is shaped so as to form the
shoulder and point that is to be pinned. Between these two revolving cutters
there is an arrangement, worked by a screw in the end of a handle, for

holding the wire from which the pillar is to be made, in a firm and suitable
position. The cutters are then made to act simultaneously on the ends of the
wire by a lever acting on the spindles, and the points and shoulders are in
this way formed in a very rapid manner, all of the same length and diameter.
These machines are in some points automatic. The pieces of wire are
arranged in quantities in a long narrow feed box that inclines towards the
lathe, and the mechanism for holding the wire is so arranged that when its
hold is loosened on the newly made pillar, the pillar drops out into a box
beneath, and a fresh piece of wire drops in and occupies its place.
In many of the factories, some clocks are manufactured having screws
in place of pins to keep the frames together, and the pillars of these clocks
are made in a different manner than that we have just described. The wire
that is used is not cut into short lengths, but a turret lathe with a hollow
spindle is used, through which the wire passes, and is held by a chuck,
when a little more than just the length that is necessary to make the pillar
projects through the chuck. The revolving turret head of the lathe has
cutting tools projecting from it at several points. One tool is adapted to bore
the hole for the screw, and when it is bored the next tool taps the hole to
receive the screw, while another forms the point and shoulder; and after that
end of the pillar is completed another tool attached to the slide of the lathe
forms the other shoulder, prepares that end for riveting, and cuts it off at the
same time. One thousand of these pillars are in this manner made in a day
on each machine. The screws that screw into them are made on automatic
screw machines. The latest improvements in this direction being to first turn
the blanks and then roll the threads on thread rolling machines.

Fig. 76. Slide Gauge Tools and Rack.
The pinion arbors, after they have been cut to length, are centered on
one end by a milling machine having a conical cutter made for the purpose.
The collets for the pinion heads, and the one to fasten the wheel by, are
punched out of sheet brass, and a hole is drilled in their centers a little
smaller than the wire; and to drive them on, in most instances, is all that is
necessary to hold them. At one time it was the practice to drive these collets
by hand. One was placed on the point of the arbor, and the point was then
placed over a piece of steel, with a series of holes in it of such depths that
the collets would be in their proper position on the arbor when the point
was driven to the bottom of the hole, but this method has now been
superseded by automatic machinery, which will be described later. It is
impossible to give an intelligible description of these machines without
drawings. All we can say at present is that they perform their work in a very
rapid and effective manner, and are in use by all the larger clock factories.
The barrels of weight clocks are mostly made from brass castings, and
slight projections are raised on the surface of their arbors by swedging, so
as to prevent the arbors from getting loose in the barrels after repeated
winding of the clock. This swedging and all the other operations in making
arbors used to be done on separate machines; but the largest companies now

use a powerful and comprehensive machine that works automatically, and
straightens any size of wire necessary to be used in a clock, cuts it to the
length, centers it, and also swedges the projections on the barrel arbors, or
any of the other arbors that may be necessary. A roll of wire is placed on a
reel at one end of the machine, first passing through a straightening
apparatus, and afterwards to that portion of the machine where the cutting,
swedging and centering are executed, and the finished arbors drop into a
box placed ready to receive them. The saving effected by the use of this
machine is very great, and in some instances amounts to a thousand per cent
over the method of straightening, cutting, swedging and centering on
different machines, at different operations.
Boring the holes in the arbors of the locking work, to receive the
smaller wires, and the pin holes in the points of the pillars, is done by small
twist-drills, run by small vertical drill presses. The work is held in
adjustable frames under the drill, and when more than one hole has to be
bored this frame is moved backward or forward between horizontal slides to
the desired distance, which is regulated by an adjustable stop, so that every
hole in each piece is exactly in the same position. In arbors where holes
have to be bored at right angles to each other, the arbor is turned round to
the desired position by means of an index. The holes in the locking work
arbors are bored just the size to fit the wire that is to go into them, and these
small wires are easily and rapidly fastened in place by holding them in a
clamp made for the purpose, and riveting them either with a hammer or
with a hammer and punch.

Fig. 77. Automatic Pinion Making Machine of the
Davenport Machine Company.
The Slide Gauge Lathe.—The system of turning with the slide gauge
lathe, formerly adopted for lantern pinions in the clock factories, would
seem to the watchmaker of a peculiarly novel nature. The turning tools are
not held in the hand, in the manner generally practiced, neither are they held
in the ordinary slide rest, but are used by a combination of both methods,
which secures the steadiness of the one plan and the rapidity of the other.
Adjustable knees are fastened to the head and tail stocks of the lathe, Figs.
75 and 76, which answer the purpose of a rest; both the perpendicular and
horizontal parts of these knees being fastened perfectly parallel with the
centers of the lathe. A straight, round piece of iron, of equal thickness, and
having a few inches in the center of a square shape, mortised for the
reception of cutters, is laid on these knees, and answers the purpose of a
handle to hold the cutting tools. Two handles will thus hold eight tools, one
set for brass and one for steel. On every side of the square part of this iron

bar, or what we will now call the turning tool handle, a number of cutting
tools are fastened by set screws, and the method of using them is as follows:
The operator holds the tool handle with both hands on to the knees that are
fastened to the head and tail stocks of the lathe, with the turning tool that is
desired to be used pointing towards the center, and it is allowed to come in
contact with the work running in the lathe in the usual manner practiced in
turning. Fig. 76 is from a photo furnished by Mr. H. E. Smith of the Smith
Novelty Co., Hopewell, N. J., and shows the tools in the rack, which is
wound with leather so that the tools may be rapidly thrown in place without
injury.

Fig. 78. Showing Successive Steps in Turning on
Automatic Pinion Making Machine..

If a plain, straight piece of work is to be turned, the tool is adjusted in
the handle so that the work will be of the proper diameter when the round
parts of the handle come in contact with the perpendicular part of the knees
or rest; and while the handle is thus held and moved gently along in the
corners of the knees, with the tool sliding on the T-rest, the work is easily
turned perfectly parallel, smooth and true. Sometimes a roughing cut is
taken by holding the bar loosely and then a finishing cut is made with the
same tool by holding it firmly in place. In turning a pinion arbor, for
instance, the wire having been previously straightened and cut to length and
centered, and the brass collets to make the pinion and to fasten the wheel
having been driven on, one end is held in the lathe by a spring chuck
fastened to the spindle of the lathe, while the other end works in a center in
the other head. One turning tool is shaped and adjusted in the handle for the
purpose of turning the brass collets for the pinion to the proper diameter,
another turns the sides of the brass work, while others are adapted for the
arbors, pivots, and so on, pins being placed in holes in the T-rest to act as
stops for the tools. After the brass work has been turned, the positions of the
shoulders of the pivots are marked with a steel gauge, and by simply
turning round the handle of the turning tool till the proper shaped point
presents itself, each operation is accomplished rapidly, and the cutting is so
smooth that even for the pivots all that is necessary to finish them is simply
to bring them in contact with a small burnisher. The article is not taken from
the lathe during the whole process of turning, and when completed the
centers are broken off, having been previously marked pretty deep at the
proper place with a cutting point. Five hundred to 1,200 arbors per day, per
man, is the usual output. All the pinions, arbors, and barrels—in fact every
part of an American clock movement that requires turning—were formerly
done in this manner, at long rows of lathes in rooms, and by workmen set
apart for the purpose. But perhaps it may be well to mention that in the
machine shops of these factories, where they make the tools, the ordinary
methods of turning with the common hand tool, and by the aid of ordinary
and special slide rests, are practiced the same as it is among other
machinists. In the large factories automatic turret machines are now coming
into use and these are shown in Figs. 77, 78 and 79.

Fig. 79. Automatic Pinion Drill of the
Davenport Machine Company.
The lantern pinions of an American clock have long been a mystery to
those unacquainted with the method of their manufacture, and the usual
accuracy in the position of the small wires or “rounds,” combined with
great cheapness, has often been a subject of remark. The holes for the wires
in these pinions are drilled in a machine constructed as follows: An iron bed
with two heads on it, Fig. 80, one of which is so constructed that by pulling
a lever the spindle has a motion lengthwise as well as the usual circular
motion, and on the point of this spindle, which is driven at 22,000
revolutions, the drill is fastened that is to bore the holes in the pinions; the
other head has an arbor passing through it with an index plate attached,

having holes in the plate, and an index finger attached to a strong spring
going into the holes, the same as in a wheel cutting engine; on this head,
and on the end of it that faces the drill, there is a frame fastened in which
the pinion that is to be bored is placed between centers, and is carried round
with the arbor of the index plate, in the same manner as a piece of work is
carried round in an ordinary lathe by means of a dog, or carrier; only in the
pinion drilling machine the carrier is so constructed that there is no shake in
any way between the pinion and the index arbor. This head is carried on a
slide having a motion at right angles to the spindle of the other head, by
which means the pitch diameter of the proposed pinion is adjusted. The
head is moved in the slide by an accurately cut screw, to which a
micrometer is attached that enables the workman to make an alteration in
the diameter of a pinion as small as the one-thousandth part of an inch. The
drill that bores the holes is the ordinary flat-pointed drill, and has a shoulder
on its stem that stops the progress of the drill when it has gone through the
first part of the pinion head and nearly through the other. All operators
make their own drills and the limits of error are for pitch diameter .0005
inch; error of size of drills .0001. The reader can see that these men must
know something of drill making.

Fig. 80. Pinion Drilling Machine.
The action of the machine is simple. The pinion, after it has been turned,
pivoted and dogged, is placed in its position in the machine, and by pulling
a lever, the drill, which is running at a speed of about 22,000 revolutions a
minute, comes in contact with the brass heads of the pinion and bores the
one through and the other nearly through. The lever is then let go, and a
spring pulls the drill back; the index is turned round a hole, and another
hole bored in the pinion, and so on till all the holes are bored. An ordinary
expert workman, with a good machine, will bore about fourteen hundred of
medium-sized pinions in a day. The wires or “rounds” are cut from drill rod
and are put into the holes by hand by girls who become very expert at it.
This is called “filling.” We have already stated that the holes are only bored
partly through one of the pieces of the brass, and after the wire has been put
in, the holes are riveted over, and in this manner the wires are fastened so
that they cannot come out. Some factories close the holes by a thin brass
washer forced on the arbor, instead of riveting.

Figs. 77, 78 and 79 show the automatic pinion turning machine and its
processes in successive operations. These machines are used by most of the
large clock manufacturers of the United States and some of the European
concerns also. They are entirely automatic, will make 1,500 pinions per day,
as an average, and one man can run four machines.
Fig. 79 shows an automatic pinion drilling machine, which takes up the
work where it is left by the machine shown in Fig. 77. This machine will
drill 4,000 to 5,000 pinions per day according to the size hole and the
number of holes. The operator places the pinions in the special chain shown
in the front of the machine, from which the transport arms carry them to the
spindle, where they are drilled and when completed drop out. One operator
can feed three of these machines.
Making Solid Pinions.—The solid steel pinions are not hardened, but
are made of Bessemer steel, which could only be case hardened—a thing
hardly ever done. The process of making these pinions is as follows: Rods
of Bessemer steel are cut into suitable lengths. The pieces obtained are
pointed or centered on both ends. The stock not needed for the pinion head
is cut away, leaving the arbors slightly tapering, for the purpose of fastening
them by this means in a hole on the cutting machine. On the end of the
arbor of the index plate are two deep cuts across its center, and at right
angles to each other. These cuts are of the same shape that would be made
by a knife edged file. The effect of these cuts is to produce a taper hole in
the end of the arbor, with four sharp corners. Into this hole the end of the
arbor of the pinion or ratchet that is to be cut is placed, and a spring center
presses on the other end, and the sharp corners in the hole hold the work
firm enough to prevent it from turning round when the teeth are being cut.
The marks that are to be seen on the shoulder of the back pivot of the arbor
that carries the minute hand of a Yankee clock is an illustration of this
method of holding the pinion when the leaves are being cut, and no
injurious effects arise from it. The convenience the plan affords for
fastening work in the engine enables twenty-five hundred of these pinions
to be cut in a day, one at a time. The pinion head is cut subject to the proper
dividing plate by a splitting circular saw, and by a milling tool (running in
oil) for forming the shape of the leaves, both of which tools are generally
carried on the same arbor, both being shifted into their proper places by an
adjusting attachment. Pinion leaves of the better class are generally shaped

by two succeeding milling cutters, the second one of which does the
finishing, obviating any other smoothing. For very cheap work the arbors
receive no further finish. The shaping of the pivots, done by an automatic
lathe, finishes the job.
Figure 81 shows an automatic pinion cutting machine which has
extensive use in clock factories for cutting pinions up to one-half inch
diameter and also the smaller wheels. For wheels the work is handled in
stacks suited to the traverse of the machine, the work being treated as if the
stacks were long brass pinions.

Fig. 81. Automatic Wheel and Pinion Cutters.
Wheels are cut in two ways, on automatic wheel cutters as just
described and on engines containing parallel spindles for the cutters, carried
in a yoke which rises and falls, so that it clears the work while the carriage
is returning to the starting point on each trip and engages it on the outward
trip. The cutters are about three inches in diameter and rapidly driven; the
first is a saw, the second a roughing cutter, and the third a finishing cutter.
The carriage is driven by a rack and pinion operated by a crank in the hands

of the workman and streams of soda water are used on the cutters and work
to carry away the heat, as brass expands rapidly under heat, and if the stack
were cut dry the cut would get deeper as the cutting proceeded, owing to the
expansion of the brass, and hence the finished wheel would not be round
when cold, if many teeth were being cut. The stacks of wheels are about
four inches in length and the slide thus travels about twenty inches in order
to clear the three arbors and engage with the shifter for the index. The last
wheel of the stack has a very large burr formed by the cutters as they leave
the brass and this wheel is removed from the stack when the arbor is taken
out and placed aside to have the burrs removed by rubbing on emery paper.

Fig. 82. Wheel Cutting Engine.
This is one of the few instances in which automatic machinery has been
unable to displace hand labor, as the work is done so quickly that the time
of the attendant would be nearly all taken up in placing and removing the
stacks, and so the feeding is done by him as well. About 35,000 wheels per
day can be thus cut by one man, with girls to stack the blanks on the arbors,
and an automatic feed would not release the man from attendance on the
machine, so that the majority of clock wheels are cut to-day as they were

forty years ago. Still, some of the factories are adding an automatic feed to
the carriage in the belief that the increased evenness of feed will give a
more accurately cut wheel, a proposition which the men most vigorously
deny. Such a machine, they say, to be truly automatic, must take its stacks
of wheels from a magazine and discharge the work when done, so that one
attendant could look after a number of machines. This would result in
economy, as well as accuracy, but has not been done owing to the great
variations in sizes of wheels and numbers of teeth required in clock work.
Figure 82 shows one of these machines, a photograph of which was
taken especially for us by the courtesy of the Seth Thomas Clock Company
at their factory in Thomaston, Conn.
About every ten years some factory decides to try stamping out the teeth
of wheels at the same time they are being blanked; this can, of course, be
done by simply using a more expensive punch and die, and at first it looks
very attractive; but it is soon found that the cost of keeping up such
expensive dies makes the wheels cost more than if regularly cut and for
reasons of economy the return is made to the older and better looking cut
wheels.
After an acid dip to remove the scale on the sheet brass, followed by a
dip in lacquer, to prevent further tarnish, the wheels are riveted on the
pinions in a specially constructed jig which keeps them central during the
riveting and when finished the truth of every wheel and its pinions and
pivots are all tested before they are put into the clocks. The total waste on
all processes in making wheels and pinions is from two to five per cent, so
that it will readily be seen that accuracy is demanded by the inspectors.
European writers have often found fault with nearly everything else about
the Yankee clock, but they all unite in agreeing that the cutting and
centering of wheels, pinions and pivots (and the depthing) are perfect, while
the clocks of Germany, France, Switzerland and England (particularly
France) leave much to be desired in this respect; and much of the reputation
of the Yankee clock in Europe comes from the fact that it will run under
conditions which would stop those of European make.
We give herewith a table of clock trains as usually manufactured, from
which lost wheels and pinions may be easily identified by counting the
teeth of wheels and pinions which remain in the movement and referring to

the table. It will also assist in getting the lengths of missing pendulums by
counting the trains and referring to the corresponding length of pendulums.
Thus, with 84 teeth in the center wheel, 70 in the third, 30 in the escape and
7-leaf pinions, the clock is 120 beat and requires a pendulum 9.78 inches
from the bottom of suspension to the center of the bob.
To Calculate Clock Trains.—Britten gives the following rule: Divide
the number of pendulum vibrations per hour by twice the number of escape
wheel teeth; the quotient will be the number of turns of escape wheel per
hour. Multiply this quotient by the number of escape pinion teeth, and
divide the product by the number of third wheel. This quotient will be the
number of times the teeth of third wheel pinion must be contained in center
wheel.
Clock Trains and Lengths of Pendulums.

Vibrations Length of
Escape
Wheels Pinions of Pendulum Pendulum
wheel
—Min. in Inches
120 90 75 10 10 9 Double *30 156.56
3 legged
120 90 90 10 9 9 Do. *40 88.07
128 120 16 30 60 39.14
112 105 14 30 60 39.14
96 90 12 30 60 39.14
80 75 10 30 60 39.14
64 60 8 30 60 39.14
68 64 8 30 68 30.49
70 64 8 30 70 28.75
72 64 8 30 72 27.17
75 60 8 32 75 25.05
72 65 8 32 78 23.15
75 64 8 32 80 22.01
84 64 8 30 84 19.97
86 64 8 30 86 19.06
88 64 8 30 88 18.19

Vibrations Length of
Escape
Wheels Pinions of Pendulum Pendulum
wheel
—Min. in Inches
84 78 7 20 89.1 17.72
80 72 8 30 90 17.39
84 78 7 21 93.6 16.08
94 64 8 30 94 15.94
84 78 8 28 95.5 15.45
108 100 12 & 10 32 96 15.28
84 84 9 & 8 30 98 14.66
84 78 7 22 98 14.66
84 78 8 29 98.9 14.41
80 80 8 30 100 14.09
85 72 8 32 102 13.54
84 78 8 30 102.4 13.44
84 78 7 23 102.5 13.4
105 100 10 30 105 12.78
84 78 8 31 105.8 12.59
84 78 7 24 107 12.3
96 72 8 30 108 12.08
84 78 8 32 109.2 11.82
88 80 8 30 110 11.64
84 77 7 25 110 11.64
84 78 7 25 111.4 11.35
84 80 8 32 112 11.22
84 78 8 33 112.6 11.11
96 76 8 30 114 10.82
115 100 10 30 115 10.65
84 78 7 26 115.9 10.49
96 80 8 30 120 9.78
84 70 7 30 120 9.78
84 78 7 27 120.3 9.73
90 84 8 31 122 9.46

Vibrations Length of
Escape
Wheels Pinions of Pendulum Pendulum
wheel
—Min. in Inches
84 78 7 28 124.8 9.02
100 80 8 30 125 9.01
90 84 8 32 126 8.87
100 96 10 40 128 8.59
84 78 7 29 129.3 8.42
100 78 8 32 130 8.34
84 77 7 30 132 8.08
84 78 7 30 133.7 7.9
90 90 8 32 135 7.73
84 78 7 31 138.2 7.38
84 80 8 40 140 7.18
120 71 8 32 142 6.99
84 78 7 32 142.6 6.93
100 87 8 32 145 6.69
84 78 7 33 147.1 6.5
100 96 8 30 150 6.26
84 78 7 34 151.6 6.1
96 95 8 32 152 6.09
84 77 7 35 154 5.94
104 96 8 30 156 5.78
84 78 7 35 156 5.78
120 96 9&8 30 160 5.5
84 78 7 36 160.5 5.47
84 78 7 37 164.9 5.15
132 100 9&8 27 165 5.17
84 78 7 38 169.4 4.88
128 102 8 25 170 4.87
84 78 7 39 173.8 4.65
36 36 35 6 25 175 4.6
84 77 7 40 176 4.55

Vibrations Length of
Escape
Wheels Pinions of Pendulum Pendulum
wheel
—Min. in Inches
84 78 7 40 178.3 4.43
45 36 36 6 20 180 4.35
47 36 36 6 20 188 3.99

*These are good examples of turret clock trains; the
great wheel (120 teeth) makes in both instances a rotation in
three hours. From this wheel the hands are to be driven. This
may be done by means of a pinion of 40 gearing with the
great wheel, or a pair of bevel wheels bearing the same
proportion to each other (three to one) may be used, the
larger one being fixed to the great wheel arbor. The
arrangement would in each case depend upon the number
and position of the dials. The double three-legged gravity
escape wheel moves through 60° at each beat, and therefore
to apply the rule given for calculating clock trains it must be
treated as an escape wheel of three teeth.
Take a pendulum vibrating 5,400 times an hour, escape wheel of 30,
pinions of 8, and third wheel of 72. Then 5,400 ÷ 60 = 90. And
90 × 8 ÷ 72 = 10. That is, the center wheel must have ten times as many
teeth as the third wheel pinion, or ten times 8 = 80.
The center pinion and great wheel need not be considered in connection
with the rest of the train, but only in relation to the fall of the weight, or
turns of mainspring, as the case may be. Divide the fall of the weight (or
twice the fall, if double cord and pulley are used) by the circumference of
the barrel (taken at the center of the cord); the quotient will be the number
of turns the barrel must make. Take this number as a divisor, and the
number of turns made by the center wheel during the period from winding
to winding as the dividend; the quotient will be the number of times the
center pinion must be contained in the great wheel. Or if the numbers of the
great wheel and center pinion and the fall of the weight are fixed, to find the
circumference of the barrel, divide the number of turns of the center wheel

by the proportion between the center pinion and the great wheel; take the
quotient obtained as a divisor, and the fall of the weight as a dividend (or
twice the fall if the pulley is used), and the quotient will be the
circumference of the barrel. To take an ordinary regulator or 8-day clock as
an example—192 (number of turns of center pinion in 8 days) ÷ 12
(proportion between center pinion and barrel wheel) = 16 (number of turns
of barrel). Then if the fall of the cord = 40 inches, 40 × 2 ÷ 16 = 5, which
would be circumference of barrel at the center of the cord.
If the numbers of the wheels are given, the vibrations per hour of the
pendulum may be obtained by dividing the product of the wheel teeth
multiplied together by the product of the pinions multiplied together, and
dividing the quotient by twice the number of escape wheel teeth.
The numbers generally used by clock makers for clocks with less than
half-second pendulum are center wheel 84, gearing with a pinion of 7; third
wheel 78, gearing with a pinion of 7.
The product obtained by multiplying together the center and third
wheels = 84 × 78 = 6,552. The two pinions multiplied together = 7 × 7 = 49.
Then 6,552 ÷ 49 = 133.7. So that for every turn of the center wheel the
escape pinion turns 133.7 times. Or 133.7 ÷ 60 = 2.229, which is the
number of turns in a minute of the escape pinion.
The length of the pendulum, and therefore the number of escape wheel
teeth, in clocks of this class is generally decided with reference to the room
to be had in the clock case, with this restriction, the escape wheel should
not have less than 20 nor more than 40 teeth, or the performance will not be
satisfactory. The length of the pendulum for all escape wheels within this
limit is given in the preceding table. The length there stated is of course the
theoretical length, and the ready rule adopted by clockmakers is to measure
from the center arbor to the bottom of the inside of the case, in order to
ascertain the greatest length of pendulum which can be used. For instance,
if from the center arbor to the bottom of the case is 10 inches, they would
decide to use a 10-inch pendulum, and cut the escape wheel accordingly
with the number of teeth required as shown in the table. But they would
make the pendulum rod of such a length as just to clear the bottom of the
case when the pendulum was fixed in the clock.

In the clocks just referred to the barrel or first wheel has 96 teeth, and
gears with a pinion of eight.
Month clocks have an intermediate wheel and pinion between the great
and center wheels. This extra wheel and pinion must have a proportion to
each other of 4 to 1 to enable the 8-day clock to go 32 days from winding to
winding. The weight will have to be four times as heavy, plus the extra
friction, or if the same weight is used there must be a proportionately longer
fall.
Six-months clock have two extra wheels and pinions between the great
and center wheels, one pair having a proportion of 4½ to 1 and the other of
6 to 1. But there is an enormous amount of extra friction generated in these
clocks, and they are not to be recommended.
The pivot holes and all the other holes in the frames, are punched at one
operation after the frames have been blanked and flattened. They are placed
in the press, and a large die having punches in it of the proper size and in
the right position for the holes, comes down on the frame and makes the
holes with great rapidity and accuracy. These holes are finished afterwards
by a broach. In some kinds of clocks, where some of the pivot holes are
very small, the small holes are simply marked with a sharp point in the die,
and afterwards drilled by small vertical drills. These machines are very
convenient for boring a number of holes rapidly. The drill is rotated with
great speed, and a jig or plate on which the work rests is moved upwards
towards the drill by a movement of the operator’s foot. All the boring,
countersinking, etc., in American clocks, is done through the agency of
these drills. Bending the small wires for the locking work, the pendulum
ball, etc., is rapidly effected by forming. As no objectionable marks have
been made on the surface of either the thick or smaller wires during any
process of construction, all that is necessary to finish the iron work is
simply to clean it well, which is done in a very effective manner by placing
a quantity of work in a revolving tumbling box, which is simply a barrel
containing a quantity of sawdust.
Milling the winding squares on barrel arbors is an ingenious operation.
The machine for milling squares and similar work is made on the principle
of a wheel cutting engine. The work is held in a frame, attached to which is
a small index plate, like that of a cutting engine. In the machine two large

mills or cutters, with teeth in them like a file, are running, and the part to be
squared is moved in between the revolving cutters, which operation
immediately forms two sides of the square. The work is then drawn back,
and the index turned round, and in a like manner the other two sides of the
square are formed. The cutting sides of the mills are a little bevelled, so that
they will produce a slight taper on the squares.
Winding keys have shown great improvements. Some manufacturers
originally used cast iron ones, but the squares were never good in them, and
brass ones were adopted. At first the squares were made by first drilling a
hole and driving a square punch in with a hammer; and to make the squares
in eighteen hundred keys by this method was considered a good day’s work.
Restless Yankee ingenuity, however, has contrived a device by which
twenty or twenty-five thousand squares can be made in a day, while at the
same time they are better and straighter squares than those by the old
method; but we are not at liberty to describe the process at present, but only
to state that it is done by what machinists call drilling a square hole.
Pendulum rods are made from soft iron wire, and the springs on the
ends rolled out by rollers. Two operations are necessary. The first roughs
the spring out on rollers of eccentric shape, and the spring is afterwards
finished on plain smooth rollers. The pendulum balls in the best clocks are
made of lead, on account of its weight, and cast in an iron mold in the same
manner as lead bullets, at the rate of about eighteen hundred a day. A
movable mandrel is placed in the mold to produce the hole that is in the
center of the ball. The balls are afterwards covered with a shell of brass,
polished with a bloodstone burnisher. The various cocks used in these
clocks are all struck up from sheet brass, and the pins in the wheels in the
striking part are all swedged into their shape from plain wire. The hands are
die struck out of sheet steel, and afterwards polished on emery belts, and
blued in a furnace.
All the little pieces of these clocks are riveted together by hand, and the
different parts of the movement, when complete, are put together by
workmen continually employed in that department. Although the greatest
vigilance is used in constructing the different parts to see that they are
perfect, when they come to be put together they are subjected to another
examination, and after the movements are put in the case the clocks are put
to the test by actual trial before they are packed ready for the market. As a

general rule, all the different operations are done by workmen employed
only at one particular branch; and in the largest factories from thirty to fifty
thousand clocks of all classes may be seen in the various stages of
construction.
Such is a description of the main points in which the manufacture of
American clock movements differs from those manufactured by other
systems. All admit that these clocks perform the duties for which they are
designed in an admirable manner, while they require but little care to
manage, and when out of order but little skill is necessary to repair them. Of
late years there has been a growing demand for ornamental mantel-piece
clocks in metallic cases of superior quality, and large numbers of these
cases of both bronze and gold finish are being manufactured, which, for
beauty of design and fine execution, in many instances rival those of French
production. The shapes of the ordinary American movements were,
however, unsuitable for some patterns of the highest class of cases, and the
full plate, round movements of the same size as the French, but with
improvements in them that in some respects render them more simple than
the French, are now manufactured. Exactly the same system is employed in
the manufacture of the different parts of these clocks that is practiced in
making the ordinary American movements.

CHAPTER XV.
SPRINGS, WEIGHTS AND POWER.

We see by the preceding calculations that there is one definite point in
the time train of a clock; the center arbor, which carries the minute hand,
must revolve once in one hour; from this point we may vary the train both
ways, toward the escape wheel to suit the length of pendulum which we
desire to use, and toward the barrel to suit the length of time we want the
clock to run. The center arbor is therefore generally used as the point at
which to begin calculations, and it is also for this reason that the number of
teeth in the center wheel is the starting point in train calculations toward the
escape wheel, while the center pinion is the starting point in calculations of
the length of time the weight or spring is to drive the clock. Most writers on
horology ignore this point, because it seems self-evident, but its omission
has been the cause of much mystification to so many students that it is
better to state it in plain terms, so that even temporary confusion may be
avoided.
Sometimes there is a second fixed point in a time train; this occurs only
when there is a seconds hand to be provided for; when this is the case the
seconds hand must revolve once every minute. If it is a seconds pendulum
the hand is generally carried on the escape wheel and the relation of
revolutions between the hour and seconds wheels must then be as one is to
sixty. This might be accomplished with a single wheel having sixty times as
many teeth as the pinion on the seconds arbor; but the wheel would take up
so much room, on account of its large circumference, that the movement
would become unwieldy because there would be no room left for the other
wheels; so it is cheaper to make more wheels and pinions and thereby get a
smaller clock. Now the best practical method of dividing this motion is by
giving the wheels and pinions a relative velocity of seven and a half and
eight, because 7.5 × 8 = 60.
Thus if the center wheel has 80 teeth, gearing into a pinion of 10, the
pinion will be driven eight times for each revolution of the center wheel,
while the third wheel, with 75 teeth, will drive its pinion of 10 leaves 7.5

times, so that this arbor will go 7.5 times eight, or 60 times as fast as the
center wheel.
If the clock has no seconds hand this second fixed point is not present in
the calculations and other considerations may then govern. These are
generally the securing of an even motion, with teeth of wheels and pinions
properly meshing into each other, without incurring undue expense in
manufacture by making too many teeth in the pinions and consequently in
the wheels. For these reasons pinions of less than seven or more than ten
leaves are rarely used in the common clocks, although regulators and fine
clocks, where the depthing is important, frequently have 12, 14 or 16 leaves
in the pinions, as is also the case with tower clocks, where the increased
size of the movement is not as important as a smoothly running train.
Clocks without pendulums, carriage clocks, locomotive levers and nickel
alarms, also have different trains, many of which have the six leaf pinion,
with its attendant evils, in their trains.
Weights.--Weights have the great advantage of driving a train with
uniform power, which a spring does not accomplish: They are therefore
always used where exactness of time is of more importance than
compactness or portability of the clock. In making calculations for a weight
movement, the first consideration is that as the coils of the cord must be
side by side upon the barrel and each takes up a definite amount of space, a
thicker movement (with longer arbors) will be necessary, as the barrel must
give a sufficient number of turns of the cord to run the clock the desired
time and the length of the barrel, with the wheel and maintaining power all
mounted upon the one arbor, will determine the thickness of the movement.
If the clock is to have striking trains their barrels will generally be of more
turns and consequently longer than the time barrel and in that case the
distance between the plates is governed by the length of the longest barrel
and its mechanism.
The center wheel, upon the arbor of which sits the canon pinion with the
minute hand, must, since the hand has to accomplish its revolution in one
hour, also revolve once in an hour. When, therefore, the pinion of the center
arbor has 8 leaves and the barrel wheel 144, then the 8 pinion leaves, which
makes one revolution per hour, would require the advancing of 8 teeth of
the barrel wheel, which is equal to the eighteenth part of its circumference.
But when the eighteenth part in its advancing consumes 1 hour, then the

entire barrel wheel will consume 18 hours to accomplish one revolution. If,
now, 10 coils of the weight cord were laid around the barrel, the clock
would then run 10 × 18 = 180 hours, or 7½ days, before it is run down.
Referring to what was said in a previous chapter on wheels being
merely compound levers, it will be seen that as we gain motion we lose
power in the same ratio. We shall also see that by working the rule
backwards we may arrive at the amount of force exerted on the pendulum
by the pallets. If we multiply the circumference of the escape wheel in
inches by the number of its revolutions in one hour we will get the number
of inches of motion the escape wheel has in one hour. Now if we multiply
the weight by the distance the barrel wheel travels in one hour and divide
by the first number we shall have the force exerted on the escape wheel. It
will be simpler to turn the weight into grains before starting, as the division
is less cumbersome.
Another way is to find how many times the escape wheel revolves to
one turn of the barrel and divide the weight by that number, which will give
the proportion of weight at the escape wheel, or rather would do so if there
were no power lost by friction. It is usual to estimate that three-quarters of
the power is used up in frictions of teeth and pivots, so that the amount
actually used for propulsion of the pendulum is very small, being merely
sufficient to overcome the bending moment of the suspension spring and
the resistance of the air.
It is for this reason that clocks with finely cut trains and jeweled pivots,
thus having little train friction, will run with very small weights. The writer
knows of a Howard regulator with jeweled pivots and pallets running a 14-
pound pendulum with a five-ounce driving weight. Of course this is an
extreme instance and was the result of an experiment by an expert
watchmaker who wanted to see what he could do in this direction.
Usually the method adopted to determine the amount of weight that is
necessary for a movement is to hang a small tin pail on the weight cord and
fill it with shot sufficient to barely make the clock keep time. When this
point has been determined, then weigh the pail of shot and make your
driving weight from eight to sixteen ounces heavier. In doing this be sure
the clock is in beat and that it is the lack of power which stops the clock; the
latter point can be readily determined by adding or taking out shot from the

pail until the amount of weight is determined. The extra weight is then
added as a reserve power, to counteract the increase of friction produced by
the thickening of the oil.
Many clock barrels have spiral grooves turned in them to assist in
keeping the coils from riding on each other, as where such riding occurs the
riding coils are farther from the center of the barrel than the others, which
gives them a longer leverage and greater power while they are unwinding,
so that the power thus becomes irregular and affects the rate of the clock,
slowing it if the escapement is dead beat and making it go faster if it is a
recoil escapement.
Clock cords should be attached to the barrel at the end which is the
farthest from the pendulum, so that as they unwind the weight is carried
away from the pendulum. This is done to avoid sympathetic vibrations of
the weight as it passes the pendulum, which interfere with the timekeeping
when they occur. If the weight cannot be brought far enough away to avoid
vibrations a sheet of glass may be drilled at its four corners and fixed with
screws to posts placed in the back of the case at the point where vibration
occurs, so that the glass is between the pendulum rod and the weight, but
does not interfere with either. This looks well and cures the trouble.
We have, heretofore, been speaking of weights which hang directly
from the barrel, as was the case with the older clocks with long cases, so
that the weight had plenty of room to fall. Where the cases are too short to
allow of this method, recourse is had to hanging the weight on a pulley and
fastening one end of the cord to the seat board. This involves doubling the
amount of weight and also taking care that the end of the cord is fastened
far enough from the slot through which it unwinds so that the cords will not
twist, as they are likely to do if they are near together and the cord has been
twisted too much while putting it on the barrel. Twisting weight cords are a
frequent source of trouble when new cords have been put on a clock. The
pulley is another source of trouble, especially if wire cords (picture cords)
or cables are used. Wire cable should not be bent in a circle smaller than
forty times its diameter if flexibility is to be maintained, hence pulleys
which were all right for gut or silk frequently prove too small when wire is
substituted and kinks, twisted and broken cables frequently result from this
cause. This is especially the case with the heavy weight of striking trains of
hall and chiming clocks, where double pulleys are used, and also leads to

trouble by jamming and cutting the cables and dropping of the weights in
tower clocks where a new cable of larger size is used to replace an old one
which has become unsafe from rust, or cut by the sheaves.
Weight cords on the striking side of a clock should always be left long
enough so that they will not run down and stop before the time train has
stopped. This is particularly the case with the old English hall clocks, as
many of them will drop or push their gathering racks free of the gathering
pinion under such conditions and then when the clock is wound it will go
on striking continuously until the dial is taken off and the rack replaced in
mesh with the gathering pinion. As clocks are usually wound at night, the
watchmaker can see the disturbance that would be caused in a house in the
“wee sma’ hours” by such a clock going on a rampage and striking
continuously.
Oiling Cables.--Clock cables, if of wire and small in size, should be
oiled by dipping in vaseline thinned with benzine of good quality. Both
benzine and vaseline must be free from acid, as if the latter is present it will
attack the cable. This thinning will permit the vaseline to permeate the
entire cable and when the benzine evaporates it will leave a thin film of
vaseline over every wire, thus preventing rust. Tower clock cables should
be oiled with a good mineral oil, well soaked into them to prevent rusting.
Gut clock cords, when dry and hard, are best treated with clock oil, but
olive oil or sperm oil will also be found good to soften and preserve them.
New cords should always be oiled until they are soft and flexible. If the
weight is under ten pounds silk cords are preferable to gut or wire as they
are very soft and flexible.
In putting on a new cable or weight cord the course of the weight and
cord should be closely watched at all points, to see that they remain free and
do not chafe or bind anywhere and also that the coils run evenly and freely,
side by side; sometimes, especially with wire, a new cable gets kinked by
riding the first time of winding and is then very difficult to cure of this
serious fault. Another point to watch is to see that the position of the cord
when wound up will not cause an end thrust upon the barrel, which will
interfere with the timekeeping if it is overwound, so that the weight is
jammed against the seatboard; this frequently happens with careless
winding, if there is no stop work.

To determine the lengths of clock cords or weights, we may have to
approach the question from either end. If the clock be brought in without
the cords, we first count the number of turns we can get on the barrel. This
may be done by measuring the length of the barrel and dividing it by the
thickness of the cord, if the barrel is smooth, or by counting the grooves if it
be a grooved barrel. Next we caliper the diameter and add the thickness of
one cord, which gives us the diameter of the barrel to the center of the
cords, which is the real or working diameter. Multiply the distance so found
by 3.14156, which gives the circumference of the barrel, or the length of
cord for one turn of the barrel. Multiply the length of one turn by the
number of turns and we have the length of cord on the barrel, when it is
fully wound. If the cord is to be attached to the weight, measure the
distance from the center of barrel to the bottom of the seat board and leave
enough for tying. If the weight is on a pulley it will generally require about
twelve inches to reach from the barrel through the slot of the seat board,
through the pulley to the point of fastening.
To get the fall of the weight, stand it on the bottom of the case and
measure the distance from the top of the point of attachment to the bottom
of the seat board. This will generally allow the weight to fall within two
inches of the bottom and thus keep the cable tight when the clock runs
down; thus avoiding kinks and over-riding when we wind again after
allowing the clock to run down. If the weight has a pulley and double cord,
measure from the top of the pulley to the seatboard, with the weight on the
bottom, and then double this measurement for the length of the cord. This
measure is multiplied by as many times as there are pulleys in the case of
additional sheaves. Striking trains are frequently run with two coils or
layers of cord, on the barrel, time trains never have but one.
Now, having the greatest available length of cord determined according
either of the above conditions, we can determine the number of turns for
which we have room on our barrel and divide the length of cord by the
number of turns. This will give us the length of one turn of the cord on our
barrel and thus having found the circumference it is easy to find the
diameter which we must give our barrel in suiting a movement to given
dimensions of the case. This is frequently done where the factory may want
a movement to fit a particular style and size of case which has proved

popular, or when a watchmaker desires to make a movement for which he
has, or will buy, a case already made.
As to tower clock cables, getting the length of cable on the barrel is, of
course, the same as given above, but the rest of it is an individual problem
in every case, as cables are led so differently and the length of fall varies so
that only the professional tower clock men are fitted to make the
measurements for new work and they require no instruction from me. It
might be well to add, however, that in the tower clocks by far the greater
part of the cable is always outside the clock and only the inner end coils and
uncoils about the barrel. It is for this reason that the outer ends of the cables
are so generally neglected by watchmakers in charge of tower clocks and
allowed to cut and rust until they drop their weights. Caretakers of tower
clocks should remember that the inner ends of cables are always the best
ends; the parts that need watching are those in the sheaves or leading to the
sheaves. Tower clocks should have the cables marked where to stop to
prevent overwinding.
In chain drives for the weights of cuckoo and other clocks with exposed
weights, we have generally a steel sprocket wheel with convex guiding
surfaces each side of the sprocket and projecting flanges each side of the
guides; one of these flanges is generally the ratchet wheel. The ratchet
wheel, guide, sprocket, guide and flange, form a built-up wheel which is
loose on the arbor and is pinned close to the great wheel, which is driven by
a click on the wheel working into the ratchet of the drive. It must be loose
on the arbor, because the clock is wound by pulling the sprocket and ratchet
backward by means of the chain until the weight is raised clear up to the
seat board. There are no squares on the arbors, which have ordinary pivots
at both ends, and the great wheel is fast on the arbor. The diameter of the
convex portion of the wheel each side of the sprocket is the diameter of the
barrel, and the chain should fit so that alternate links will fit nicely in the
teeth of the sprocket; where this is not the case they will miss a link
occasionally and the weight will then fall until the chain catches again,
when it will stop with a jerk; bent or jammed links in the chain will do the
same thing. Sometimes a light chain on a heavy weight will stretch or
spread the links enough to make their action faulty. If examination shows a
tendency to open the links, they should be soldered; if they are stretching, a
heavier chain of correct lengths of links should be substituted. Twisted

chains are another characteristic fault and are usually the result of bent or
jammed links. A close examination of such a chain will generally reveal
several links in succession which are not quite flat and careful straightening
of these links will generally cure the tendency to twist.
Mainsprings for Clocks.--There are many points of difference between
mainsprings for clocks and those for watches. They differ in size, strength,
number of coils and in their effect on the rates of the clock.
Watch springs are practically all for 30-hour lever escapements, with a
few cylinder, duplex and chronometer escapements. If a fusee watch
happens into a shop nowadays it is so rare as to be a curiosity worth
stopping work to look at.
The clocks range all the way from 30 hours to 400 days in length of
time between windings and include lever, cylinder, duplex, dead beat, half
dead beat, recoil and other escapements. Furthermore some of these, even
of the same form of escapements, will vary so in weight and the consequent
influence of the spring that what will pass in one case will give a wildly
erratic rate in another instance. Many of the small French clocks have such
small and light pendulums that very nice management of the stop works is
necessary to prevent the clock from gaining wildly when wound or stopping
altogether when half run down.
Nothing will cause a clock with a cylinder escapement to vary in time
more than a set or gummy mainspring, for it will gain time when first
wound and lose when half run down, or when there is but little power on
the train. In such a case examine the mainspring and see that it is neither
gummy nor set. If it is set, put in a new spring and you can probably bring it
to time.
With a clock it depends entirely on the kind of escapement that it
contains, whether it runs faster or slower, with a stronger spring; if you put
a stronger mainspring in a clock that contains a recoil escapement the clock
will gain time, because the extra power, transmitted to the pallets will cause
the pendulum to take a shorter arc, therefore gain time, where the reverse
occurs in the dead-beat escapement. A stronger spring will cause the dead-
beat pendulum to take a longer arc and therefore lose time.

If a pendulum is short and light these effects will be much greater than
with a long and heavy pendulum.
At all clock factories they test the mainsprings for power and to see that
they unwind evenly; those that do are marked No. 1, and those that do not
are called “seconds.” The seconds are used only for the striking side of the
clocks, while the perfect ones are used for the running, or time side.
Sometimes, however, a seconds’ spring will be put on the time side and will
cause the clock to vary in a most erratic way. This changing of springs is
very often done by careless or ignorant workmen in cleaning and then they
cannot locate the trouble.
All mainsprings for both clocks and watches should be smooth and well
polished. Proper attention to this one item will save many dollars’ worth of
time in examining movements to try to detect the cause of variations.
A rough mainspring (that is, an emery finished mainspring) will lose
one-third of its power from coil friction, and in certain instances even one-
half. The deceptive feature about this to the watchmaker is that the clock
will take a good motion with a rough spring fully found, but will fall off
when partly unwound, and the consequence is that he finds a good motion
when the spring is put in and wound, and he afterward neglects to examine
the spring when he examines the rate as faulty. The best springs are cheap
enough, so that only the best quality should be used, as it is easy for a
watchmaker to lose three or four dollars’ worth of time looking for faults in
the escapement, train and everywhere else, except the barrel, when he has
inserted a rough, thick, poorly made spring. The most that he can save on
the cheaper qualities of springs is about five cents per spring and we will
ask any watchmaker how long it would take to lose five cents in
examination of a movement to see what is defective.
Here is something which you can try yourself at the bench. Take a rough
watch mainspring; coil it small enough to be grasped in the hand and then
press on the spring evenly and steadily. You will find it difficult to make the
coils slide on one another as the inner coils get smaller; they will stick
together and give way by jerks. Now open your hand slowly and you will
feel the spring uncoiling in an abrupt, jerky way, sometimes exerting very
little pressure on the hand, at other times a great deal. A dirty, gummy
spring will do the same thing. Now take a clean, well polished spring and

try it the same way; notice how much more even and steady is the pressure
required to move the coils upon each other, either in compressing or
expanding. Now oil the well polished spring and try it again. You will find
you now have something that is instantly responding, evenly and smoothly,
to every variation of pressure. You can also compress the spring two or
three turns farther with the same force. This is what goes on in the barrel of
every clock or watch; you have merely been using your hand as a barrel and
feeling the action of the springs.
Now a well finished mainspring that is gummy is as irregular in its
action as the worst of the springs described above, yet very few
watchmakers will take out the springs of a clock if they are in a barrel. One
of them once said to me, “Why, who ever takes out springs? I’ll bet I clean
a hundred clocks before I take out the springs of one of them!” Yet this
same man had then a clock which had come back to him and which was the
cause of the conversation.
There must be in this country over 25,000 fine French clocks in
expensive marble or onyx cases, which were given as wedding presents to
their owners, and which have never run properly and in many instances
cannot be made to run by the watchmakers to whom they were taken when
they stopped. Let me give the history of one of them. It was an eight-day
French marble clock which cost $25 (wholesale) in St. Louis and was given
as a wedding present. Three months later it stopped and was taken to a
watchmaker well known to be skillful and who had a fine run of expensive
watches constantly coming to him. He cleaned the clock, took it home and
it ran three hours! It came back to him three times; during these periods he
went over the movement repeatedly; every wheel was tested in a depthing
tool and found to be round: all the teeth were examined separately under a
glass and found to be perfect; the pinions were subjected to the same careful
scrutiny; the depthings were tried with each wheel and pinion separately;
the pivots were tested and found to be right; the movement was put in its
case and examined there; it would run all right on the watchmaker’s bench,
but not in the home of its owner. It would stop every time it was moved in
dusting the mantel. He became disgusted and took the clock to another
watchmaker, a railroad time inspector; same results. In this way the clock
moved about for three years; whenever the owner heard of a man who was
accounted more than ordinarily skillful he took him the clock and watched

him “fall down” on it. Finally it came into the hands of an ex-president of
the American Horological Society. He made it run three weeks. When he
found the clock had stopped again he refused pay for it. Three months later
he called and got the clock, kept it for three weeks, brought it back without
explanation and lo, the clock ran! It would even run considerably out of
beat! When asked what he had done to the clock, he merely laughed and
said “Wait.”
A year later the clock was still going satisfactorily and he explained.
“That was the first time I ever got anything I couldn’t fix and it made me
ashamed. I kept thinking it over. Finally one night in bed I got to
considering why a clock wouldn’t run when there was nothing the matter
with it. The only reason I could see was lack of power. Next morning I got
the clock and put in new mainsprings, the best I could find. The clock was
cured! None of these other men who had the clock took out the springs.
They came to me all gummed up, while the rest of the clock was clean,
bright and in perfect order. I cleaned the springs and returned the clock; it
ran three weeks. When I took it back I put in stronger springs, because I
found them a little soft on testing them. If any of your friends have French
clocks that won’t go, send them to me.”
Three-quarters of the trouble with French clocks is in the spring box;
mainspring too weak, gummy or set; stop works not properly adjusted, or
left off by some numskull who thought he could make the clock keep time
without it when the maker couldn’t; mainspring rough, so that it uncoils by
jerks; spring too strong, so that the small and light pendulum cannot control
it. These will account for far more cases than the “flat wheel” story that so
often comes to the front to account for a failure on the part of the workman.
Of course he must say something to his boss to account for his failure and
the “wheels out of round” and “the faulty depthing” have been standard
excuses for French clocks for a century. Of course they do occur, but not
nearly as often as they are credited with, and even then such a clock may be
made to perform creditably if the springs are right.
Another source of trouble is buckled springs, caused by some workman
taking them out or putting them in the barrel without a mainspring winder.
There are many men who will tell you that they never use a winder; they
can put any spring in without it. Perhaps they can, but there comes a day
when they get a soft spring that is too wide for this treatment and they

stretch one side of it, or bend, or kink it, and then comes coil friction with
its attendant evils. These may not show with a heavy pendulum, but they
are certain to do so if it happens to be an eight-day movement with light
pendulum or balance, and this is particularly true of a cylinder.
All springs should be cleaned by soaking in benzine or gasoline and
rubbing with a rag until all the gum is off them before they are oiled. Heavy
springs may be wiped by wrapping one or two turns of a rag around them
and pushing it around the coils. The spring should be well cleaned and dried
before oiling. A quick way of cleaning is to wind the springs clear up; stick
a peg in the escape wheel; remove the pallet fork; plunge the whole
movement into a pail of gasoline large enough to cover it; let it stand until
the gasoline has soaked into the barrels; remove the peg and let the trains
run down. The coils of the spring will scrub each other in unwinding; the
pivots will clean the pivot holes and the teeth of wheels and pinions will
clean each other. Then take the clock apart for repairs. Springs which are
not in barrels should be wound up and spring clamps put on them before
taking down the clock. About six sizes of these clamps (from 2½ inches to
¾ inch) are sufficient for ordinary work.
Rancid oil is also the cause of many “come-backs.” Workmen will buy a
large bottle of good oil and leave it standing uncorked, or in the sun, or too
near a stove in winter time, until it spoils. Used in this condition it will dry
or gum in a month or two and the clock comes back, if the owner is
particular; if not, he simply tells his friends that you can’t fix a clock and
they had better go elsewhere with their watches.
For clock mainsprings, clock oil, such as you buy from material dealers,
is recommended provided it is intended for French mainsprings. If the
lubricant is needed for coarse American springs, mix some vaseline with
refined benzine and put it on liberally. The benzine will dissolve the
vaseline and will help to convey the lubricant all over the spring, leaving no
part untouched. The liquid will then evaporate, leaving a thin coating of
vaseline on the spring.
It is best to let springs down, with a key made for the purpose. It is a
key with a large, round, wooden handle, which fills the hand of the
watchmaker when he grasps it. Placing the key on the arbor square, with the
movement held securely in a vise, wind the spring until you can release the

click of the ratchet with a screwdriver, wire or other tool; hold the click free
of the ratchet and let the handle of the key turn slowly round in the hand
until the spring is down. Be careful not to release the pressure on the key
too much, or it will get away from you if the spring is strong, and will
damage the movement. This is why the handle is made so large, so that you
can hold a strong spring.
It is of great importance, if we wish to avoid variable coil friction, that
the spring should wind, from the very starting, concentrically; i. e., that the
coils should commence to wind in regular spirals, equidistant from each
other, around the arbor. In very many cases we find, when we commence to
wind a spring, that the innermost coil bulges out on one side, causing, from
the very beginning, a greater friction of the coils on that side, the outer ones
pressing hard against it as you continue to wind, while on the outer side of
the arbor they are separated from each other by quite a little space between
them, and that this bulge in the first coil is overcome and becomes
concentric to the arbor only after the spring is more than half way wound
up. This necessarily produces greater and more variable coil friction. When
a spring is put into the barrel the innermost coil should come to the center
around the arbor by a gradual sweep, starting from at least one turn around
away from the other coils. Instead of that, we more often find it laying close
to the outer coils to the very end, and ending abruptly in the curl in the soft
end that is to be next the arbor. When this is the case in a spring of uniform
thickness throughout, it is mainly due to the manner of first winding it from
its straight into a spiral form. To obviate it, I generally wind the first coils,
say two or three, on a center in the winder, a trifle smaller than the regular
one, which is to be of the same diameter of the arbor center in the barrel.
You will find that the substitution of the regular center, afterwards, will not
undo the extra bending thus produced on the inner coils, and that the spring
will abut by a more gradual sweep at the center, and wind more
concentrically.
The form of spring formerly used with a fusee in English carriage
clocks and marine chronometers is a spring tapering slightly in thickness
from the inner end for a distance of two full coils, the thickness increasing
as we move away from the end, then continuing of uniform thickness until
within about a coil and a half from the other end, when it again increases in
thickness by a gradual taper. The increase in the thickness towards the outer

end will cause it to cling more firmly to the wall of the barrel. The best
substitute for this taper on the outside is a brace added to some of the
springs immediately back of the hole. With this brace, and the core of the
winding arbor cut spirally, excellent results are obtained with a spring of
uniform thickness throughout its entire length. Something, too, can be done
to improve the action of a spring that has no brace, by hooking it properly
to the barrel. The hole in the spring on the outside should never be made
close to the end; on the contrary, there should be from a half to three-
quarters of an inch left beyond the hole. This end portion will act as a brace.
When the spring is down, the innermost coil of it should form a gradual
spiral curve towards the center, so as to meet the arbor without forcing it to
one side or the other. This curve can be improved upon, if not correct, with
suitably shaped pliers; or it can be approximated by winding the innermost
coils first on an arbor a little smaller in diameter than the barrel arbor itself.
Another and very important factor in the development of the force of
the spring is the proper length and thickness of it. For any diameter of barrel
there is but one length and one thickness of spring that will give the
maximum number of turns to wind. This is conditioned by the fact that the
volume which the spring occupies when it is down must not be greater nor
less than the volume of the empty space around the arbor into which it is to
be wound, so that the outermost coil of the spring when fully wound will
occupy the same place which the innermost occupies when it is down. In a
barrel, the diameter of whose arbor is one-third that of the barrel, the
condition is fulfilled when the measure across the coils of the spring as it
lays against the wall of the barrel, is 0.39 of the empty space, or, taking the
diameter of the barrel as a comparison, 0.123 of the latter; in other words,
nearly one-eighth of the diameter of the barrel. This is the width that will
give the greatest number of turns to wind, whatever may be the length or
thickness of any spring. If now we desire a spring to wind a given number
of turns, there is but one thickness and one length of it that will permit it to
do so. The thickness remaining the same, if we make the spring longer or
shorter, we reduce the number of turns it will wind; more rapidly by making
it shorter, less so by making it longer. It is therefore not only useless, but
detrimental, to put into a barrel a greater number of coils, or turns, than are
necessary, not only because it will reduce the number of turns the barrel

will wind, but it will produce greater coil friction by filling up the space
with more coils than are necessary.
A mainspring in the act of uncoiling in its barrel always gives a number
of turns equal to the difference between the number of coils in the up and
the down positions. Thus, if 17 be the number of coils when the spring is
run down, and 25 the number when against the arbor, the number of turns in
uncoiling will be 8, or the difference between 17 and 25.
The cause of breakage is usually, that the inner coils are put to the
greatest strain, and then the slightest flaw in the steel, a speck of rust,
grooves cut in the edges of the spring by allowing a screwdriver to slip over
them, or an unequal effect of change of temperature, causes the fracture,
and leaves the spring free to uncoil itself with very great rapidity.
Now this sudden uncoiling means that the whole energy of the spring is
expended on the barrel in a very small fraction of a second. In reality the
spring strikes the inner side of the rim of the barrel, a violent blow in the
direction the spring is turning, that is, backwards; this is due to the
mainspring’s inertia and its very high mean velocity. The velocity is nothing
at the outer end, where the spring is fixed, but rises to the maximum at the
point of fracture, and the kinetic energy at various points of the spring could
no doubt be calculated mathematically or otherwise.
For instance, take a going barrel spring of eight and a half turns,
breaking close up to the center while fully wound. A point in the spring at
the fracture makes eight turns in the opposite direction to which it was
wound, a point at the middle four turns, and a point at the outer end
nothing, an effect similar to the whole mass of the spring making four turns
backwards. At its greatest velocity it is suddenly stopped by the barrel,
wheel teeth engaging its pinion; this stoppage or collision is what breaks
center pinions, third pivots, wheel teeth, etc., unless their elasticity, or some
interposed contrivance, can safely absorb the stored-up energy of the
mainspring, the spring being, as every one knows, the heaviest moving part
in an ordinary clock, except where the barrel is exceptionally massive.
Stop Works.--Stop works are devices that are but little understood by
the majority of workmen in the trade. They are added to a movement for
either one or both of two distinct purposes: First, as a safety device, to
prevent injury to the escape wheel from over winding, or to prevent undue

force coming on the pendulum by jamming the weight against the top of the
seat board and causing a variation in time in a fine clock; or, second, to use
as a compromise by utilizing only the middle portion of a long and
powerful spring, which varies too much in the amount of its power in the up
and down positions to get a good rate on the clock if all the force of the
spring were utilized in driving the movement.
With weight clocks, the stop work is a safety device and should always
be set so that it will stop the winding when the barrel is filled by the cord;
consequently the way to set them is to wind until the barrel is barely full
and set the stops with the fingers locked so as to prevent any further action
of the arbor in the direction of the winding and the cord should then be long
enough to permit the weight to be free. Then unwind until within half a coil
of the knot in the cord where it is attached to the barrel and see that the
weight is also free at the bottom of the case, when the stops again come into
action. This will allow the full capacity of the barrel to be used.
When stop work is found on a spring barrel, it may be taken for granted
that the barrel contains more spring than is being wound and unwound in
the operation of the clock and it then becomes important to know how many
coils are thus held under tension, so that we may put it back correctly after
cleaning. Wind up the spring and then let it slowly down with the key until
the stop work is locked, counting the number of turns, and writing it down.
Then hold the spring with the letting down key and take a screw driver and
remove the stop from the plate; then count the number of turns until the
spring is down and also write that down. Then take out the spring and clean
it. You may find such a spring will give seventeen turns in the barrel
without the stop work on, while it will give but ten with the stop work; also
that the arbor turned four revolutions after you removed the stop. Then the
spring ran the clock from the fourth to the fourteenth turns and there were
four coils unused around the arbor, ten to run the clock and three unused at
the outer end around the barrel. This would indicate a short and light
pendulum or balance, which is very apt to be erratic under variations of
power, and if the rate was complained of by the customer you can look for
trouble unless the best adjustment of the spring is secured. Put the spring
back by winding the four turns and putting on the stop work in the locked
position; then wind. If the clock gains when up and loses when down, shift
the stop works half a turn backwards or forwards and note the result,

making changes of the stop until you have found the point at which there is
the least variation of power in the up and down positions. If the variation is
still too great a thinner spring must be substituted.
There are several kinds of stop work, the most common being what is
known as the Geneva stop, a Maltese cross and a finger such as is
commonly seen on watches. For watches they have five notches, but for
clocks they are made with a greater number of notches, according to the
number of turns desired for the arbor. The finger piece is mounted on a
square on the barrel arbor and the star wheel on the stud on the plate. In
setting them see that the finger is in line with the center of the star wheel
when the stop is locked, or they will not work smoothly.
There is another kind of stopwork which is used in some American
clocks, and as there is no friction with it, and no fear of sticking, nor any
doubt of the certainty of its action, it is perhaps the most suitable for
regulators and other fine clocks which have many turns of the barrel in
winding. This stop is simple and sure. It consists of a pair of wheels of any
numbers with the ratio of odd numbers as 7 and 6, 9 and 10, 15 and 16, 30
and 32, 45 and 48, etc.; the smaller wheel is squared on the barrel arbor and
the larger mounted on a stud on the plate. These wheels are better if made
with a larger number of teeth. On each wheel a finger is planted, projecting
a little beyond the outsides of the wheel teeth, so that when the fingers meet
they will butt securely. The meeting of these fingers cannot take place at
every revolution because of the difference in the numbers of the teeth of the
wheels; they will pass without touching every time till the cycle of turns is
completed, as one wheel goes round say sixteen times while the other goes
fifteen, and when this occurs the fingers will engage and so stop further
winding. When the clock has run down sixteen turns of the barrel the
fingers will again meet on the opposite side, and so the barrel will be
allowed to turn backwards and forwards for sixteen revolutions, being
stopped by the fingers at each extreme. When in action the fingers may butt
either at a right or an obtuse angle, only not too obtuse, as this would put a
strain on, tending to force the wheels apart. If preferred the fingers may be
made of steel, but this is not necessary.

Fig. 83.
Maintaining Powers.--Astronomical clocks, watchmaker’s regulators
and tower clocks are, or at least should be, fitted with maintaining power. A
good tower clock should not vary in its rate more than five to ten seconds a
week. Many of them, when favorably situated and carefully tended, do not
vary over five to ten seconds per month. It requires from five to thirty
minutes to wind the time trains of these clocks and the reader can easily see
where the rate would go if the power were removed from the pendulum for
that length of time; hence a maintaining power that will keep nearly the
same pressure on the escape wheel as the weight does, is a necessity.
Astronomical clocks and fine regulators have so little train friction,
especially if jeweled, that when the barrel is turned backwards in winding
the friction between the barrel head and the great wheel is sufficient to stop
the train, or even run it backwards, injuring the escape wheel and, of course,
destroying the rate of the clock; therefore they are provided with a device
that will prevent such an occurrence. Ordinary clocks do not have the
maintaining power because only the barrel arbor is reversed in winding, and
that reversal is never for more than half a turn at a time, as the power is
thrown back on the train every time the winder lets go of the key to turn his
hand over for another grip.

Fig. 84.

Fig. 85.
Figs. 83, 84 and 85 show the various forms of maintaining powers,
which differ only in their mechanical details. In all of them the maintaining
power consists of two ratchet wheels, two clicks and either one or two
springs; the springs vary in shape according to whether the great wheel is
provided with spokes or left with a web. If the great wheel has spokes the
springs are attached on the outside of the large ratchet wheel so that they
will press on opposite spokes of the great wheel and are either straight,
curved or coiled, according to the taste of the maker of the clock and the
amount of room. If made with a web a circular recess is cut in the great
wheel, see Fig. 83, wide and deep enough for a single coil of spring wire
which has its ends bent at right angles to the plane of the spring and one end
slipped in a hole of the ratchet and the other in a similar hole in the recess
of the great wheel. A circular slot is cut at some portion of the recess in the
great wheel where it will not interfere with the spring and a screw in the
ratchet works back and forth in this slot, limiting the action of the spring.
Stops are also provided for the spokes of the great wheel in the case of
straight, curved or coiled springs, Figs. 84 and 85. These stops are set so as
to give an angular movement of two or three teeth of the great wheel in the
case of tower clocks and from six to eight teeth in a regulator. The springs
should exert a pressure on the great wheel of just a little less than the pull of
the weight on the barrel; they will then be compressed all the time the
weight is in action, and the stops will then transmit the power from the large
ratchet to the great wheel, which drives the train. Both the great wheel and
the large ratchet wheel are loose on the arbor, being pinned close to the
barrel, but free to revolve. A smaller ratchet, having its teeth cut in the
reverse direction from those of the larger one, is fast to the end of the barrel.
A click, called the winding click, on the larger ratchet acts in the teeth of the
smaller one during the winding, holding the two ratchets together at all
other times. A longer click, called the detent click, is pivoted to the clock
plate, and drags idly over the teeth of the larger ratchet while the clock is
being driven by the weight and the maintaining springs are compressed.
When the power is taken off by the reversal of the barrel in winding, the
friction between the sides of the two ratchets and great wheel would cause
them to also turn backward, if it were not for this detent click, with its end
fast to the plate, which drops into the teeth of the large ratchet and prevents
it from turning backward. We now have the large ratchet held motionless by

the detent click on the clock plate and the compressed springs which are
carried between the large ratchet and the great wheel will then begin to
expand, driving the loose great wheel until their force has been expended,
or until winding is completed, when they will again be compressed by the
pull of the weight. In some tower clocks curved pins are fixed to opposite
spokes of the great wheel and coiled springs are wound around the pins,
Fig. 85; eyes in the large ratchet engage the outer ends of the pins and
compress the springs.

Fig. 86.
The clicks for maintaining powers should not be short, and the planting
should be done so that lines drawn from the barrel center to the click points
and from the click centers to the points, will form an obtuse angle, like B,
Fig. 86, giving a tendency for the ratchet tooth to draw the click towards the
barrel center. The clicks should be nicely formed, hardened and tempered
and polished all over with emery. Long, thin springs will be needed to keep
the winding clicks up to the ratchet teeth. The ratchet wheel must run freely
on the barrel arbor, being carried round by the clicks while the clock is
going, and standing still while the weight is being wound up. It is retained
at this time by a long detent click mounted on an arbor having its pivots
fitted to holes in the clock frame. The same remark as to planting applies to
this click as well as the others, and to all clicks having similar objects; but
as this click has its own weight to cause it to fall no spring is required. To

prevent it lying heavily on the wheel, causing wear, friction and a
diminution of driving power, it is as well to have it made light. There is no
absolute utility in fixing the click to its collet with screws, but if done, it can
be taken off to be polished, and the appearance will be more workmanlike.
This click should have its point hardened and tempered, as there is
considerable wear on it.

Fig. 87.
If the great wheel has spokes the best form for the two springs for
keeping the train going whilst being wound is that of the letter U, as shown
to the left of Fig. 84, one end enlarged for the screw and steady pin and the
blade tapering all along towards the end which is free. The springs may be
made straight and bent to the form while soft, then hardened and tempered
to a full blue. They are best when as large as the space between two arms of
the main wheel will allow. When screwed on the large ratchet the backs of
both should bear exactly against the respective arms of the mainwheel, and
a pair of pins is put in the ratchet, so that any opposite pair of the
mainwheel arms may rest upon them when the springs are set up by the
clock weight. The strength of the springs can be adjusted by trial, reducing
them till the weight of the clock sets them up easily to the banking pins.
There are two methods of keeping the loose wheels against the end of
the barrel, while allowing them to turn freely during winding; one is a
sliding plate with a keyhole slot, Fig. 87, to slip in a groove on the arbor, as
is generally adopted in such house clocks as have fuzees, as well as on the
barrels of old-fashioned weight clocks; the other is a collet exactly the same
as on watch fuzees. They are both sufficiently effective, but perhaps the
latter is the best of the two, because the collet may be fitted on the arbor
with a pipe, and being turned true on the broad inside face, gives a larger

and steadier surface for the mainwheel to work against, whereas the former
only has a small bearing on the shoulder of the small groove in the arbor,
which fitting is liable to wear and allow the main and the other loose wheel
to wobble sideways, displacing the contact with the detent click and causing
the mainwheel to touch the collet of the center wheel if very near together;
so, on the whole, a collet, as on a watch fuzee, seems the better
arrangement, where there is plenty of room for it on the arbor.
There is an older form of maintaining power which is sometimes met
with in tower clocks and which is sometimes imitated on a small scale by
jewelers who are using a cheap regulator and wish to add a maintaining
power where there is no room between the barrel and plates for the ratchets
and great wheel.
The maintaining power, Fig. 88, consists of a shaft, A, a straight lever,
B, a segment of a pinion, C, a curved, double lever, D, a weight, E. The
shaft, A, slides endwise to engage the teeth of the pinion segment with the
teeth of the great wheel. No. 2, the straight lever has a handle at both ends
to assist in throwing the pinion out or in and a shield at the outer end to
cover the end of the winding shaft, No. 3, when the key is not on it.
The curved lever is double, and the pinion segment turns loosely
between the halves and on the shaft, A; it is held up in its place by a light
spring, F; the weight, E, is also held between the two halves of the double
lever.

Fig. 88. Maintaining Power.
The action is as follows: The end of the lever, B, covers the end of the
winding shaft so that it is necessary to raise it before putting the key on the
winding shaft; it is raised till it strikes a stop, and then pushed in till the
pinion segment engages with the going wheel of the train, when the weight,
E, acting through the levers, furnishes power to drive the clock train while
the going weight is being wound up. Of course the weight on the
maintaining power must be so proportioned to the leverage that it will be
equal to the power of the going barrel and its weight, a simple proposition
in mechanics.
The number of teeth on the pinion segment, C, is sufficient to maintain
power for fifteen minutes, at the end of which time the lever, B, will come
down and again cover the end of the winding shaft; or, it may be pumped
out of gear and dropped down. In case it is forgotten, the spring, F, will

allow the segment to pass out of gear of itself and will simply allow it to
give a click as it slips over each tooth in the going wheel; if this were not
provided for, it would stop the clock.

CHAPTER XVI.
MOTION WORK AND STRIKING TRAINS.

Motion work is the name given to the wheels and pinions used to make
the hour hand go once around the dial while the minute hand goes twelve
times. Here a few preliminary observations will do much toward clearing
up the operations of the trains. The reader will recollect that we started at a
fixed point in the time train, the center arbor which must revolve once per
hour, and increased this motion by making the larger wheels drive the
smaller (pinions) until we reached sixty or more revolutions of the escape
wheel to one of the center arbor. This gearing to increase speed is called
“gearing up” and in it the pinions are always driven by the wheels. In the
case of the hour hand we have to obtain a slowing effect and we do so by
making the smaller wheels (pinions) drive the larger ones. This is called
“gearing back” and it is the only place in the clock where this method of
gearing occurs.
We drew attention to a common usage in the gearing up of the time
trains—that of making the relations of the wheels and pinions 8 to one and
7.5 to one; 7.5 × 8 = 60. So we find a like usage in our motion work, viz., 3
to one and 4 to one; 3 × 4 = 12. Say the cannon pinion has twelve teeth;
then the minute wheel generally has 36, or three to one, and if the minute
wheel pinion has 10, the hour wheel will have 40, or four to one. Of course,
any numbers of wheels and pinions may be used to obtain the same result,
so long as the teeth of the wheels multiplied together give a product which
is twelve times that of the pinions multiplied together; but three and four to
one have been settled upon, just as the usage in the train became fixed, and
for the same reasons; that is, these proportions take up the least room and
may be made with the least material. Also, the pinion with the greatest
number of teeth, being the larger, is usually selected as the cannon pinion,
as it gives more room to be bored out to receive the cannon, or pipe. If
placed outside the clock plate, the minute wheel and pinion revolve on a
stud in the clock plate; but if placed between the frames, they are mounted
on arbors like the other wheels. The method of mounting is merely a matter

of convenience in the arrangement of the train and is varied according to the
amount of room in the movement, or convenience in assembling the
movement at the factory, little attention being paid to other considerations.

Fig. 89. Fig. 90.
The cannon pinion is loose on the center arbor and behind it is a spring,
called the center spring, or “friction,” Figs. 89 and 90, which is a disc that is
squared on the arbor at its center and presses at three points on its outer
edge against the side of the cannon pinion; or it may be two or three coils of
brass wire. This center spring thus produces friction enough on the cannon
to drive it and the hour hand, while permitting the hands to be turned
backward or forward without interfering with the train. In French mantel
clocks the center spring is dispensed with and a portion of the pipe is
thinned and pressed in so as to produce a friction between the pipe and the
center arbor which is sufficient to drive the hands; this is similar to the
friction of the cannon pinion in a watch.

Fig. 91.
In some old English house clocks with snail strike, the cannon pinion
and minute wheel have the same number of teeth for convenience in letting
off the striking work by means of the minute wheel, which thus turns once
in an hour. Where this is the case the hour wheel and its pinion bear a
proportion to each other of twelve to one; usually there is a pinion of six
leaves engaging a wheel of 72 teeth, or seven and eighty-four are
sometimes found.
In tower clocks, where the striking is not discharged by the motion
work, the cannon pinion is tight on its arbor and the motion work is similar
to that of watches. See Fig. 91.
The cannon pinion drives the minute wheel, which, together with its
pinion, revolves loosely on a stud in the clock plate, or on an arbor between
the frames. The meshing of the minute wheel and cannon pinion should be
as deep as is consistent with perfect freedom, as should also that of the hour
wheel and minute pinion in order to prevent the hour hand from having too
much shake, as the minute wheel and pinion are loose on the stud and the

hour wheel is loose on the cannon, so that a shallow depthing here will give
considerable back lash, which is especially noticeable when winding.
The hour wheel has a short pipe and runs loosely on the cannon pinion
in ordinary clocks. In quarter-strike cuckoos a different train is employed
and the wheels for the hands are both on a long stud in the plate and both
have pipes; the minute wheel has 32 teeth and carries four pins on its under
side to let off the quarters. The hour wheel has 64 teeth and works close to
the minute wheel, its pipe surrounding the minute wheel pipe, and held in
position by a screw and nut on the minute pipe. A wheel of 48 and a pinion
of 8 teeth are mounted on the sprocket arbor with a center spring for a
friction, the wheel of 48 meshing with the minute wheel of 32 and the 8-leaf
pinion with the hour wheel of 64. It will be recollected that the sprocket
wheel takes the place of the barrel in this clock and there is no center arbor
as it is commonly understood. The sprocket arbor in this case turns once in
an hour and a half, hence it requires 48 teeth to drive the minute wheel of
32 once in an hour, as it turns one-third of a revolution (or 16 teeth) every
half hour. The sprocket arbor, turning once in an hour and a half, makes
eight revolutions in twelve hours and its pinion of eight leaves working in
the hour wheel of 64 teeth turns the hour hand once in twelve hours.
In ordinary rack and snail striking work the snail is generally mounted
on the pipe of the hour wheel, so that it will always agree with the position
of the hour hand and the striking will thus be in harmony with the position
of the hands.
Striking Trains.--It is only natural, after finding certain fixed relations
in the calculations of time trains and motion work, that we should look for a
similar point in striking trains, well assured that we shall find it here also. It
is evident that the clock must strike the sum of the numbers 1, 2, 3, 4, 5, 6,
7, 8, 9, 10, 11, 12, or 78 blows of the hammer, in striking from noon to
midnight; this will be repeated from midnight to noon, making 156 blows in
24 hours, and if it is a 30-hour clock, six hours more must be added; blows
for these will be 21 more, making a total of 177 blows of the hammer for a
30-hour strike train. The hammer is raised by pins set in the edge of a
wheel, called the pin wheel, and as one pin must pass the hammer tail for
every blow, it is evident that the number of pins in this wheel will govern
the number of revolutions it must make for 177 blows, so that here is the
base or starting point in our striking train. If there are 13 pins in the pin

wheel, it must revolve 13.5 times for 177 blows; if there are 8 pins, then the
wheel must revolve 22.125 times in giving 177 blows; consequently the
pinions and wheels back to the spring or barrel must be arranged to give the
proper number of revolutions of the pin wheel with a reasonable number of
turns of the spring or weight cord, and it is generally desirable to give the
same, or nearly the same, number of turns to both time and striking barrels.
If it is an eight-day clock the calculation is a little different. There are
156 blows every 24 hours; then as the majority of “eight-day” clocks are
really calculated to keep time for seven and a half days, although they will
run eight, we have: 156 × 7.5 = 1,070 blows in 7.5 days. With 13 pins we
have 1,070 ÷ 13 = 80 and ⁴⁄₁₃ths revolutions in the 7.5 days. If now we put
an 8-leaf pinion on the pin wheel arbor and 84 teeth in the great wheel or
barrel, we will get 10.5 turns of the pin wheel for every turn of the spring or
barrel; consequently eight turns of the spring will be enough to run the
clock for the required time, as such clocks are wound every seventh day.
Figuring forward from the pin wheel, we find that we shall have to lock
our striking train after a stated number of blows of the hammer each hour;
these periods increase by regular steps of one blow every hour, so that we
must have our locking mechanism in position to act after the passage of
each pin, whether it is then used or not; so the pinion that meshes with the
pin wheel, and carries the locking plate or pin on its arbor must make one
revolution every time it passes a pin. If this is a 6-leaf pinion, the pins on
the pin wheel must therefore be 6 teeth apart; or an 8-leaf pinion must have
the pins 8 teeth apart; and vice versa. For greater convenience in
registering, the pins are set in a radial line with the spaces of the teeth in the
pin wheel, as this allows us to measure from the center of the pinion leaf.
It will thus be seen that the calculation of an hour striking train is a
simple matter; but if half hours are also to be struck from the train, it will
change these calculations. For a 30-hour train 24 must be added to the 156
blows for 24 hours, 180 blows being required to strike hours and half hours
for 24 hours. These blows may be provided for by more turns of the spring,
or different numbers of the wheels and pinions, which would then also vary
the spacing of the pins.
Half hours may also be struck directly from the center arbor, by putting
an extra hammer tail on the hammer arbor, further back, where it will not

interfere with the hammer tail for the pin wheel, and putting a cam on the
center arbor to operate this second hammer tail. This simplifies the train, as
it enables the use of a shorter spring or smaller wheels while providing a
cheap and certain means of striking the half hours. Half-hour trains are
frequently provided with a separate bell of different tone for the half hours,
as with only one bell the clock strikes one blow at 12:30, 1 and 1:30,
making the time a matter of doubt to one who listens without looking, as
frequently happens in the night.

Fig. 92. Eight Day Hour and Half Hour Strike.
Fig. 92 shows an eight-day, Seth Thomas movement, which strikes the
hours on a count wheel train and the half hours from the center arbor. All

the wheels, pinions, arbors, pins, levers and hooks are correctly shown in
proper position, but the front plate has been left off for greater clearness.
The reader will therefore be required to remember that the escape wheel,
pallets, crutch, pendulum and the stud for the pendulum suspension are
really fixed to the front plate, while in the drawing they have no visible
means of support, because the plate is left off.
The time train occupies the right-hand side of the movement and the
striking train the left hand. Running up the right-hand from the spring to the
escape wheel, we find an extra wheel and pinion which is provided to
secure the eight days’ run. We also see that what would ordinarily be the
center arbor is up in the right corner and does not carry the hands; further,
the train is bent over at a right angle, in order to save space and get the
escape wheel in the center at the top of the movement. The striking train is
also crowded down out of a straight line, the locking cam being to the right
of the pin wheel and the warning wheel and fly as close to the center as
possible. This leaves some space between the pin wheel and the
intermediate wheel of the time train and here we find our center arbor,
driven from the intermediate wheel by an extra pinion on the minute wheel
arbor, the minute wheel meshing with the cannon pinion on the center arbor.
This rearranging of trains to save space is frequently done and often shows
considerable ingenuity and skill; it also will many times serve to identify
the maker of a movement when its origin is a matter of doubt and we need
some material, so that the planting of trains is not only a matter of interest,
but should be studied, as familiarity with the methods of various factories is
frequently of service to the watchmaker.
Fig. 93 is the upper portion of the same striking train, drawn to a larger
scale for the sake of clearness. It also shows the center arbor, both hammer
tails and the stop on the hammer arbor, which strikes against the bottom of
the front plate to prevent the hammer-spring from throwing the hammer out
of reach of the pins. The pin wheel, R, and count wheel, E, are mounted
close together and are about the same size, so that they are shown broken
away for a part of their circumferences for greater clearness in explaining
the action of the locking hook, C, and the locking cam, D.
Fig. 94 shows the same parts in the striking position, being shown as
just about to strike the last blow of 12. Similar parts have similar letters in
both figures.

The count wheel, E, is loose on a stud in the plate, concentric with the
arbor of the pin wheel, R. The pivot of R runs through this stud. The sole
office of the count wheel is to regulate the distance to which the locking
hook C, is allowed to fall. The count hook, A, and the locking hook, C, are
mounted on the same arbor, B, so that they move in unison. If A is allowed
to fall into a deep slot of the count wheel, C will fall far enough to engage
the locking face of the cam D and stop the train, as in Fig. 93. If, on the
contrary, A drops on the rim of the wheel, C will be held out of the locking
position as D comes around (see Fig. 94), and the train will keep on
running. It will be seen that after passing the locking notch, D, Fig. 94, will
in its turn raise the hook C, which will ride on the edge of D, and hold A
clear of the count wheel until the locking notch of D is again reached, when
a deep notch in the wheel will allow C to catch, as in Fig. 93, unless C is
stopped by A falling on the rim of the wheel, as in Fig. 94.

Fig. 93. Upper Portion of Striking Train Locked.

Fig. 94. Striking Train Unlocked and Running.
One leaf, F, of the pinion of the locking arbor sticks out far enough to
engage with the count wheel teeth and rotate the wheel one tooth for each
revolution of D, so that F forms a one-leaf pinion similar to that of a rack
striking train. Here we have our counting mechanism; F and D go around
together; F moves E one tooth every revolution. A holds C out of action
(Fig. 94) until A reaches a deep slot, when C stops the train by engaging D
(Fig. 93).
The count wheel, E, must have friction enough on its stud so that it will
stay where the pin F leaves it, when F goes out of action and thus it will be
in the right position to suitably engage F on the next revolution. Too much
friction of the count wheel on its stud will use too much power for F to

move it and thus slow the train; if there is too little friction here the count
wheel may get in such a position that F will get stalled on the top of a tooth
and stop the train.
The count hook, A, must strike exactly in the middle of the deep slots,
without touching the sides of the slots in entering or leaving, as to do this
would shift the position of the count wheel if the rubbing were sufficient, or
it might prevent A from falling (as A and C are both very light) and the
clock would go on striking. If the hook A does not strike the middle of the
spaces between the teeth of the count wheel, it will gradually encroach on a
tooth and push the wheel forward or back, thus disarranging the count.
Many a clock has struck 13 for 12 in this way because the hook was a little
out. This did not occur in the smaller numbers because the action was not
continued long enough to allow the hook to reach a tooth. The pin, F,
should also mesh fairly and freely in the teeth of the count wheel, or a
similar defect is likely to occur.
When repairing or making new count hooks, A, Figs. 93 and 94, they
must be of such a length that they will enter the slots on a line radial with
the center of the wheel. The proper length and direction are shown at A,
Fig. 95, while B and C are wrong. With hooks like either B or C you can set
or bend the hook to strike right at one and as you turn the clock ahead the
hook does not fall in far enough and at twelve it only strikes eleven. Then if
you bend the same hook to strike right at twelve it will strike two at one and
as you turn the clock ahead it will strike right at about five or seven. A, Fig.
95, being of the proper length and shape will give no trouble. Many of the
count wheels of the older clocks were divided by hand and are not as
accurate as they should be; when a wheel of this kind is found and a new
wheel cannot be substituted (because the clock is an antique and must have
the original parts preserved) it will sometimes require nice management of
the hook A to obtain correct striking. A little manipulation of the pinion, F,
Fig. 93 is sometimes desirable also, if the count wheel is very bad.

Fig. 95. The proper length of the count hook.
The locking face of the cam, D, must also be on a line radial to its
center, or it will either unlock too easily and go off on the slightest jar or
movement of the clock, or the face will have too much draw and the hook C
will not be unlocked when the clock is fully wound, and the spring pressure
is greatest. In this case the clock will not strike when fully wound, but will
do so when partly run down, and as the count wheel train strikes in rotation,
without regard to the position of the hands, you will have irregular striking
of a most puzzling sort. Repairs to this notch are sometimes required, when
the corner has become rounded, and the best way to make them is to cut a
new face on the cam with a sharp graver, being careful to keep the face
radial with its center.
Because the count wheel strikes the hours in rotation, regardless of the
position of the hands, if the hands are turned backwards past the figure 12
on the dial the striking will be thrown out of harmony with the hands. To
remedy this the count hook, A, has an eye on its rear end and a wire, shown
in Fig. 92, hangs down to where it can be reached with the hand when the

dial is on. Pulling this wire will lift A and C and cause the clock to strike;
by this means the clock may be struck around until the position of the
striking train agrees with that of the hands. Where this wire is not present
the striking is corrected by turning the hands back and forth between IX and
XII until the proper hour is struck.
Now we come to the releasing mechanism, which causes the clock to
strike at stated times. I, Figs. 93 and 94, is an arbor pivoted between the
plates and carrying three levers, H, K and J, in different positions on the
arbor. H is directly under the count hook, A, and lifts A and C whenever J is
pushed far enough to one side by L on the center arbor, which revolves once
an hour. Thus L, through J, H and A, C, unlocks the train once every hour.
When C is thus lifted the train runs until the warning pin, O, Figs. 93 and
94, strikes against the lever K, which is on the same arbor with H and J.
This preliminary run of the train makes a little noise and is called
“warning,” as the noise notifies us that the train is in position to commence
striking. The lever K and the warning pin, O, then hold the train until L has
been carried out of action with J and released it, when O will push K out of
its path at every revolution and the clock will strike.
The half hours are struck by L¹ pressing the short hammer tail, G¹, and
thus raising and releasing the hammer once an hour.
In setting up the striking train after cleaning, place the pin wheel so that
the hammer tail, G, may be about one-fourth of the distance from the next
pin, as shown in Fig. 93; this allows the train to get well under way before
meeting with any resistance and will insure its striking when nearly run
down. If the hammer tail is too close to the pin, it might stop the train when
there is but little power on.
Then place D in the locked position, with A in a deep slot of the count
wheel and C in the notch of D. Next place the warning wheel with its pin,
O, on the opposite side of its arbor from the lever K, see Fig. 93. This is
done to make sure that when it is unlocked for “warning” the train will run
far enough to get the corner of the lock, D, safely, past C, so that it will not
allow C to fall into the notch again and lock the train when J, K and H are
released by L. This is the rule followed in assembling these clocks at the
factories and is simple, correct and easily understood. A study of these