60 2 



NA TURE 



[April 27, 1905 



infinite distance in all directions, and gradually in- 

 creasing in intensity as they approach the molecule. 

 We do not think such cases exist, but we did not 

 expect to discover radium a few years ago. 



Let us now see how Mr. Jeans attempts to deal 

 with the difficulties here suggested. In the first 

 seven chapters he follows fairly closely on conventional 

 lines, and deduces the Boltzmann-Maxwell law of dis- 

 tribution, the minimum theorem, the law of partition 

 of energy, and the isothermal equations according to 

 the Boyle-Mariotte and van der Waals's laws. In 

 chapter viii. the author throws over the principle of 

 conservation of energy and assumes that his gas is a 

 dissipative system in which loss of energy occurs by 

 radiation. On this hypothesis he finds that when the 

 rate of dissipation has become very slow probability 

 considerations indicate a tendency to assume a 

 definite statistical specification different from that 

 given by the ordinary theory. It further appears 

 that such a gas has one principal and a number 

 of subsidiary temperatures, a notion which we be- 

 lieve has been previously advanced. In chapters 

 ix. and x. Mr. Jeans considers applications of the 

 theory of a non-conservative gas, particularly in con- 

 nection with rates of dissipation of energy, and ratios 

 of specific heats. 



We thus have a definite attempt to break away from 

 traditional methods and boldly introduce the notion of 

 dissipation into the kinetic theory. The idea is 

 certainly an excellent one. Whether it is free from 

 objection is a matter which cannot be answered as 

 the mere result of a critical examination. Often 

 objections to theories strike the mind of a reader quite 

 unexpectedly. 



In the remaining chapters Mr. Jeans deals with 

 " free path phenomena " such as diffusion, conduction 

 of heat, viscosity, and the escape of gases from 

 planetary atmospheres. In this work he is more on 

 the ordinary lines. We notice as an important 

 feature the sections dealing with encounters according 

 to the law of the inverse fifth power. This series of 

 chapters is of considerable use in affording easy access 

 to investigations contained in a much longer form in 

 the original papers of Boltzmann and other writers. 



Turning back to the chapter on equipartition of 

 energy, we are led to the following inference : — 

 Mr. Jeans leaves it an open question whether the 

 'conventional law of distribution with its attendant 

 consequences of equipartition may represent the 

 ultimate state of a gas, but concludes that in actual 

 gases such as we see around us where dissipation of 

 energy occurs a different distribution holds good. 



The second conclusion seems plausible. But the 

 assumption that equipartition of energy holds even in 

 a conservative system presents difficulties in connec- 

 tion with Stefan's law of radiation in a black cavity. 

 According to that law the energy of the ether should 

 vary as the fourth power of that of the molecules. 

 It might be said that in the " conservative system " 

 Stefan's law would not necessarily hold good, and 

 that there would be no objection to assuming the 

 energy of the ether to be then directly proportional 

 to that of the molecules, or to the temperature. But 

 the usual thermodynamic investigation — which is more 

 NO. 1852, VOL. 71] 



certain to be valid in the case of the conservative 

 than in that of the dissipative system — would then 

 give a different form for the radiation pressure — 

 apparently/=i(c(log\(^+constant) — and this result would 

 have to be admitted. On the whole it appears more 

 likely that while distributions satisfying Maxwell's 

 law of equipartition are always theoretically possible, 

 other distributions may exist, and may, indeed, 

 represent a normal and persistent state of affairs even 

 in conservative systems. 



It is remarkable that physicists strain at gnats 

 when put down to study kinetic theory or thermo- 

 dynamics, and yet they swallow camels with com- 

 placency when they read the subject of Mr. Whittaker's 

 book, " .'Vnalytical Dynamics." Some writers even 

 go so far as to introduce pages and pages of the 

 most unreal dynamical problems into what thev call 

 treatises on physics. 



" The soluble problems of particle dynamics " 

 mostly represent things which have no existence. It 

 is impossible for a particle to move on a smooth 

 curve or surface because, in the first place, there is 

 no such thing as a particle, and in the second place 

 there is no such thing as a smooth curve or surface. 

 What constitutes the chief interest of " Analytical 

 Dynamics " is the possibility of forming clear mental 

 pictures of its results by imagining bodies capable of 

 performing the motions discussed. 



Mr. Whittaker's treatment is essentially mathe- 

 matical and advanced in character. He opens with 

 sections on the displacements of rigid bodies in which 

 Klein's parameters and Halphen's theorems on 

 composition of screws figure near the commencement. 

 In his chapter on equations of motion physico- 

 philosophical discursions on force and mass are re- 

 duced to a minimum. This is as it should be, for there 

 are plenty of people who can write about such matters, 

 but few whose knowledge extends to the more 

 important theorems which follow later. The 

 Lagrangian equations are reached by § 26, which is 

 preceded by a definition of holonomic systems. This 

 distinction might with advantage be put into treatises 

 in physics, for at present students of that subject are 

 apt to assume that Lagrange's equations in their 

 ordinary form are universally applicable, which is far 

 from true, Passing on to chapter v., which deals, 

 inter alia, with moments of inertia, our old friend the 

 " principle of parallel axes " is treated generally for 

 a quadratic function of coordinates, velocities and 

 accelerations, readers being doubtless assumed to 

 know the proof for simple cases. Chapter vii. deals 

 with the general theory of vibrations, and the next 

 chapter with non-holonomic and dissipative systems, 

 the first of these two chapters consisting mainly of 

 theory, and the second mainly of examples. The 

 most important chapters are those which follow, deal- 

 ing with the principles of Hamilton and Gauss, the 

 integral invariants of the Hamiltonian system, and the 

 representation of a dynamical system of equations by 

 means of contact transformations. 



Mr. Whittaker some time ago presented a 

 valuable report to the British Association on the 

 problem of three bodies, and he tells us that between 

 1750 and 1904 more than eight hundred memoirs were 



