pulley, in descending through 10 ft. it is capable of raising nearly
a pound weight attached to the other end of the string, through
the same height, and thus can do nearly 10 foot-pounds of work.
The smoother we make the pulley the more nearly does the
amount of useful work which the weight is capable of doing
approach 10 foot-pounds, and if we take into account the work
done against the friction of the pulley, we may say that the work
done by the descending weight is 10 foot-pounds, and hence
when the weight is in its elevated position we have at disposal
10 foot-pounds more energy than when it is in the lower position.
It should be noticed, however, that this energy is possessed by
the system consisting of the earth and pound together, in virtue of
their separation, and that neither could do work without the other
to attract it. The system consisting of the earth and the pound
therefore possesses an amount of energy which depends on the
relative positions of its two parts, on account of the latent physical
connexion existing between them. In most mechanical systems
the working stresses acting between the parts can be determined
when the relative positions of all the parts are known; and the
energy which a system possesses in virtue of the relative positions
of its parts, or its configuration, is classified as “potential energy,”
to distinguish it from energy of motion which we shall presently
consider. The word potential does not imply that this energy is
not real; it exists in potentiality only in the sense that it is
stored away in some latent manner; but it can be drawn upon
without limit for mechanical work.
It is a fundamental result in dynamics that, if a body be projected vertically upwards in vacuo, with a velocity of v centimetres per second, it will rise to a height of v2/2g centimetres, where g represents the numerical value of the acceleration produced by gravity in centimetre-second units. Now, if m represent the mass of the body in grammes its weight will be mg dynes, for it will require a force of mg dynes to produce in it the acceleration denoted by g. Hence the work done in raising the mass will be represented by mg·v2/2g, that is, 12mv2 ergs. Now, whatever be the direction in which a body is moving, a frictionless constraint, like a string attached to the body, can cause its velocity to be changed into the vertical direction without any change taking place in the magnitude of the velocity. Thus it is merely in virtue of the velocity that the mass is capable of rising against the resistance of gravity, and hence we recognize that on account of its motion the body possessed 12mv2 units of energy. Energy of motion is usually called “kinetic energy.”
A simple example of the transformation of kinetic energy into potential energy, and vice versa, is afforded by the pendulum. When at the limits of its swing, the pendulum is for an instant at rest, and all the energy of the oscillation is static or potential. When passing through its position of equilibrium, since gravity can do no more work upon it without changing its fixed point of support, all the energy of oscillation is kinetic. At intermediate positions the energy is partly kinetic and partly potential.
Available kinetic energy is possessed by a system of two or more bodies in virtue of the relative motion of its parts. Since our conception of velocity is essentially relative, it is plain that any property possessed by a body in virtue of its motion can be effectively possessed by it only in relation to those bodies with respect to which it is moving. If a body whose mass is m grammes be moving with a velocity of v centimetres per second relative to the earth, the available kinetic energy possessed by the system is 12mv2 ergs if m be small relative to the earth. But if we consider two bodies each of mass m and one of them moving with velocity v relative to the other, only 14mv2 units of work is available from this system alone. Thus the estimation of kinetic energy is intimately affected by the choice of our base of measurement.
When the stresses acting between the parts of a system depend only on the relative positions of those parts, the sum of the kinetic energy and potential energy of the system is always the same, provided the system be not acted upon by anything outside it. Such a system is called “conservative,” and is well illustrated by the swinging pendulum above referred to. But there are stresses which depend on the relative motion of the visible bodies between which they appear to act. When work is done against these forces no full equivalent of potential energy may be produced; this applies especially to frictional forces, for if the motion of the system be reversed the forces will be also reversed and will still oppose the motion. It was long believed that work done against such forces was lost, and it was not till the 19th century that the energy thus transformed was traced; the conservation of energy has become the master-key to unlock the connexions in inanimate nature.
It was pointed out by Thomson (Lord Kelvin) and P. G. Tait that Newton had divined the principle of the conservation of energy, so far as it belongs purely to mechanics. But what became of the work done against friction and such non-conservative forces remained obscure, while the chemical doctrine that heat was an indestructible substance afterwards led to the idea that it was lost. There was, however, even before Newton’s time, more than a suspicion that heat was a form of energy. Francis Bacon expressed his conviction that heat consists of a kind of motion or “brisk agitation” of the particles of matter. In the Novum Organum, after giving a long list of the sources of heat, he says: “From these examples, taken collectively as well as singly, the nature whose limit is heat appears to be motion.... It must not be thought that heat generates motion or motion heat (though in some respects this is true), but the very essence of heat, or the substantial self of heat, is motion and nothing else.”
After Newton’s time the first vigorous effort to restore the universality of the doctrine of energy was made by Benjamin Thompson, Count Rumford, and was published in the Phil. Trans. for 1798. Rumford was engaged in superintending the boring of cannon in the military arsenal at Munich, and was struck by the amount of heat produced by the action of the boring bar upon the brass castings. In order to see whether the heat came out of the chips he compared the capacity for heat of the chips abraded by the boring bar with that of an equal quantity of the metal cut from the block by a fine saw, and obtained the same result in the two cases, from which he concluded that “the heat produced could not possibly have been furnished at the expense of the latent heat of the metallic chips.”
Rumford then turned up a hollow cylinder which was cast in one piece with a brass six-pounder, and having reduced the connexion between the cylinder and cannon to a narrow neck of metal, he caused a blunt borer to press against the hollow of the cylinder with a force equal to the weight of about 10,000 ℔, while the casting was made to rotate in a lathe. By this means the mean temperature of the brass was raised through about 70° Fahr., while the amount of metal abraded was only 837 grains.
In order to be sure that the heat was not due to the action of the air upon the newly exposed metallic surface, the cylinder and the end of the boring bar were immersed in 18.77 ℔ of water contained in an oak box. The temperature of the water at the commencement of the experiment was 60° Fahr., and after two horses had turned the lathe for 212 hours the water boiled. Taking into account the heat absorbed by the box and the metal, Rumford calculated that the heat developed was sufficient to raise 26.58 ℔ of water from the freezing to the boiling point, and in this calculation the heat lost by radiation and conduction was neglected. Since one horse was capable of doing the work required, Rumford remarked that one horse can generate heat as rapidly as nine wax candles burning in the ordinary manner.
Finally, Rumford reviewed all the sources from which the heat might have been supposed to be derived, and concluded that it was simply produced by the friction, and that the supply was inexhaustible. “It is hardly necessary to add,” he remarks, “that anything which any insulated body or system of bodies can continue to furnish without limitation cannot possibly be a material substance; and it appears to me to be extremely difficult, if not quite impossible, to form any distinct idea of anything capable of being excited and communicated in the manner that heat was excited and communicated in these experiments, except it be motion.”
About the same time Davy showed that two pieces of ice could be melted by rubbing them together in a vacuum, although
