amount of work agree in showing a real cohesion in so far as it was proved that particles of gas attract, and do not repel, each other. Herein is a weighty support of our hypothesis, since in face of this fact the possibility of explaining, as Newton attempted, the expansive tendency of a gas by the repulsion of its particles disappears; and there remains as the only admissible hypothesis the opposite view that in a motion of its molecules consists the expansive tendency of a gas.

4. Character of the Heat-motion in Gases

It is now easy to determine the way in which we have to represent to ourselves this molecular motion. We first assume that the gas under consideration is removed from the action of external forces-such as gravity, for instanceand we then introduce the further assumption, which is sufficiently, though not strictly, accurate, that there is no cohesion in the gas worthy of account.

If these two suppositions are realised the molecules of a gaseous substance move freely without being subject to the action of any force. Now, according to the law of inertia, free motion without the action of force takes place with unchanging speed in unchanging direction. Hence the hypothesis which must form the groundwork of the theory of gases is this:

The heat-motion of the molecules of a gas consists in a uniform rectilinear translatory motion.

We must add to this what is nearly obvious, namely, that a molecule can proceed along its straight path only so long as it meets with no obstruction. If it should strike a wall or collide with another molecule, its motion must suffer an abrupt change in direction by reason of the impenetrability of matter. Two colliding molecules therefore rebound from each other, and possibly just like two elastic balls.

If, now, we take account of the action of external forces, such as gravity, which is practically uniform, we have to represent the paths of the molecules as no longer straight, but in general curved, the path for a constant force being a

parabola. This curvature of the path under the action of gravity will, however, be quite insignificant if the speed of the molecules is very great. Since this condition is actually fulfilled, as the numbers in § 13 show, we may neglect this curvature and consider the molecular motions in even heavy gases as rectilinear.

Of more importance is the fact that gases are not quite free from cohesion of their particles, but exhibit distinct, though very slight, traces of it. Two gaseous molecules, however, can only attract each other when sufficiently near, so that if a gas is not too strongly compressed, but is far from the point of liquefaction, we are justified in representing an overpowering majority of its molecules as far enough apart to be nearly always outside the range of their mutual attraction; and we may therefore assume that the small amount of cohesion which does come into play is to be put to the account of the rarely occurring cases when two molecules now and then come very near each other.

If we therefore represent the molecules of a gas as moving in general in a straight line, and only changing direction when two approach very closely, this view is practically the same as that enunciated for the simple case first given, the difference between them consisting only in the substitution of a rapid, though gradual and continuous, change of direction in the motion of two molecules on very close approach to each other, in place of a sudden rebound on collision.

The most essential point of our hypothesis is not thereby touched; it remains true that a gaseous molecule moves with uniform velocity in a straight line between every two successive collisions with other molecules.

5. Founders of the Kinetic Theory

When these views on the nature of the gaseous state were published in 1856 by Krönig, and in 1857 by Clausius, they aroused very special remark by their

1 Grundzüge einer Theorie der Gase: first published separately in Berlin by A. W. Hayn, and then in Pogg. Ann. xcix. 1856, p. 315.

2 Ueber die Art der Bewegung, welche wir Wärme nennen, Pogg. Ann. c.

novelty and their entire variation from the ideas till then current. The mathematical theory which Clausius founded on this hypothesis, and published in the memoir cited, as well as in later papers, especially attracted attention, and many physicists were induced by these investigations to help in developing the theory and putting it to experimental proof.

It was, indeed, quickly found that these views on the nature of gases were not new, but had been published very often before Clausius, and indeed with perfect clearness very long before. Clausius himself mentioned in his first memoir a paper published by Joule1 in 1851, which had remained almost quite unnoticed, wherein the question is taken up and treated in essentially the same way; and Joule refers to a paper by Herapath2 which appeared in 1821. In 1845 there was also presented to the Royal Society of London a paper by Waterston,3 which proceeds on the same lines regarding molecular motion, but, for certain faults, was not printed till Lord Rayleigh published it on account of its historical interest.

A whole series of writers have further been named who are said to have held and published similar views and to have expressed them with more or less clearness; this list, beginning with the philosophers of classical antiquity, runs through the Middle Ages to the last century. Of all these writers, however, there is but a single one of consequence from the present state of the theory, viz. Daniel Bernoulli, whose memory Franz Neumann has preserved for his pupils and posterity, and to whom P. du Bois-Reymond has directed the attention of his contemporaries by a German translation of a fragment of his

1857, p. 353; Abhandlungen über die mechanische Wärmetheorie, Brunswick 1867, 2nd part, p. 229; transl. Phil. Mag. [4] xiv. 1857, p. 108.

Memoirs of the Manchester Lit. and Phil. Soc. [2] ix. 1851, p. 107; reprinted later Phil. Mag. [4] xiv. 1857, p. 211.

2 Annals of Philosophy [2] i. 1821, pp. 273, 340, 401.

3 Phil. Trans. clxxxiii. 1892, p. 1.

Hydrodynamica, Argentorati 1738, Sect. X. D. & J. Bernoulli, Nouv. Princ. de Méc. et de Phys. &c. Rec. des pièces de prix, v. 1752.

Pogg. Ann. cvii. 1859, p. 490.

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works. The writings of the others have now only a historic interest,1 as they exhibit, in the rise and fall of a philosophical system, a picture of the intellectual life of man which becomes the more distinct by a narrow limitation to a special study. The kinetic theory of our day has come to life quite independently of those forgotten predecessors. We may look on Daniel Bernoulli as the first author of the fundamental notion of the kinetic theory-so at least I think I have proved in the following pages; but he who has the honour of being acknowledged as the author of a scientific system-a mathematical theory-founded on this notion is Clausius, and with him Maxwell has done the most to promote and develop the theory.

'Gehler's Physik. Wörterbuch, iv. 1828, p. 1049; Clausius, Pogg. Ann. cxv. 1862, p. 2, Abhandl. pt. ii. p. 230; transl. Phil. Mag. [4] xxiii. 1862, pp. 417, 512; Lothar Meyer, Theorien der Chemie, 2nd ed. p. 29, 5th ed. p. 30.

2 A thorough exposition of the Fall of the kinetic theory of atoms in the seventeenth century' is given by Dr. Kurd Lasswitz in Pogg. Ann. cliii. 1874, p. 373, as well as in his Geschichte der Atomistik, 2 vols., Hamburg and Leipsig 1890. The influence of the corpuscular philosophy is there portrayed, and the harm done by Newton's doctrine of the kinetic theory of atoms. I might add that it fell into complete oblivion in the eighteenth century, when the Cartesian philosophy, with which it was in constant strife, was supplanted and Kant's arose; and it remained forgotten by all, with few exceptions, of the natural philosophers of the present century, who take but little account of older works.

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CHAPTER II

PRESSURE OF GASES

6. Boyle's Law

THE hypothesis, which we have described, of the to-and-fro motion of the molecules of a gas in straight paths, of their collisions and subsequent separations, and of their striking against the walls of the containing vessel, furnishes a very simple explanation of the cause of the pressure which the gas exerts. This pressure results from the series of impacts of the molecules, as they move to and fro, against the enclosure. As the first test of the admissibility of our hypothesis, we have to see whether this explanation of the pressure is in agreement or not with the laws of gaseous pressure that have been deduced from experiment.

The law with which we have first to deal is in Germany generally called Mariotte's law, because Mariotte enunciated it at the head of his essay 'De la Nature de l'Air,' which first appeared in 1679. As, however, there can be no doubt that the discoverer1 of this law is Robert Boyle, who determined it seventeen years earlier, I shall follow the English custom of calling it Boyle's law.

That this law-viz. that the density and pressure of a gas are proportional to each other-is not in contradiction with the kinetic theory, but, on the contrary, is a necessary result of the hypothesis of rectilinear motion, was proved by Daniel Bernoulli,3 the originator of this hypothesis.

See, for instance, Muncke in Gehler's Physikal. Wörterbuch, 1828, iv. pp. 1026, 1028.

2 A Defence of the Doctrine touching the Spring and Weight of the Air,' London 1662, Pt. II. Chap. V.

Hydrodynamica, Argentorati 1738, Sect. X. p. 200; reprinted in German, Pogg. Ann. cvii. 1859, p. 490.