H H and I I are two flat rods of iron about an eighth of
an inch thick. K K is a bar of zinc placed between them, and is
nearly a quarter of an inch thick. The corners of the iron bars are
bevelled off, which gives them a much lighter appearance. These bars
are kept together by means of three screws, O O O, which
pass through oblong holes in the bars H H and K K, and screw
into the rod I I. The bar H H is fastened to the bar of zinc
K K, by the screw _m_, which is called the adjusting screw. This
screw is tapped into H H, and passes just through K K; but
that part of the screw which passes K K has its threads turned
off. The iron bar I I has a shoulder at its upper end, and rests
on the top of the zinc bar K K and is wholly supported by it.
There are several holes for the screw _m_, in order to adjust the
compensation.
The action of this pendulum is similar to that last described, the
zinc expanding upwards as much as the iron rods expand downwards, and
consequently the instance from the point of suspension to the centre
of oscillation remains the same.
[Illustration: _Captn. Kater, del._ _H. Adlard, sc._
_London, Pubd. by Longman & Co._]
Mr. Ward states that the expansion of the zinc he used (hammered zinc)
was greater than that given in the tables. He found that the true
length of the zinc bar should be about 23 inches; our computation would
make it nearly 26.
_The Compensation Tube of Julien le Roy._
We mention this merely to state that it is similar in principal to the
apparatus represented at _fig. 204._, with merely this difference,
that, instead of the steel rod being fixed to a cross piece proceeding
from the brass bar B R, it is attached to a cap fixed upon a brass
tube (through which it passes) of the same length as that of the brass
rod B R. Cassini spoke well of this pendulum, and it was used in
the observatory of Cluny about the year 1748.
_Deparcieux’s Compensation._
This was contrived in the same year as that invented by Julien le Roy.
It is represented at _fig. 218._, where A B D F
is a steel bar, the ends of which are to be fixed to the lower
sides of pieces forming a part of the cock of the pendulum.
G E I H is of brass, and stands with its extremities
resting on the horizontal part B D of the steel frame. The upper
part E I of the brass frame passes above the cock of the pendulum,
and admits the tapped wire K, to which the pendulum spring is fixed
through a squared hole in the middle. A nut upon this tapped wire gives
the adjustment for time. The spring passes through the slit in the cock
in the usual manner.
It may be easily perceived that this pendulum is in principle the
same as that of Le Roy; the expansion of the total length of steel
A B S C downwards being compensated by the equivalent
expansion of the brass bar G E upwards. It is, however, preferable
to Le Roy’s, because the compensation is contained in the clock case.
Deparcieux had previously published, in the year 1739, an improvement
of an imperfectly compensating pendulum, proposed in the year 1733 by
Regnauld, a clockmaker of Chalons. In this pendulum Deparcieux employed
a lever with unequal arms to increase the effect of the expansion of
the brass rod, which was too short.
We may here remark, that all fixed compensations are liable to the same
objection, namely, that of not moving with the pendulum, and therefore
not taking precisely the same temperature.
_Captain Kater’s Compensation Pendulum._
In Nicholson’s Journal, for July, 1808, is the description of a
compensation pendulum by the writer of this article. In this pendulum
the rod is of white deal, three quarters of an inch wide, and a quarter
of an inch thick. It was placed in an oven, and suffered to remain
there for a long time until it became a little charred. The ends were
then soaked in melted sealing-wax; and the rod, being cleaned, was
coated several times with copal varnish. To the lower extremity of the
rod a cap of brass was firmly fixed, from which a strong steel screw
proceeded for the purpose of regulating the pendulum for time in the
usual manner.
A square tube of zinc was cast, seven inches long and three quarters
of an inch square; the internal dimensions being four tenths of an
inch. The lower part of the pendulum rod was cut away on the two sides,
so as to slide with perfect freedom within the tube of zinc. To the
bottom of this zinc tube a piece of brass a quarter of an inch thick
was soldered, in which a circular hole was made nearly four tenths of
an inch in diameter, having a screw on the inside. A cylinder of zinc,
furnished with a corresponding screw on its surface, fitted into this
aperture, and a thin plate of brass screwed upon the cylinder, served
as a clamp to prevent any shake after the length of zinc necessary for
compensation should have been determined. A hole was made through the
axis of the cylinder, through which passed the steel screw terminating
the pendulum rod.
An opening was made through the bob of the pendulum, extending to its
centre, to admit the square tube of zinc which was fixed at its upper
extremity to the centre of the bob. The pendulum rod passed through the
bob in the usual manner, and the whole was supported by a nut on the
steel screw at the extremity.
In this form the compensation acts immediately upon the centre of the
bob, elevating it along the rod as much as the rod elongates downwards:
the method of calculating the length of the required compensation is
precisely the same as that we have before given.
Assuming the length of the deal rod to be 43 inches, and multiplying
this by ·1313 from Table II., we have 5·64 inches for the length of
the zinc necessary to counteract the expansion of the deal. The length
of the steel screw between the termination of the pendulum rod and the
nut was two inches, and that of the suspension spring one inch. Now,
3 inches of steel multiplied by ·3682 would give 1·10 inches for the
length of zinc which would compensate the steel, and, adding this to
5·64 inches, we have 6·74 inches for the whole length of zinc required.
In this pendulum, the length of the compensating part may be varied by
means of the zinc cylinder furnished with a screw for that purpose.
The bob of this pendulum and its compensation are represented at
_fig. 219._
It has been objected to the use of wooden pendulum rods, that it
is difficult, if not impossible, to secure them from the action of
moisture, which would at once be fatal to their correct performance.
The pendulum now before us has, however, been going with but little
intermission since it was first constructed: it is attached to a
sidereal clock, not of a superior description, and exposed to very
considerable variations of moisture and dryness; yet the change in its
rate has been so very trifling as to authorize the belief that moisture
has little or no effect upon a wooden rod prepared in the manner we
have described. Its rate, under different temperatures, shows that it
is over-compensated; the length of the zinc remaining, as stated in
Nicholson’s Journal 7·42 inches, instead of which it appears, by our
present compensation, that it should be 6·78 inches.
_Reid’s Compensation Pendulum._
Mr. Adam Reid of Woolwich presented to the Society of Arts, in 1809, a
compensation pendulum, for which he was rewarded with fifteen guineas.
This pendulum is the same in principle with that last described;
the rod, however, is of steel instead of wood, and the compensation
possesses no means of adjustment. This pendulum is represented at
_fig. 220._, where S B is the steel rod, a little thicker
where it enters the bob C, and of a lozenge shape to prevent the bob
turning, but above and below it is cylindrical.
A tube of zinc D passes to the centre of the bob from below, and the
bob is supported upon it by a piece which crosses its centre, and which
meets the upper end of the tube.
The rod being passed through the bob and zinc tube, a nut is applied
upon a screw at the lower extremity of the rod in the usual manner. If
the compensation should be too much, the zinc tube is to be shortened
until it is correct.
The length of the zinc tube will be the same in this pendulum as in
that of Mr. Ward--about 23 inches, if his experiments are to be relied
upon.
The objection to this pendulum appears to be its great length, which
amounts to 62 inches. We conceive it would be preferable to place the
zinc above the bob, as in the modification which we have suggested of
Benzenberg’s pendulum.
_Ellicott’s Pendulum._
It appears that the idea of combining the expansions of different
metals with a lever, so as to form a compensation pendulum,
originated with Mr. Graham; for Mr. Short, in the Philosophical
Transactions for 1752, states that he was informed by Mr. Shelton, that
Mr. Graham, in the year 1737, made a pendulum, consisting of three
bars, one of steel between two of brass; and that the steel bar acted
upon a lever so as to raise the pendulum when lengthened by heat, and
to let it down when shortened by cold.
[Illustration: _Captn. Kater, del._ _H. Adlard, sc._
_London, Pubd. by Longman & Co._]
This pendulum, however, was found upon trial to move by jerks, and was
therefore laid aside by the inventor to make way for the mercurial
pendulum.
Mr. Short also says that Mr. Fotheringham, a quaker of Lincolnshire,
caused a pendulum to be made, in the year 1738 or 1739, consisting of
two bars, one of brass and the other of steel, fastened together by
screws with levers to raise or let down the bob, and that these levers
were placed above the bob.
Mr. John Ellicott of London had made very, accurate experiments on the
relative expansions of seven different metals, which, however, will be
found to differ more or less from the results of the experiments of
others. It is not, however, from this to be concluded that Ellicott’s
determinations were erroneous; for the expansion of a metal will suffer
considerable change even by the processes to which it is necessarily
subjected in the construction of a pendulum. It is therefore desirable,
whenever a compensation pendulum is to be made, that the expansions
of the materials employed should be determined after the processes of
drilling, filing, and hammering have been gone through.
It had been objected to Harrison’s gridiron pendulum, that the
adjustments of the rods was inconvenient, and that the expansion of the
bob supported at its lower edge would, unless taken into the account,
vitiate the compensation. These considerations, it is supposed, gave
rise to Ellicott’s pendulum, which is nearly similar to those we have
just mentioned.
Ellicott’s pendulum is thus constructed:--A bar of brass and a bar of
iron are firmly fixed together at their upper ends, the bar of brass
lying upon the bar of iron, which is the rod of the pendulum. These
bars are held near each other by screws passing through oblong holes in
the brass, and tapped into the iron, and thus the brass is allowed to
expand or contract freely upon the iron with any change of temperature.
The brass bar passes to the centre of the bob of the pendulum, a little
above and below which the iron is left broader for the purpose of
attaching the levers to it, and the iron is made of a sufficient length
to pass quite through the bob of the pendulum.
The pivots of two strong steel levers turn in two holes drilled in
the broad part of the iron bar. The short arms of these levers are in
contact with the lower extremity of the brass bar, and their longer
arms support the bob of the pendulum by meeting the heads of two
screws which pass horizontally from each side of the bob towards its
centre. By advancing these screws towards the centre of the bob, the
longer arms of the lever are shortened, and thus the compensation may
be readily adjusted. At the lower end of the iron rod, under the bob,
a strong double spring is fixed, to support the greater part of the
weight of the bob by its pressure upwards against two points at equal
distances from the pendulum rod. Mr. Ellicott gave a description of
this pendulum to the Royal Society in 1752, but he says the thought was
executed in 1738. As this pendulum is very seldom met with, we think it
unnecessary to give a representation of it.
_Compensation by means of a Compound Bar of Steel and Brass._
Several compensations for pendulums have been proposed, by means of
a compound bar formed of steel and brass soldered together. In a
bar of this description, the brass expanding more than the steel,
the bar becomes curved by a change of temperature, the brass side
becoming convex and the steel concave with heat. Now, if a bar of
this description have its ends resting on supports on each side the
cock of the pendulum, the bar passing above the cock with the brass
uppermost, if the pendulum spring be attached to the middle of the bar,
and it pass in the usual manner through the slit of the cock, it is
evident that, by an increase of temperature, the bar will become curved
upwards, and the pendulum spring be drawn upwards through the slit, and
thus the elongation of the pendulum downwards will be compensated. The
compensation may be adjusted by varying the distance of the points of
support from the middle of the bar.
Such was one of the modes of compensation proposed by Nicholson. Others
of the same description (that is, with compound bars) have been brought
before the public by Mr. Thomas Doughty and Mr. David Ritchie; but as
they are supposed to be liable to many practical objections, we do not
think it requisite to describe them more particularly.
There is, however, a mode of compensation by means of a compound bar,
described by M. Biot in the first volume of his Traité de Physique,
which appears to possess considerable merit, of which he mentions
having first witnessed the successful employment by the inventor, a
clockmaker named Martin. At _fig. 221._, S C, is the rod of
the pendulum, made, in the usual manner, of iron or steel; this rod
passes through the middle of a compound bar of brass and steel (the
brass being undermost), which should be furnished with a short tube and
screws, by means of which, or by passing a pin through the tube and
rod, it may be securely fixed at any part of the pendulum rod.
Two small equal weights W W slide along the compound bar, and,
when their proper position has been determined, may be securely clamped.
The manner in which this compensation acts is thus:--Suppose the
temperature to increase, the brass expanding more than the steel, the
bar becomes curved, and its extremities carrying the weights W and W
are elevated, and thus the place of the centre of oscillation is made
to approach the point of suspension as much, when the compensation is
properly adjusted, as it had receded from it by the elongation of the
pendulum rod.
There are three methods of adjusting this compensation: the first, by
increasing or diminishing the weights W and W; the second, by varying
the distance of the weights W and W from the middle of the bar; and
the third, by varying the distance of the bar from the bob of the
pendulum, taking care not to pass the middle of the rod. The effect of
the compensation is greater as the weights W and W are greater or more
distant from the centre of the bar, and also as the bar is nearer to
the bob of the pendulum.
M. Biot says that he and M. Matthieu employed a pendulum of this kind
for a long time in making astronomical observations in which they were
desirous of attaining an extreme degree of precision, and that they
found its rate to be always perfectly regular.
In all the pendulums which we have described, the bob is supposed
to be fixed to the rod by a pin passing through its centre, and the
adjustment for time is to be made by means of a small weight sliding
upon the rod.
_Of the Mercurial Pendulum._
We have been guided, in our arrangement of the pendulums which we have
described, by the similarity in the mode of compensation employed; and
we have now to treat of that method of compensation which is effected
by the expansion of the material of which the bob itself of the
pendulum is composed.
On this subject, as we have before observed, an admirable paper, from
the pen of Mr. Francis Baily, may be found in the Memoirs of the
Astronomical Society of London, which leaves nothing to be desired
by the mathematical reader. But as our object is to simplify, and
to render our subjects as popular as may be, we must endeavour to
substitute for the perfect accuracy which Mr. Baily’s paper presents,
such rules as may be found not only readily intelligible, but
practically applicable, within the limits of those inevitable errors
which arise from a want of knowledge of the exact expansion of the
materials employed.
At _fig. 222._, let S B represent the rod of a pendulum, and
F C B a metallic tube or cylinder, supported by a nut
at the extremity of the pendulum rod, in the usual manner, and having
a greater expansibility than that of the rod. Now C, the centre of
gravity, supposing the rod to be without weight, will be in the middle
of the cylinder; and if C B, or half the cylinder, be of such
a length as to expand upwards as much as the pendulum rod S B
expands downwards, it is evident that the centre of gravity C will
remain, under any change of temperature, at the same distance from the
point of suspension S. M. Biot imagined that, in effecting this, a
compensation sufficiently accurate would be obtained; but Mr. Baily has
shown that this is by no means the fact.
Let us suppose the place of the centre of oscillation to be at O,
about three or four tenths of an inch, in a pendulum of the usual
construction, below the centre of gravity. Now, the object of the
compensation is to preserve the distance from S to O invariable, and
not the distance from S to C.
The distance of the centre of oscillation varies with the length of the
cylinder F B, and hence suffers an alteration in its distance from
the point of suspension by the elongation of the cylinder, although
the distance of the centre of gravity C from the point of suspension
remains unaltered.
We shall endeavour to render this perfectly familiar. Suppose a
metallic cylinder, 6 inches long, to be suspended by a thread 36 inches
long, thus forming a pendulum in which the distance of the centre
of gravity from the point of suspension is 39 inches: the centre of
oscillation in such a pendulum will be nearly one tenth of an inch
below the centre of gravity. Now let us imagine cylindrical portions of
equal lengths to be added to each end of the cylinder, until it reaches
the point of suspension; we shall then have a cylinder of 78 inches in
length, the centre of gravity of which will still be at the distance of
39 inches from the point of suspension. But it is well known that the
centre of oscillation of such a cylinder is at the distance of about
two thirds of its length from the point of suspension. The centre of
oscillation, therefore, has been removed, by the elongation of the
cylinder, about 13 inches below the centre of gravity, whilst the
centre of gravity has remained stationary.
Now the same thing as that which we have just described takes place,
though in a very minor degree, with our former cylinder, employed as a
compensating bob to a pendulum. The rod expands downwards, the centre
of gravity remains at the same distance from the point of suspension,
and the cylinder elongates both above and below this point; the
consequence of which is, that though the centre of gravity has remained
stationary, the distance of the centre of oscillation from the point
of suspension has increased. It is, therefore, evident that the length
of the compensation must be such as to carry the centre of gravity
a little nearer to the point of suspension than it was before the
expansion took place; by which means the centre of oscillation will be
restored to its former distance from the point of suspension.
Let us suppose the expansions to have taken place, and that the
centre of gravity, remaining at the same distance from the point of
suspension, the centre of oscillation is removed to a greater distance,
as we have before explained. It is well known that the product obtained
by multiplying the distance from the point of suspension to the centre
of gravity, by the distance from the centre of gravity to the centre
of oscillation, is a constant quantity; if, therefore, the distance
from the centre of gravity to the point of suspension be lessened, the
distance from the centre of gravity to the centre of oscillation will
be proportionally, though not equally, increased, and the centre of
oscillation will, therefore, be elevated. We see, then, if we elevate
the centre of gravity precisely the requisite quantity, by employing
a sufficient length of the compensating material, that although the
distance from the centre of gravity to the point of suspension is
lessened, yet the distance from the point of suspension to the centre
of oscillation will suffer no change.
The following rule for finding the length of the compensating material
in a pendulum of the kind we have been considering will be found
sufficiently accurate for all practical purposes:--
_Find in the manner before directed the length of the compensating
material, the expansion of which will be equal to that of the rod of
the pendulum. Double this length, and increase the product by its
one-tenth part, which will give the total length required._ We shall
give examples of this as we proceed.
_Graham’s Mercurial Pendulum._
It was in the year 1721 that Graham first put up a pendulum of this
description, and subjected it to the test of experiment; but it appears
to have been afterwards set aside to make way for Harrison’s gridiron
pendulum, or for others of a similar description. For some years past,
however, its merits have been more generally known, and it is not
surprising that it should be considered as preferable to others, both
from the simplicity of its construction, and the perfect ease with
which the compensation may be adjusted.
We have already alluded to Mr. Baily’s very able paper on this
pendulum, and we shall take the liberty of extracting from it the
following description:--
At _fig. 223._ is a drawing of the mercurial pendulum, as
constructed in the manner proposed by Mr. Baily.