acting for one second. Under this convention the force of
gravity, or g, will be denoted by 9.8, since when a body is
allowed to fall under the action of gravity for one second,
it is found to have acquired the velocity of 9.8 metres 'in
one second. If we consider how far this body has fallen
in one second in order to acquire this velocity, we shall find
the distance to be 4.9 metres; and if, on the other hand, we
project a body upwards with the velocity of 9.8 metres per
second, it will rise against gravity 4.9 metres in height. A
kilogramme projected vertically upwards with the velocity
of 9.8 metres per second is therefore capable of doing 4.9
units of work before it comes to rest.
Again, it is found that a body, allowed to fall for two
seconds under the influence of gravity, will have acquired the
velocity of 19.6 metres in one second, and that during this
time it will have fallen 19.6 metres. A kilogramme projected
vertically upwards with the initial velocity of 19.6 metres
per second, will therefore rise 19.6 metres in height, and
will do 19.6 units of work before it comes to rest.
We thus see that a double velocity enables the body to
do four times as much work in fine, in order to find out
how much work a body one kilogramme in weight projected
upwards with the velocity v is capable of doing, we have
only to ask how high it will rise. This will be given by
the following formula:
31 8 REMARKS ON ENERGY.
Height of Ascent or Work Done = -. (A)
Thus, if the velocity be 9.8, we have by this formula
but if the velocity be 19.6, we have
Work = ^* 9 ' ' = 19.6 as already stated.
314. A little consideration will shew us that it is not
necessary for the body to be moving with this velocity
vertically upwards in order to be capable of doing this
work ; indeed, we have only selected the force of gravity
as one of the most prominent forces against which work
is done; but the moving body may likewise be made to
do work against a spring, or even by means of a single
fixed pulley or otherwise it may be made to raise another
body against gravity. In fact, taking the words c work done '
in their most general sense, as representing space moved
over against the action of any force, we see that the above
formula (A) will hold good without reference to the direc-
tion in which the body is moving ; and if we consider
the kilogramme as denoting the unit of mass, we have the
following general expression for the work capable of being
done against any force by a body of mass m and velocity v
the unit of work being always the amount represented by
raising one kilogramme one metre against terrestrial gravity,
or the kilogrammetre as this is termed. It ought to be
borne in mind that if the force against which the work is
done is much more powerful than gravity, then a com-
paratively small space passed over against the action of
HISTORICAL AND PRELIMINARY. 319
this force will denote a large amount of work. Thus, for in-
stance, if the force were constant and ten times as powerful
as gravity, then a decimetre passed over against this force
would be equivalent to a metre against gravity. A body,
such as a kilogramme, moving with a certain velocity may
therefore be said to have a certain amount of energy i stored
up in it in virtue of this velocity. This energy is termed
energy of motion, or kinetic energy (KIVTJO-IS, motion].
315. II. Potential energy. Suppose now that this
kilogramme moves vertically upwards with the initial velocity
of 9.8 metres per second, it will rise, we have seen, to the
height of 4.9 metres. When this height has been attained
the velocity is all spent, and the body may be supposed to
be for an instant at rest. Its kinetic energy is therefore all
spent, since it has no velocity ; but this has not been spent
without some equivalent advantage being attained : the kinetic
energy has in fact been spent in acquiring for the body a
position of advantage with regard to the force of gravity, in
virtue of which, when it falls to the point of projection, it
will have reacquired the same amount of velocity, and there-
fore of kinetic energy, with which it originally started up-
wards. When the kilogramme has attained its extreme height
of 4.9 metres it has therefore converted its energy of motion, or
kinetic energy ', into energy of position, or potential energy (an
expression first generalised by Ranking and when it has again
fallen it has reconverted its potential energy into kinetic energy.
There is thus as much energy in the kilogramme at the
summit of its flight as at the moment of its discharge, only
it is of a different kind in the two cases, being in the first
potential and in the second kinetic energy; and, further, at
any intermediate point of its course its energy is partly
potential and partly kinetic ; but the sum of these two
1 The term * Energy ' is due to Young : it means the power of doing
work against gravity or any other force.
320 REMARKS ON ENERGY.
kinds of energy is constant throughout its range, so that in
the varying motion of the kilogramme there is neither crea-
tion nor destruction of energy, but simply a transmutation
from one form to another.
316. The case of a pendulum is almost precisely similar
to that just mentioned, for when the bob of a pendulum
is passing its lowest point its energy is all kinetic ; while
at its highest point the energy is all potential. We may
pass on at once from the case we have considered to any
machine, and assert that the energy of such a machine left
to itself, and neither doing work upon other bodies nor
having work done upon it, is strictly constant and limited,
although it may vary from kinetic to potential, and from
potential back again to kinetic, according to the geometric
laws of the machine. As far as regards the combinations
of ordinary mechanics this principle was clearly enunciated
by Newton, and was even to some extent recognised by
By both these philosophers a machine was regarded not
as a means of creating energy, but rather of transforming
it from a less convenient to a more convenient kind ; and
if we study the mechanical powers, as they are called, we
shall find their office to be strictly this. The truth of this
will be seen at once from a very simple illustration. If we
take a lever, one of whose arms is twice as long as the
other, a two-kilogramme weight at the end of the short
arm will balance a one-kilogramme weight at the end of the
long one; but the one-kilogramme must fall two metres
in order that the two-kilogrammes may rise one metre. Now
according to the definition of ' work ' already given, the work
spent upon the long arm by the one-kilogramme weight
falling will be two units, while that gained by the short arm
rising will also be two units.
The product of the weight into the space moved over
HISTORICAL AND PRELIMINARY. $Zl
against gravity is the same for both arms ; but while the
space- factor of this product is the larger one for the long
arm, the weight-factor is the larger one for the short arm.
317. Functions of a machine. It thus appears that
all we can do by the lever or the other mechanical powers
is to increase the one factor at the expense of the other
that is to say, either to gain force by losing space, or to
gain space by losing force. We may generalize this state-
ment so as to make it applicable to all possible machines,
and we may view these as instruments which when sup-
plied with energy in one form convert it into other forms
according to the law of the machine.
318. Conversion of mechanical energy into heat.
It is not in ordinary mechanics that the difficulty of re-
cognising the principle of the conservation of energy is
found, but rather when visible motion has been transformed
into molecular motion, or when the opposite transformation
has taken place. Thus, for instance, when an anvil is
struck by a hammer, what becomes of the energy of the
blow ? or when a railway train is stopped by the break,
what becomes of the energy of the train ?
319. The true explanation of this difficulty has done
more than anything else to forward the theory of the con-
servation of energy, and it is only of late years that the
problem has been completely solved.
In considering the subject of percussion and friction,
two simultaneous phenomena claim our attention. In the
first place, the energy of the hammer and of the railway
train disappear from the immediate cognisance of our senses
from that category which embraces visible potential and
visible kinetic energy.
In the next place, by repeated strokes of the hammer
upon the anvil we have the production of heat, nay even
of a red heat if the process be conducted sufficiently long
3 22 REMARKS ON ENERGY.
and be sufficiently rapid ; and in like manner the stoppage
of a railway train produces heat ; indeed we may see sparks
flying out from the break-wheel on a dark night.
For a long time this production of heat was regarded
as inexplicable, because, heat being looked upon as a species
of matter, it could not be imagined where all this heat came
from. The only sort of explanation was, that in the pro-
cesses of friction and percussion heat might be drawn from
neighbouring bodies, or there might be a diminution in
the thermal capacity of the two bodies acting on each
other so that caloric was supposed to be squeezed, or
rubbed, out of them, although it is not easy to see why the
same effect should take place with two such different actions
as friction and percussion. Davy, about the end of last
century, was one of the first to refute this explanation by
a very simple experiment. This consisted in rubbing two
pieces of ice violently together until it was found that
both were nearly melted by friction. The explanation of a
diminution in thermal capacity was evidently inapplicable in
this experiment, since water contains more heat than ice ;
and other experiments performed by Davy combined to shew
that the heat produced in such cases is not abstracted from
neighbouring bodies. The result derived by Davy from
these experiments was that heat implies a kind of motion of
the corpuscules of bodies.
About the same time Count Rumford was engaged in
boring cannon at the arsenal in Munich, and was struck
with the very great amount of heat developed by this
operation ; the source of this heat appeared to him to be
inexhaustible, and he was therefore led to attribute it to
Rumford, moreover, estimated approximately the quantity
of heat produced by a definite amount of mechanical
energy, and pointed out that the agitation of liquids, such
HISTORICAL AND PRELIMINARY. 323
as churning, might form a very good means of determining
the mechanical equivalent of heat. A complete determina-
tion of this equivalent was however reserved for Jou^e,
but his experiments will form the subject of another
320. Conversion of heat into mechanical energy.
The converse problem, or the rationale of ihe^ conversion
of heat into mechanical energy, was first undertaken by
Carnot, a French philosopher. He shewed that mechanical
effect is only produced by heat when there is a transfer-
ence of heat from a body of higher to one of lower tem-
perature. He likened, very ingeniously, the mechanical
power of heat to that of water, shewing that just as a body
of water at the same level can produce no mechanical
effect, so neither can bodies at the same temperature pro-
duce any mechanical effect; and just as you must have a
fall of water from a higher to a lower level in order to
obtain mechanical effect, so likewise you must have a fall
of heat from a body of higher to one of lower tem-
perature. Carnot, in his researches, adopted the old or
material theory of heat, and his principle therefore required
to be modified so as to suit the dynamical theory. This
was done nearly simultaneously by Rankine, Clausius, and
W. Thomson. Further remarks on this subject we must
defer to a future chapter.
321. Various principles of the science of energy.
It may be desirable at this stage to distinguish between
three principles or laws connected with energy. The first
of these is the principle of the conservation of energy,
which asserts that energy is as indestructible as matter
itself, and as a whole is neither created nor destroyed, but
merely changes its form.
The second problem embraces the laws which regulate
the change of -form, consistently of course with the great
* Y 2
324 REMARKS ON ENERGY. '
law of conservation, and consistently also with the third
law, or that of the dissipation of energy. Grove in this
country and Meyer on the continent have done good service
in pointing out how the various forms of energy are cor-
related, and many of those philosophers who have been
engaged with the conservation of energy, such as Joule,
Helmholtz, Thomson, Rankine, &c., have necessarily ad-
vanced the subject; nevertheless, the complete laws which
regulate the transmutation of the various kinds of energy into
one another are as yet very imperfectly known. Rankine
especially has given the laws of transmutation of energy in
the most general form possible.
The third law, or that of the dissipation of energy, will
be considered in a future part of this work.
322. Various forms of energy. Before concluding
this chapter we will give a list of the various forms of
energy, and state very briefly some of the more prominent
transmutations from the one into the other. In the first
place, all these forms may be divided into two classes :
I. VISIBLE or MOLAR ENERGY, or energy of motions and
arrangements on the large scale.
II. MOLECULAR AND ATOMIC ENERGY.
In the first of these classes, under the head of visible
energy we have
A. Molar kinetic energy ; that is to say, the energy of
a body in visible motion.
B. Potential energy of molar arrangement ; that is to
say. a body in a position of advantage with regard to the
force of gravity, the force of a spring, or any other force
acting through large spaces. A head of water is a very good
instance of this kind of energy, and every one is familiar with
the work a head of water is capable of accomplishing.
In the class of molar energy w r e may embrace those
vibrations of bodies which give rise to sound. A body in
HISTORICAL AND PRELIMINARY. 325
vibration is very similar to an oscillating pendulum, in which
case we have already seen (Art. 316) that the energy is
alternately kinetic and potential.
In the class of invisible energy, embracing molecular and
atomic energy we have
C. The energy of electricity in motion. When a current
of electricity passes along a wire, the wire will be heated to
some extent, but if it be a very good conductor the heating
effect will be comparatively small. In such a case we know
that much more energy has passed through a given length
of the wire than can be accounted for by the heating effect
produced. This is the energy of electricity in motion.
D. The energy of radiant heat and light. This is a spe'cies
of energy which is capable of passing through interplanetary
space without sensible loss ; it is also capable of passing
through certain bodies with very little absorption.
We imagine radiant light and heat to consist of a vibratory
motion of a certain kind of matter. The energy of this
matter whose motions cause radiant light is therefore perhaps
similar to that of a vibrating body or pendulum ; that is to
say. it is alternately potential and kinetic.
E. The kinetic energy of absorbed heat. When radiant heat
and light are absorbed, or when a body becomes heated by
any means, we have reason to believe that a great portion of
the energy of this absorbed heat is transformed into a peculiar
motion of the molecules of the body.
F. Molecular potential energy. Part of the absorbed heat
is also spent in producing energy of expansion or separation
of the molecules of matter against the force by which they
are attracted to each other. It is thus spent in producing
a species of potential energy, molecular attraction being the
force in this case, just like gravity, or the force of a spring,
in the case of the potential energy of visible motion. There
are besides other forms of molecular potential energy.
326 REMARKS ON ENERGY.
G. There is also the potential energy caused by electrical
separation. Thus two separated spheres, one charged with
positive and the other with negative electricity, attract each
other. A position of advantage is thus obtained with respect
to the force of electricity analogous to that which is ob-
tained with respect to the force of gravity when a stone is
separated from the earth.
H. There is also the potential energy caused by chemical
separation. In the expansion produced by heat we have
chiefly one molecule separated from another of the same
body; but in chemical separation we have one element of a
compound body separated from the other, and in this sepa-
ration we have obtained a position of advantage with respect
to that very powerful force known as chemical affinity.
It is not of course pretended that there may not prove
to be some kind of energy which is not embraced in this
list, or that no two of these varieties here given are reducible
into one. The list is simply one of convenience.
323. Now with regard to these various forms of energy,
the principle of the conservation of energy asserts that for
a body left to itself, or for the entire material universe, we
. = a constant quantity ;
on the other hand, the various terms of the left-hand member
of this equation must be considered as variable quantities,
subject however to the above limitation, but capable of being'
transmuted into one another according to certain laws.
324. Laws of transmutations of energy. The fol-
lowing are amongst the most important cases of transmuta-
tion of these energies into one another :
A, or molar kinetic energy, is transmuted into B, or the
potential energy of molar motion, when a weight is pro-
jected upwards above the earth; into C, or electricity in
HISTORICAL AND PRELIMINARY. 327
motion (ultimately into heat), when a revolving conductor
is brought between the poles of a powerful magnet.
As far as we know at present, A is not directly trans-
muted into D, or radiant light and heat ; it is transmuted
into E and F, which embrace the energy, both kinetic
and potential, of absorbed heat, when friction stops a body
in motion and the body becomes heated in consequence ;
into G, or the potential energy of electrical separation, in
the machines which produce frictional electricity. The elec-
trical separation produced makes it harder to drive the
machine. A is possibly not converted directly into H, or
B, or the potential energy of mo'lar motion, is generally
converted first into A, or molar kinetic energy, and through
it into other forms of energy. It is converted into A when
a stone is rolled down a mountain, or when a head of water
is made to drive a mill-wheel.
C, or the energy of electricity in motion, is converted
into A, or visible kinetic energy, when two wires con-
veying electrical currents in the same direction attract each
other ; a certain amount of the strength of the two currents
is thus spent in producing the kinetic energy of the visible
motion as they approach each other; into E and F, or
absorbed heat, when an electric current passes through a
body which presents any resistance to its passage ; into H,
or chemical separation, when a current of electricity is made
to decompose a body.
D, or the energy of radiant light and heat, is converted
into E and F, or absorbed heat, when radiant heat is ab-
sorbed by a body; into H, or chemical separation, when
a ray of sunlight decomposes chloride of silver.
E and F, or the energy (kinetic and potential) of absorbed
heat, is converted into A and B, or the energy (kinetic and
potential) of molar motion, in the case of any heat-engine ;
3^8 REMARKS ON ENERGY.
into C, or the energy of electricity in motion, in thermo-
electric currents (Art. 163); into D, or radiant light and
heat, when a hot body radiates, which it always does ; into
G, or electrical separation, when tourmalines and other
crystals are heated (Art. 167); into H, or chemical se-
paration, when a body is decomposed by heat.
G, or electrical separation, is transformed into A, or the
kinetic energy of molar motion, when two bodies oppositely
electrified approach each other ; into C, or the energy of
electricity in motion, when they are connected together by
a wire or when a spark passes.
H, or the potential energy of chemical separation, is trans-
muted into C, or the energy of electricity in motion, when
a voltaic battery of zinc and copper-plates is in action ; into
E and F, or heat, when a body burns in air, or generally
when chemical combination takes place; into G, or elec-
trical separation, when two dissimilar metals are brought into
325. These are some of the chief instances of transmu-
tation of energy. In the remainder of this work we shall
confine our attention to those transmutations' in which the
energy of heat embraced under the heads D, E and F is
converted into other forms of energy, or in which other
forms of energy are converted into heat.
RELATION BETWEEN HEAT, &C. 329
Relation between Heat and Mechanical Effect.
FIRST LAW OF THERMO-DYXAMICS.
326. Allusion has already been made to the experiments
of Davy, in which ice was melted by the friction against
each other of two pieces of this substance; and also to
those of Rumford, in which the friction of boring cannon
was found to produce great heat, sufficient even to cause
a considerable quantity of water to boil. The opinions of
these philosophers were also quoted, in both of which it
was distinctly stated that in friction motion is converted
into heat. Motion is, in fact, annihilated as visible motion,
while at the same instant heat is created. Visible motion
is likewise converted into heat in certain cases of deforma-
tion, in compression, in percussion, and also in a vibrating
body, in which the energy of vibration is ultimately con-
verted into heat; but this transmutation can best be studied
in the case of friction.
If, therefore, by means of friction, percussion, &c., there
is a transmutation of mechanical energy into heat, it becomes
an experimental question of great importance to ascertain
how much mechanical energy is required to produce one
unit of heat ; or in other words, what is the relation between
the unit of mechanical energy and the unit of heat ; the latter
unit being chosen as the amount of heat necessary to raise
one kilogramme of water from oC to iC. We have, in
fact, to inquire how far a kilogramme of water must fall
RELATION BETWEEN HEAT
under the influence of gravity in order to acquire mechanical
energy by the fall which, when entirely converted into heat,
will raise its temperature i c C.
327. Joule's experiments. I. Fluid friction. This
experimental question has been answered by Joule. His
experiments began in 1843 an( ^ were continued until 1849.
During this time he had learned to perfect his apparatus and
to eliminate the various sources of error in such a manner
that the results of different processes coincided in giving
almost identical values for the mechanical equivalent of heat.
His experiments on the friction of fluids were conducted
in the following manner. A known weight is attached to
a pulley as in Fig. 72, the axle of this pulley resting upon
friction rollers at f\ a string passing over the pulley is
also wrapped round the roller r y so that by descent of the
weight a rapid motion round a vertical axis is communicated
to this roller.
AND MECHANICAL EFFECT. 331
This roller communicates its motion to a system of
paddles placed in a fluid which fills the box B. A vertical
section of one of these paddles is given in the figure.
There are eight sets of these revolving between four sta-
tionary vanes, which thus prevent the liquid from being
whirled in the direction of rotation; The mechanical energy
employed in producing the rotation was measured by the
descent of a known weight through a known distance, and
by undoing a small peg p the weight could be wound up
again without moving the paddles in B. Great care was
taken to correct for the amount of energy expended in
friction of the axles of the pulleys employed. In this ex-
periment it is evident that the mechanical energy of the
weight is expended in fluid friction in the box B, and by