Graham, but it was too bulky and inconvenient for use. M. le Roy made
one of a more simple construction. It consisted of a metal tube, about
a foot long, placed vertically upon a stand, and containing in the
inside a spiral spring, having above it a graduated rod terminating in
a globe. This rod entered the tube more or less in proportion to the
force applied to the globe, and the divisions indicated the quantity of
this force. Therefore, when a man pressed upon the globe with all his
strength, the divisions upon the rod showed the number of pounds weight
to which it was equal.
An instrument of this kind for determining the force of a blow struck
by a man with his fist was lately exhibited at the National Repository.
It was fixed to a wall, from which it projected horizontally. In
place of the globe there was a cushion to receive the blow, and as
the suddenness with which the spring returned rendered it impossible
to read the division upon the rod, another rod similarly divided was
forced in by the plate forming the basis of the cushion, and remained
stationary when the spring returned. The common spring steelyard,
however, which we first described, is in principle the same as M. le
Roy’s dynamometer, and is much more conveniently constructed for the
purpose we are considering. The ring at one end may be fixed to an
immovable object, and the hook at the other attached to a man, or to
an animal, and the extent to which the graduated rod is drawn out of
the cylinder shows at once the force which is applied. Though this is
perhaps the best, and certainly the most simple dynamometer, others
have been contrived, which are, however, but modifications of the
spring steelyard. One of these is represented at _fig. 202._ The
spiral spring acts in the manner before described, but its divisions
are increased in size, and therefore rendered more perceptible by means
of a rack fixed to the plate, acting against the spiral spring, the
teeth of which move a pinion upon which the arm I is fixed, pointing to
the graduated arc K.
Another dynamometer has been invented by Mr. Salmon; it is represented
at _fig. 203._ and is a combination of levers with the spring.
By means of these levers a much more delicate spring, and which is
therefore more sensible, may be employed than in the dynamometer last
described.
The manner in which these levers and spring act will be readily
understood by an inspection of the figure. Like the weighing machine
for carriages, the fulcrum of each lever is at one end, and the force
is diminished in passing to the spring, in the ratio of the length of
its arms. The spring moves a pinion by means of a rack, upon which
pinion a hand is placed, indicating by divisions upon a circular
dial-plate, the amount of the force employed.
The spring used in this machine is calculated to weigh only about
50 lbs. instead of about 5 cwt., as in the last described;
but by means of the levers which intervene between it and the force
applied, it will serve to estimate a force equal to 6 cwt., and
might obviously be made to go to a much greater extent, by varying the
ratio of the length of the arms of the levers.
ON COMPENSATION PENDULUMS.
(336.) It is said of Galileo that, when very young, he observed a
lamp suspended from the roof of a church at Pisa, swinging backwards
and forwards with a pendulous motion. This, if it had been remarked
at all by an uneducated mind, would, most probably, have been passed
by as a common occurrence, unworthy of the slightest notice; but to
the mind imbued with science no incident is insignificant; and a
circumstance apparently the most trivial, when subjected to the giant
force of expanded intellect, may become of immense importance to the
improvement and to the well-being of man. The fall of an apple, it is
said, suggested to Newton the theory of gravitation, and his powerful
mind speedily extended to all creation that great law which brings an
apple to the ground. The swinging of a lamp in a church at Pisa, viewed
by the piercing intellect of Galileo, gave rise to an instrument which
affords the most perfect measure of time, which serves to determine the
figure of the earth, and which is inseparably connected with all the
refinements of modern astronomy.
The properties of the pendulum, and the manner in which it serves
to measure time, have been fully explained in chapter xi.; and if
a substance could be found not susceptible of any change in its
dimensions from a change of temperature, nothing more would be
necessary, as the centre of oscillation would always remain at the
same distance from the point of suspension. As every known substance,
however, expands with heat, and contracts with cold, the length of the
pendulum will vary with every alteration of temperature, and thus the
time of its vibration will suffer a corresponding change. The effect
of a difference of temperature of 25°, or that which usually occurs
between winter and summer, would occasion a clock furnished with a
pendulum having an iron rod to gain or lose six seconds in twenty-four
hours.
It became, then, highly important to discover some means of
counteracting this variation to which the length of the pendulum was
liable, or, in other words, to devise a method by which the centre of
oscillation should, under every change of temperature, remain at the
same distance from the point of suspension: happily, the difference in
the rate of expansion of different metals presented a ready means of
effecting this.
Graham, in the year 1715, made several experiments to ascertain the
relative expansions of various metals, with a view of availing himself
of the difference of the expansions of two or more of them when opposed
to each other, to construct a compensating pendulum. But the difference
he found was so small, that he gave up all hope of being able to
accomplish his object in that way. Knowing, however, that mercury was
much more affected by a given change of temperature than any other
substance, he saw that if the mercury could be made to ascend while
the rod of the pendulum became longer, and _vice versâ_, the centre of
oscillation might always be kept at the same distance from the point
of suspension. This idea happily gave birth to the mercurial pendulum,
which is now in very general use.
[Illustration: _Captn. Kater, del._ _H. Adlard, sc._
_London, Pubd. by Longman & Co._]
In the mean time, Graham’s suggestion excited the ingenuity of
Harrison, originally a carpenter at Barton in Lincolnshire, who, in
1726, produced a pendulum formed of parallel brass and steel rods,
known by the name of the gridiron pendulum.
In the mercurial pendulum, the bob or weight is the material affording
the compensation; but in the gridiron pendulum the object is attained
by the greater expansion of the brass rods, which raise the bob upwards
towards the point of suspension as much as the steel rods elongate
downwards.
In the present article, we shall describe such compensation pendulums
as appear to us likely to answer best in practice; and we trust we
shall be able to simplify the subject so as to render a knowledge
of mathematics in the construction of this important instrument
unnecessary.
The following table contains the linear expansion of various substances
in parts of their length, occasioned by a change of temperature
amounting to one degree. We have taken the liberty of extracting
it from a very valuable paper by F. Bailey, Esq., on the mercurial
compensation pendulum, published in the Memoirs of the Astronomical
Society of London for 1824.
TABLE I.
_Linear Expansion of various Substances for One Degree of Fahrenheit’s
Thermometer._
+----------------------+-------------+-----------------------+
| Substances. | Expansions. | Authors. |
+----------------------+-------------+-----------------------+
|White Deal, { | ·0000022685 | Captain Kater. |
| { | ·0000028444 | Dr. Struve. |
|English Flint Glass, | ·0000047887 | Dulong and Petit. |
|Iron (cast), { | ·0000061700 | General Roy. |
| { | ·0000065668 | Dulong and Petit. |
|Iron (wire), | ·0000068613 | Lavoisier and L. |
|Iron (bar), | ·0000069844 | Hasslar. |
|Steel (rod), | ·0000063596 | General Roy. |
| | | {Commissioners of |
|Brass, | ·0000104400 | {Weights and Measures |
| | | {--mean of several |
| | | {experiments. |
|Lead, | ·0000159259 | Smeaton. |
|Zinc, | ·0000163426 | Ditto. |
|Zinc (hammered), | ·0000172685 | Ditto. |
|Mercury _in bulk_, | ·00010010 | Dulong and Petit. |
+----------------------+-------------+-----------------------+
From this table it is easy to determine the length of a rod of any
substance the expansion of which shall be equal to that of a rod of
given length of any other substance.
The lengths of such rods will be inversely proportionate to their
expansions. If, therefore, we divide the lesser expansion by the
greater (supposing the rod the length of which is given to be made of
the lesser expansible material), and multiply the given length by this
quotient, we shall have the required length of a rod, the expansion
of which will be equal to that of the rod given. For example:--The
expansion of a rod of steel being, from the above table, ·0000063596,
and that of brass, ·0000104400; if it were required to determine the
length of a rod of brass which should expand as much as a rod of steel
of 39 inches in length, we have ·0000063596/·0000104400 = ·6091, which,
multiplied by 39, gives 23·75 inches for the length of brass required.
We shall here, in order to facilitate calculation, give the ratio of
the lengths of such substances as may be employed in the construction
of compensation pendulums.
TABLE II.
+---------------------------------------------------+
| Steel rod and brass compensation, as 1: ·6091 |
| Iron wire rod and lead compensation, ·4308 |
| Steel rod and lead compensation, ·3993 |
| Iron wire rod and zinc compensation, ·3973 |
| Steel rod and zinc compensation, ·3682 |
| Glass rod and lead compensation, ·3007 |
| Glass rod and zinc compensation, ·2773 |
| Deal rod and lead compensation, ·1427 |
| Deal rod and zinc compensation, ·1313 |
| Steel rod and mercury in a steel cylinder, ·0728 |
| Steel rod and mercury in a glass cylinder, ·0703 |
| Glass rod and mercury in a glass cylinder, ·0529 |
+---------------------------------------------------+
It is evident that in this table the decimals express the length of a
rod of the compensating material, the expansion of which is equal to
that of a pendulum rod whose length is unity.
As we are not aware of the existence of any work which contains
instructions that might enable an artist or an amateur to make a
compensation pendulum, we shall endeavour to give such detailed
information as may free the subject from every difficulty.
The pendulum of a clock is generally suspended by a spring, fixed
to its upper extremity, and passing through a slit made in a piece
which is called the cock of the pendulum. The point of suspension is,
therefore, that part of the spring which meets the lower surface of the
cock. Now the distance of the centre of oscillation of the pendulum
from this point may be varied in two ways; the one by drawing up the
spring through this slit, and the other by raising the bob of the
pendulum. Either of these methods may be practised in the compensation
pendulum, but the former is subject to objections from which the latter
is exempt.
Suppose it were required to compensate a pendulum of 39 inches in
length, of steel, by means of the expansion of a brass rod. Here,
referring to _fig. 204._, we have S C 39 inches (which is
to remain constant) of steel; the pendulum spring, passing through
the cock at S, is attached to another rod of steel, which is fixed to
the cross piece R A at A. The other end of the cross piece at R
is fastened to a brass rod, the lower extremity of which is fixed to
the cock of the pendulum at B. Now the brass rod B R must expand
upwards, as much as the steel rod A C expands downwards; and the
length of the brass must be such as to effect this, leaving 39 inches
of the steel rod below the cock of the pendulum.
Let us first try 80 inches of steel. Multiplying this by ·6091, we have
48·73 inches for the length of brass, which compensates 80 inches of
steel. But as 48·73 inches of the steel, equal in length to the brass,
would in this case be above the cock of the pendulum, it would leave
only 31·27 inches below it, instead of 39 inches.
Let us now try 100 inches of steel. This, multiplied as before by
·6091, gives 60·91 inches, according to the expansions which we have
used, for the length of the brass rod, and leaves 39·09 inches below
the cock of the pendulum, which is sufficiently near for our present
purpose.
From what has been said we may perceive that the total length of the
material of which the pendulum rod is composed must be always equal to
the length of the pendulum added to the length of the compensation.
In this instance we have effected our object, by drawing the
pendulum-spring through the slit; but we will now show how the
same thing may be done by moving the bob of the pendulum. At
_fig. 205._, let S C, as before, be equal to 39 inches. Let
the steel rod S D turn off at right angles at D, and let a rod
of brass B R, of 61 inches in length, ascend perpendicularly from
this cross piece to R. To the upper part of the brass rod fix another
cross piece R A, and from the extremity A let a steel rod descend
to E, bending it as in the figure till it reaches C. Now the total
length of the pieces of steel expanding downwards is equal to S D,
D F, and F C (amounting together to 39 inches), to which must
be added a length of steel equal to that of the brass rod B R, (61
inches), making together 100 inches of steel as before, the expansion
of which downwards is compensated by that of the brass rod, of 61
inches in length, expanding upwards.
This form, however, is evidently inconvenient, from the great length
of brass and steel which is carried above the cock of the pendulum;
but it is the same thing whether the brass and steel be each in one
piece, or divided into several, provided the pieces of steel be all
so arranged as to expand downwards, and those of brass upwards. Thus,
at _fig. 206._, the portions of steel expanding downwards are
together equal, as before, to 100 inches, and the two brass pieces
expanding upwards are together equal to 61 inches. So that, in fact,
the two last forms of compensation which we have described differ in
no respect from each other in principle, but only in the arrangement
of the materials. The last is the half of the gridiron pendulum, the
remaining bars being merely duplicates of those we have described, and
serving no other purpose but to form a secure frame-work.
_Harrison’s Gridiron Pendulum._
After what has been said, little more is necessary than to give a
representation of this pendulum. This is done at _fig. 207._, in
which the darker lines represent the steel rods, and the lighter those
of brass. The central rod is fixed at its lower extremity to the middle
of the third cross piece from the bottom, and passes freely through
holes in the cross pieces which are above, whilst the other rods are
secured near their extremities to the cross pieces by pins passing
through them. In order to render the whole more secure, the bars pass
freely through holes made in two other cross pieces, the extremities of
which are fixed to the exterior steel wires. As different kinds of the
same metal vary in their rate of expansion, the pendulum when finished
may be found upon trial to be not duly compensated. In this case one or
more of the cross pieces is shifted higher or lower upon the bars, and
secured by pins passed through fresh holes.
_Troughton’s Tubular Pendulum._
This is an admirable modification of Harrison’s gridiron pendulum.
It is represented at _fig. 208._, where it may be seen that it
has the appearance of a simple pendulum, as the whole compensation is
concealed within a tube six tenths of an inch in diameter.
A steel wire, about one tenth of an inch in diameter, is fixed in the
usual manner to the spring by which the pendulum is suspended. This
wire passes to the bottom of an interior brass tube, in the centre of
which it is firmly screwed. The top of this tube is closed, the steel
rod passing freely through a hole in the centre. Into the top of this
interior tube two steel wires, of one tenth of an inch in diameter,
are screwed into holes made in that diameter, which is at right angles
to the motion of the pendulum. These wires pass down the tube without
touching either it or the central rod, through holes made in the piece
which closes the bottom of the interior tube. The lower extremities of
these wires, which project a little beyond the inner tube, are securely
fixed in a piece which closes the bottom of an exterior brass tube,
which is of such a diameter as just to allow the interior tube to pass
freely through it, and of a sufficient length to extend a little above
it. The top of the exterior tube is closed like that of the interior,
having also a hole in its centre, to allow the first steel rod to pass
freely through it. Into the top of the exterior tube, in that diameter
which coincides with the motion of the pendulum, a second pair of
steel wires of the same diameter as the former are screwed, their
distance from the central rod being equal to the distance of each from
the first pair. They consequently pass down within the interior tube,
and through holes made in the pieces closing the lower ends of both the
interior and exterior tubes. The lower ends of these wires are fastened
to a short cylindrical piece of brass of the same diameter as the
exterior tube, to which the bob is suspended by its centre.
[Illustration: _Captn. Kater, del._ _H. Adlard, sc._
_London, Pubd. by Longman & Co._]
_Fig. 209._ is a full sized section of the rod; the three
concentric circles represent the two tubes, and the rectangular
position of the two pair of wires round the middle one is shown by the
five small circles.
_Fig. 210._ is the part which closes the upper end of the interior
tube. The two small circles are the two wires which proceed from it,
and the three large circles show the holes through which the middle
wire and the other pair of wires pass.
_Fig. 211._ is the bottom of the interior tube. The small circle
in the centre is where the central rod is fastened to it, the others
the holes for the other four wires to pass through.
_Fig. 212._ is the part which closes the top of the external tube.
In the large circle in the centre a small brass tube is fixed, which
serves as a covering for the upper part of the middle wire, and the two
small circles are to receive the wires of the last expansion.
_Fig. 213._ represents the bottom of the exterior tube, in which
the small circles show the places where the wires of the second
expansion are fastened, and the larger ones the holes for the other
pair of wires to pass through.
_Fig. 214._ is a cylindrical piece of brass, showing the manner in
which the lower ends of the wires of the last expansion are fastened
to it, and the hole in the middle is that by which it is pinned to
the centre of the bob. The upper ends of the two pair of wires are,
as we have observed, fastened by screwing them into the pieces which
stop up the ends of the tubes, but at the lower ends they are all
fixed as represented in _fig. 214._ The pieces represented by
_figs. 213._ and _214._ have each a jointed motion, by means
of which the fellow wires of each pair would be equally stretched,
although they were not exactly of the same length.
The action of this pendulum is evidently the same as that of the
gridiron pendulum, as we have three lengths of steel expanding
downwards, and two of brass expanding upwards. The weight of the
pendulum has a tendency to straighten the steel rods, and the tubular
form of the brass compensation effectually precludes the fear of its
bending; an advantage not possessed by the gridiron pendulum, in which
brass rods are employed.
Mr. Troughton, to the account he has given of this pendulum in
Nicholson’s Journal, for December, 1804, has added the lengths of
the different parts of which it was composed, and the expansions of
brass and steel from which these lengths were computed. The length of
the interior tube was 31·9 inches, and that of the exterior one 32·8
inches, to which must be added 0·4, the quantity by which in this
pendulum the centre of oscillation is higher than the centre of the
bob. These are all of brass. The parts which are of steel are,--the
middle wire, which, including 0·6, the length of the suspension spring,
is 39·3 inches. The first pair of wires 32·5 inches; and the second
pair, 33·2 inches. The expansions used were, for brass ·00001666,
and for steel ·00000661, in parts of their length for one degree of
temperature.
_Benzenberg’s Pendulum._
This pendulum is mentioned in Nicholson’s Journal for April, 1804, and
is taken from Voigt’s Magazin für den Neuesten Zustande der Naturkunde,
vol. iv. p. 787. The compensation appears to have been
effected by a single rod of lead in the centre, of about half an inch
thick; the descending rods were made of the best thick iron wire.
As this pendulum deserves attention from the ease with which it may
be made, and as others which have since been produced resemble it in
principle, we have given a representation of it at _fig. 215._,
where A B C D are two rods of iron wire riveted into the
cross pieces A C B D. E F is a rod of lead pinned
to the middle of the piece B D, and also at its upper extremity
to the cross piece G H, into which the second pair of iron wires
are fixed, which pass downwards freely through holes made in the cross
piece B D. The lower extremities of these last iron wires are
fastened into the piece K L, which carries the bob of the pendulum.
To determine the length of lead necessary for the compensation, we must
recollect, as before, that the distance from the point of suspension
to the centre of the bob (speaking always of a pendulum intended to
vibrate seconds) must be 39 inches. Let us suppose the total length
of the iron wire to be 60 inches; then, from the table which we have
given, we have ·4308 for the length of a rod of lead, the expansion
of which is equivalent to that of an iron rod whose length is unity.
Multiplying 60 inches by ·4308, we have 25·84 inches of lead, which
would compensate 60 inches of iron; but this, taken from 60 inches,
leaves only 34·16 instead of 39 inches. Trying again, in like manner,
68·5 inches of iron, we find 29·5 inches of lead for the length,
affording an equivalent compensation, and which, taken from 68·5
inches, leaves 39 inches.
The length of the rod of lead then required as a compensation in this
pendulum is about 29-1/2 inches.
The writer of this article would suggest another form for this
pendulum, which has the advantage of greater simplicity of construction.
S A, _fig. 216._, is a rod of iron wire, to which the
pendulum spring is attached. Upon this passes a cylindrical tube of
lead, 29-1/2 inches long, which is either pinned at its lower extremity
to the end of the iron rod S A, or rests upon a nut firmly screwed
upon the extremity of this rod.
A tube of sheet iron passes over the tube of lead, and is furnished at
top with a flanche, by which it is supported upon the leaden tube; or
it may be fastened to the top of this tube in any manner that may be
thought convenient.
The bob of the pendulum may be either passed upon the iron tube
(continued to a sufficient length) and secured by a pin passing through
the centre of the bob, or the iron tube may be terminated by an iron
wire serving the same purpose.
Here we have evidently the same expansions upwards and downwards as in
the gridiron form, given to this pendulum by Mr. Benzenberg, joined to
the compactness of Troughton’s tubular pendulum.
_Ward’s Compensation Pendulum._
In the year 1806, Mr. Henry Ward, of Blandford in Dorsetshire, received
the silver medal of the Society of Arts for the compensation pendulum
which we are about to describe.