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.
[Illustration: 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.
[Illustration: 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.
[Illustration: Fig. 7. Wood rod and lead bob.
Fig. 8. Bob of metal casing 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.
-----------+------------------------
| Weight in Pounds.
Diameter +--------+-------+-------
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
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.
[Illustration: Fig. 9. Pendulum with compensated rod of steel and zinc.]
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 iron and zinc sections
where 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, ³/₁₆ 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.
[Illustration: 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.