CHAPTER I

FOUNDATIONS OF THE HYPOTHESIS

1. The Nature of Heat

THE proposition that heat is not a substance, but a form of energy, is no longer considered a hypothesis, but the expression of a certainly proved fact. Experiment shows that heat is generated when mechanical motion is destroyed by friction or otherwise; and, on the other hand, the performance of work by engines that are driven by heat is taken as a proof that heat can be converted into ordinary mechanical energy.

From these and other observations it follows that heat is of the same nature as mechanical work, kinetic energy of visible motion, and all other forms in which energy shows. itself in nature. Measurement further proves that the same amount of heat always corresponds to a given expenditure of mechanical energy. Heat therefore undoubtedly forms one of those indestructible magnitudes which we class as energy; or, in other words, heat is energy.

But in every branch of physics generally, as in mechanics, there are two species of energy, which may be distinguished as potential and kinetic, and in heat both species are recognised; latent heat, for instance, is-for the most part

'The term potential energy was applied by Rankine (Phil. Mag. [4], v. 1853, p. 106) to the magnitude called vis mortua by Leibniz (Acta Erud. Lips. 1695, p. 149; collected works, Gerhardt's ed. vi. 1860, p. 238), and later called Spannkraft by Helmholtz.

2 The term kinetic energy was first employed by Thomson (Lord Kelvin) and Tait (Treatise on Natural Philosophy, Oxford 1867) in place of actual energy, Rankine's name for half of the magnitude called vis viva by Leibniz. This was termed simply energy by Thomas Young (Lectures on Nat. Phil. lect. viii. London 1808, p. 79; new ed. 1845, p. 59).

at least-potential energy, as it consists of the work spent in overcoming cohesion, while sensible heat, which we feel with our hand and measure with the thermometer, is kinetic energy.

We cannot, therefore, in general use Rumford's1 expression, and say that heat is motion, but we may assume that sensible heat is a mode of motion, though this motion is invisible and almost unknown to us. As its carrier we take the particles, supposed immeasurably small, of which bodies are composed, and to these ultimate particles we ascribe motions of different kinds, assuming that some may move forward in straight lines, that others may oscillate periodically, that others again may revolve about each other -in this small world imitating the planets-and that each may further rotate about an axis of its own; and the sum of the kinetic energies of these motions represents the mechanical energy of the contained heat.

In the mechanical theory of heat we extend this speculation, as a rule, no further, so as not unnecessarily to make our reasonings and conclusions depend on doubtful hypotheses. In this connection physical investigation has special reason to avoid hypothesis, as the high value and great significance of the mechanical theory of heat rest on the general and unconditional validity of its propositions, whereby we are enabled to measure forces of unknown nature equally with known forces, and to subject them to calculation with equal certainty.

It would, however, be a censurable restriction of investigation to follow out only those laws of nature which have a general application and are free from hypothesis; for mathematical physics has won most of its successes in the opposite way, namely, by starting with an unproved and unprovable, but probable, hypothesis, analytically following out its consequences in every direction, and determining its value by comparison of these conclusions with the results of experiment.

For the mechanical theory of heat, too, this method has already borne good fruit. By ascribing special forms to

1 Phil. Trans. lxxxviii. 1798, p. 80.

the motion which we call heat-forms which necessarily differ with the nature of the body considered, its state of aggregation and other qualities-we have succeeded in showing that a whole series of important laws of nature. necessarily follow from these assumptions, and we may therefore be sure that we have discovered the mechanical cause of these laws in the circumstances of the ultimate particles of bodies. Specially successful have been the labours of those who sought to explain the nature of the gaseous state-doubtless because the heat-motion in gases obeys the simplest laws. From a very simple assumption as to the nature of this motion we have deduced, not only all the laws already known for gaseous bodies, but also new properties which have been most beautifully verified by experiment.

There has thus arisen from the joint labours of the workers in this field a special theory of the gaseous state which was formerly known as the dynamical,' but is now better called the kinetic, theory of gases. In this work I have endeavoured to collect and arrange the scattered contributions of individual authors that have appeared in periodicals of all kinds.

2. Hypotheses with regard to Heat-motion

The ultimate elements of bodies whose motion we wish to investigate are not freely movable each by itself; they are bound together by mutual forces-their affinity, whence arise combinations of atoms into larger masses called molecules.

We may therefore distinguish two kinds of heat-motion, atomic and molecular. By the latter we understand the translatory motion of the centroid of the atoms that form the molecule, while as atomic motion we count all the

Maxwell, Phil. Mag. [4] xix. 1860, p. 19, xx. 1860, p. 21.

So far as I know, this name was first used by Lord Kelvin (Sir W. Thomson) in an address before the British Association at Edinburgh (B.A. Rep. 1871, p. 93); Maxwell afterwards adopted it (Nature, viii. 1873, p. 298; Scientific Papers, ii. p. 343).

motions which the atoms can individually execute without breaking up the molecule. Atomic motion includes, therefore, not only the oscillations that take place within the molecule, but also the rotation of the atoms about the centroid of the molecule.

This division of the whole heat-motion corresponds to the division of physical science into physics and chemistry -not, indeed, in every respect, but in so far as chemistry deals chiefly with the equilibrium of atoms, while physics treats more of the mechanics of molecules.

Chemical equilibrium, or the unchanged existence of molecules, is attained when the affinity which holds the atoms together is in equilibrium with the forces that tend to break up the molecule; such forces arise from the motion of the atoms, partly from the collisions of those which vibrate, and partly from the centrifugal tendency of those which rotate. Since then, in a chemically stable body, the atomic motions are kept in continuous dynamical equilibrium with the chemical forces, and their action is overcome by the latter, only the molecular motion comes primarily into account in the investigation of purely physical forces and phenomena, and we therefore limit the range of our discussion in the first place to the latter.

Just as the atomic motion tends to break up a molecule, so the molecular motion tends to loosen the connection between the parts of a body, partly in consequence of collisions between the molecules, and partly from their centrifugal tendency; and equilibrium is maintained-at least when there is no external pressure-by cohesion, a force in which we need see nothing different from affinity. It seems enough to account for cohesion in an excess of affinity over the dissociating action of atomic motion, which is not large enough to attract an atom into the pale of a molecule and to keep it there, but is sufficient to bind together neighbouring molecules in a much less close bond.

The problem of discovering the laws of molecular motion is therefore identical with that of determining the laws of cohesion, since when the medium is in equilibrium the

forces due to this motion are equilibrated by those of cohesion.

The difficulty of this problem disappears in the special case which is the subject of this work.

3. Behaviour of Gases

In gaseous bodies scarcely a trace of cohesion can be found. In these most attenuated of all known media the molecules seem so far apart that one experiences no attraction by another, except in the rarely occurring case of two molecules coming accidentally very close, or even into collision, in consequence of their motion.

This theoretical view explains in the simplest manner the tendency of gases to expand, and it has a further support, derived from experiment, in the thermal behaviour of gases when changing volume. For if a gas expands without overcoming pressure, and therefore doing work-if, for instance, it streams into vacuous space-its temperature falls so little that for long it was admitted, on the evidence of Gay-Lussac's experiments, that under such circumstances no fall of temperature at all occurs.

This behaviour would not be possible if on expansion a gas had to overcome any considerable cohesion, since for this an expenditure of energy, and therefore of heat, would be requisite. Just as little can the assumption of repulsive forces between the molecules be reconciled with this experiment, since such forces would come into play during expansion and generate energy in the shape of an increase of heat in the gas.

By the more exact experiments made by Joule and Lord Kelvin on the heat-effects of gases in motion, it is, indeed, shown that there is cohesion between the particles even of gases; but the above conclusions are not thereby invalidated, since Joule and Lord Kelvin's values for the work done by an expanding gas in overcoming its own cohesion are of nearly vanishing magnitude.

It is specially important for our theory to note that all experiments that have been made to determine this small