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.
[Illustration: Fig. 13.]
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 ⁵/₁₆ inch diameter; jar about
2.1 inches diameter inside and 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.
[Illustration: 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.
[Illustration: COLUMN OF MERCURY Fig. 15.]
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, 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.