11(> BEPORT— 1891, 



direction, and therefore capable of unlimited increase.' ' According to 

 Thomson, however,^ ' what has hitherto by Maxwell, and CJausius, and 

 others after them, been called an "elastic sphere " is not an clastic solid 

 capable of rotation and of elastic deformation, and therefore capable of an 

 infinite number of modes of steady vibration, of finer and finer degrees of 

 nodal subdivision, and shorter and shorter periods, into which all trans- 

 lational energy would, if the Boltzmann-Maxwell generalised proposition 

 were true, be ultimately transformed. The smooth "elastic spheres" 

 are really Boscovich point-atoms with their translational inertia, and witb 

 for law of foi'ce zero force at every distance between two points exceeding 

 the sum of the radii of the two balls, and infinite repulsion at exactly 

 this distance.' 



It may also be observed that a sphere in which vibratory energy is 

 set up on impact cannot be regarded as a 'perfectly elastic sphere ' witb 

 coefficient of restitution equal to unity. The necessity of adopting Thom- 

 son's representation by Boscovich point-atoms is otherwise apparent 

 when we remember that as long as the portions of matter with which we 

 are dealing are capable of subdivision, so long will the energy contained 

 in them be capable of subdivision. Un]es5, therefore, we suppose each 

 molecule to consist of one or a finite number of indivisible atoms, it 

 would be unreasonable to expect that heat would entirely take the form 

 of atomic motion. 



46. Applications to the Second Law. — The simplest proof of the Second 

 Law of Thermodynamics based on the hypothesis of the Boltzmann- 

 Maxwell law of distribution of speed is that due to Mr. S. H. Barbury.^ 

 The proof is too well known to need description here. It leads to the 

 same form for the entropy as Boltzmann's original investigation for 

 the case of a system of point-atoms.^ Although Watson and Burbnry 

 take the temperature as represented by the average kinetic energy of 

 translation of the molecules, the fact that the average energy is assumed 

 to be distributed equally among the coordinates shows that the proof 

 would be equally valid if the whole average kinetic energy were taken to 

 represent the temperature. Hence the proposition (when valid) does not 

 afford any evidence as to what part of the molecular energy plays the 

 part of temperature. 



Another proof has been given by R. C. Nichols,-^ and is based on the 

 virial equation of Clausius, 



Here T is the total mean ris viva of the system, so that if Nichols' proof 

 be valid, it does not seem possible to reconcile the views of Tait (§ 43) 

 regarding the nature of temperature with the definition afforded by the 

 Second Law. 



A general proof of the Second Law, based on Maxwell's generalisation 

 of Boltzmann's theorem, has been given by Boltzmann in 1885.'' The 



' Prof. W. M. Hicks, B.A. I.'i'port, ISS.'S. 



^ A'ature, August 13, 1891, § 3. I have slightly rearranged the original wording, 

 .so as to make the sentence more intelligible. 



3 Phil. Mag. January 187G, p. (Jl ; Watson's Kinetic Theory of Gases, Trop. XIII. 



* ' Analyt. Beweis des 2"" Haupts,' Wicn. Sitzh. Bd. 63, 11. Abth. 



^ 'On the Proof of the Second Law of Thermodynamics,' Phil. Mag. 187G (1), 

 p. 3G9. 



" Crelle, Journal, c. p. 213. 



