ON OUR KNOWLEDGE OF THEEMODTNAMICS. 85 



Report of a Committee, consisting of Messrs. J. Larmor aoid 

 Gr. H. Bryan, 07i the present state of our knotdedge of Thermo- 

 dynam,ics, specially with regard to the Second Laiv. 



[Ordered by the General Committee to be printed among the Reports.] 



Paet I. — Researches relating to the connection of the Second Law 

 WITH Dynamical Principles. Drawn up by G. H. Bryan. 



Introdiidion. 



1. The present report treats exclusively of the attempts that have 

 been made to deduce the Second Law of Thermodynamics from, purely 

 mechanical principles. 



Before considering the several methods in detail it may be well to sum- 

 marise the meaning of the various terms which enter into the mathe- 

 matical expressions of the laws of thermodynamics, with a view of showing 

 more fully what conditions must be kept in view in establishing the 

 dynamical analogues. This has been done more or less fully by several 

 authors of papers on the subject, but more especially by von Helmholtz 

 in his paper on the ' Statics of Monocyclic Systems.' ' The substance of 

 this paper will be dealt with more fully later on in the present Eeport, 

 but we will now mention the principal points touched on in the introduc- 

 tion. 



2. Meaning cf the Second Laiv. — Let a quantity c?Q of work in the 

 form of heat be communicated to a body whose absolute temperature is 6. 

 Let E be the internal energy of the body, dW the work done against 

 external forces by the change in the configuration of the body which 

 takes place during the addition of dQ. It is not assumed that the 

 external forces are conservative. 



Then the First and Second Laws are expressed by the equations 



dQ=d^ + dW (1) 



dq=edS (2) 



where dS is a perfect differential of a quantity S, called the entropy, whose 

 value depends only on the state of the body at the instant considered. 



The essential principle involved in the Second Law does not lie solely 

 in the fact that dQ, has an integrating divisor 0. In fact, if we assume 

 that the state of a body is completely defined by tivo variables x and y, it 

 must always be jDOSsible to put dQ in the form 



dQ='M.dx + 'Ndy, 



where M, N are functions of x and y only. And it is always possible to 

 find an integrating factor for an expression of this form. 



Moreover, if one integrating factor can be found for dQ, an infinite 

 number of such factors can be found. For in equation (2) let .s be any 

 arbitrary function of S ; then we may write the equation in the form 



dQ=e'^ds. 

 ds 



' Crelle, Jmirnal, vol. scviii. 



