NA TURE 



197 



THURSDAY', MAY 4, 191 6. 



THERMODYNAMIC AND KINETIC 

 THEORIES. 



(ij Statistical Theory of Energy and Matter. By 

 Dr. T. W'ereide. Pp. xvi + 170. (Kristiania : 

 Gyldendalske Boghandel Nordisk Forlag^, 1915.) 

 No price. 



{2) Eight Lectures on Theoretical Physics de- 

 livered at Columbia University in 1909. By Dr. 

 Max Planck; translated by Prof. A. P. Wills. 

 Pp. xii-i30. (New York: Columbia University 

 Press, 191 5.) Price i dollar. 



1^' the development of modern theoretical 

 physics two lines of inquiry have played an 

 important part. One has been the attempt to 

 deduce reversible physical phenomena from the 

 inequalities of irreversible thermodynamics ; the 

 other the endeavour to reconcile irreversible 

 phenomena with the equations of reversible 

 dynamics. Between the two we have arrived at 

 a more or less satisfactory' representation of many 

 phenomena of an essentially statical character. 

 Progress has, however, been somewhat retarded 

 since the death of Boltzmann, nor can we forget 

 Lord Kelvin's healthy criticisms and the steady- 

 ing influence in times gone by of representatives 

 of the old rigorous school of Cambridge philo- 

 sophy, such as Watson and Burbury. 



(i) Dr. Thornstein Wereide's introduction to 

 the statistical theory of energy and matter is cal- 

 culated to revive interest in these oft-debated 

 problems. The author will scarcely be surprised 

 I at our statement that the book does not appear to 

 I throw light on any new facts or contain any ori- 

 ginal work of a fundamental character, but the 

 method of treatment and of exposition is novel in 

 many respects, and the account of Soret's pheno- 

 mena describes experimental researches the results 

 of which appear to be inconsistent with precon- 

 eived hypotheses. 



The book is divided into two sections. The 

 first is occupied exclusively with the deduction 

 of the fundamental formulae of statistical mech- 

 anics, and occupies practically the first sixty-four 

 pages, since "Maxwell's distribution of veloci- 

 ties," though placed at the beginning of section 

 ii., really belongs to the first section. The second 

 section describes the applications of the theory 

 to various physical phenomena, including specific 

 heat, equilibrium, phenomena associated with 

 change of state, diffusion, the phase rule, magnet- 

 5m, radiation, and finally the quantum hypothesis 

 >f Planck. 



A study of the first section might with advan- 

 age be supplemented by reading some of the 

 )Ider classical treatises and papers on the kinetic 

 heor>', in which the application of Lagrange's 

 md Hamilton's equations of motion is developed 

 n greater detail. For example, the proof of 

 i-agrange's^ equations is unsatisfactory, and the 

 uscussion in § 9 cannot be regarded as consti- 

 ,uting a rigorous t>roof of the stated property 

 |nat the density of probabilitv of a system in 

 NO. 2427, VOL. 97] 



statistical equilibrium is a function of the energy 

 alone. To understand this property thoroughly 

 it is necessary to read the older proofs based on 

 the formulation of the Jacobian determinant of 

 the co-ordinates and momenta of the system. 



Irreversibility is postulated in the following 

 argument : — 



"Let us suppose that the system at a given 

 moment passes through a number of elements, W, 

 that are not all possible. It is then very improb- 

 able that the system will cease frequenting the 

 elements hitherto frequented, and never visit them 

 any more. On the other hand, it is very probable 

 that the system, as time passes, will take up more 

 and more elements into its circuit provided that 

 an entrance into these elements is possible." 



This assumed, the author deduces that — 



"A system that is left to itself will change in 

 such a manner that the density of probability 

 for a given state will either remain constant or 

 decrease. The density of probability can never 

 increase." 



And he goes on further to restate the hypo- 

 thesis as follows : — 



" A system that is left to itself will move in such 

 a manner that the number of configurations either 

 is constant or it increases. The number of con- 

 figurations can never decrease." 



Unfortunately this assumption is the exact 

 opposite of the second law of thermodynamics, 

 which states that in an isolated system the num- 

 ber of configurations which it is possible for a 

 system to assume is always decreasing. In this 

 case the decrease takes place by the gradual 

 wiping out, one by one, of the possible configura- 

 tions for which the sum of the p)otential and 

 kinetic energies of visible motions is a maximum. 



The quantum hypothesis is, of course, an inno- 

 vation since the days of the classical treatises on 

 the kinetic theory. What the author of this 

 book says in commenting on this theory is 

 sensible enough, namely, that by means of this 

 hypothesis Planck has explained phenomena that 

 others have failed to explain, and it cannot, there- 

 fore, be rejected merely because it fails to account 

 for everything. 



Dr. Wereide thinks that the best way of throw- 

 ing light on this question is by a renewed study 

 of the trustworthiness or otherwise of statistical 

 methods. 



Now it so happens that the writer of this review, 

 before abandoning gases in favour of aeroplanes, 

 endeavoured to direct attention to a method of 

 investigation in statistical mechanics under the 

 title of "Energy Accelerations." The essential 

 feature of this method was to study the second 

 differential coefficients with respect to the time 

 of the squares and products of the velocities of a 

 statistical dynamical system, these determining 

 accelerations of energy which would not be altered 

 in sign bv reversing the motions, just as the 

 second differential coefficients of the co-ordinates 

 determine the accelerations of the masses. Un- 

 fortunately this suggestion does not appear to 



