Feb. 5, 1880] 



NATURE 



319 



positive or negative; the sign = means "matches," -+■ 

 means "superposed," and — directs the term to be taken 

 to the other side of the equation. 



These researches of Maxwell's are now so well known, 

 in consequence especially of the amount of attention 

 which has been called to the subject by Helmholtz' great 

 work on Physiological Optics, that we need not farther 

 discuss them here. 



The last of his greatest investigations is the splendid 

 Series on the Kinetic Theory of Gases, with the closely 

 connected question of the sizes, and laws of mutual 

 action, of the separate particles of bodies. The Kinetic 

 Theory seems to have originated with D. Bernoulli ; but 

 his successors gradually reverted to statical theories of 

 molecular attraction and repulsion, such as those of 

 Boscovich. Herapath (in 1847) seems to have been the 

 first to recall attention to the Kinetic Theory of gaseous 

 pressure. Joule in 1848 calculated the average velocity 

 of the particles of hydrogen and other gases. Kronig 

 in 1856 {JPogg. Ann.) took up the question, but he does 

 not seem to have advanced it farther than Joule had 

 gone ; except by the startling result that the weight of a 

 mass of gas is only half that of its particles when at 

 rest. 



Shortly afterwards (in 1859) Clausius took a great step 

 in advance, explaining, by means of the kinetic theory, 

 the relations between the volume, temperature and 

 pressure of a gas, its cooling by expansion, and the slow- 

 ness of diffusion and conduction of heat in gases. He also 

 investigated the relation between the length of the mean 

 free path of a particle, the number of particles in a given 

 space, and their least distance when in collision. The 

 special merit of Clausius' work lies in his introduction of 

 the processes of the theory of probabilities into the treat- 

 ment of this que=tion. 



Then came Clerk-Maxwell. His first papers are entitled 

 " Illustrations of the Dynamical Theory of Gases,'' and 

 appeared in the Phil. Mag. in i860. By very simple pro- 

 cesses he treats the collisions of a number of perfectly 

 elastic spheres, first when all are of the same mass, 

 secondly when there is a mixture of groups of different 

 masses. He thus verifies Gay-Lussac's law, that the 

 number of particles per unit volume is the same in all 

 gases at the same pressure and temperature. He explains 

 gaseous friction by the transference to and fro of particles 

 between contiguous strata of gas sliding over one another, 

 and shows that the coefficient of viscosity is inde- 

 pendent of the density of the gas. From Stokes' 

 calculation of that coefficient he gave the first deduced 

 approximate value of the mean length of the free path ; 

 which could not, for want of data, be obtained from the 

 relation given by Clausius. He obtained a closely ac- 

 cordant value of the same quantity by comparing his 

 results for the kinetic theory of diffusion with those of one 

 of Graham's experiments. He also gives an estimate of 

 the conducting power of air for heat ; and he shows that 

 the assumption of non-spherical particles, which during 

 collision change part of their energy of translation into 

 energy of rotation, is inconsistent with the known ratio of 

 the two specific heats of air. 



A few years later he made a series of valuable experi- 

 mental determinations of the viscosity of air and other 

 gases at different temperatures. These are described in 



Phil. Trans. 1866 ; and they led to his publishing (in the 

 next volume) a modified theory, in which the gaseous 

 particles are no longer regarded as perfectly elastic, but 

 as repelling one another according to the law of the 

 inverse fifth power of the distance. This paper contains 

 some very powerful analysis, which enabled him to sim- 

 plify the mathematical theory for many of its most im- 

 portant applications. Three specially important results 

 are given in conclusion, and they are shown to be inde- 

 pendent of the particular mode in which gaseous particles 

 are supposed to act on one another. These are :— 



1. In a mixture of particles of two kinds differing in 

 amounts of mass, the average energy of translation of a 

 particle must be the same for either kind. This is Gay 

 Lussac's Law already referred to. 



2. In a vertical column of mixed gases, the density of 

 each gas at any point is ultimately the same as if no 

 other gas were present. This law was laid down by 

 Dalton. 



' 3. Throughout a vertical column of gas gravity has no 

 effect in making one part hotter or colder than another; 

 whence (by the dynamical theory of heat) the same must 

 be true for all substances. 



Maxwell has published in later years several additional 

 papers on the Kinetic Theory, generally of a more 

 abstruse character than the majority of those just described. 

 His two latest papers (in the Phil. Trans, and Camb. 

 Phil. Trans, of last year) are on this subject : — one 

 is an extension and simplification of some of Boltz- 

 mann's valuable additions to the Kinetic Theory. The 

 other is devoted to the explanation of the motion of the 

 radiometer by means of this theory. Several years ago 

 (Nature, vol. xii. p. 217), Prof. Dewar and the writer 

 pointed out, and demonstrated experimentally, that the 

 action of Mr. Crookes' very beautiful instrument was to 

 be explained by taking account of the increased length of 

 the mean free path in rarefied gases, while the then 

 received opinions ascribed it either to evaporation or 

 to a quasi-corpuscular theory of radiation. Stokes 

 extended the explanation to the behaviour of disks with 

 concave and convex surface-, but the subject was not at 

 all fully investigated from the theoretical point of view 

 till Maxwell took it up. During the last ten years of his 

 life he had no rival to claim concurrence with him in 

 the whole wide domain of molecular forces, and but 

 two or three in the still more recondite subject of elec- 

 tricity. 



" Every one must have observed that when a slip of 

 "paper falls through the air, its motion, though un- 

 " decided and wavering at first, sometimes becomes 

 "regular. Its general path is not in the vertical direc- 

 "tion, but inclined to it at an angle which remains nearly 

 "constant, and its fluttering appearance will be found to 

 "be due to a rapid rotation round a horizontal axis. The 

 "direction of deviation from the vertical depends on the 

 "direction of rotation. . . . These effects are commonly 

 "attributed to some accidental peculiarity in the form of 

 "the paper. ..." So writes Maxwell in the Cam. and 

 Dub. Math. Jour. (May, 1854), and proceeds to give an 

 exceedingly simple and beautiful explanation of the 

 phenomenon. The explanation is, of course, of a very 

 general character, for the complete working out of such a 

 problem appears to be, even yet, hopeless; but it is 



