Intelligence and Miscellaneous Articles, 155 



consequently 



/• 7 f Clt o ill 



jda—ja — ==mu — . 

 % i 



The portion of the work relative to an elementary transforma- 

 tion is therefore, for the motion we are considering, 



d(^mu 2 ) -+- mu 2 — . 



The same reasoning applies to each of the three rectangular di- 

 rections in which the motion of the material point is projected. 

 The work dL, relative to an elementary transformation, is the sum 

 of the quantities analogous to the preceding ; so that, calling mv 2 

 the mean vis viva of a material point, we shall have for the entire 

 system, rl - 



dL = dZQmv 2 ) + 2(mv 2 ) ™. 

 i 



We thus find again the expression given by Clausius. If we re- 

 present by M the weight of the body, by 7c its absolute specific heat, 

 by E the mechanical equivalent of the heat, on the hypothesis 

 adopted concerning heat, 



2(im?, 2 ) = MKTE. 



The value of the elementary work dL can then be put under the 

 form y r7 - x 



dL =MKE ( cZT + 2T f? ]. 



Admitting, as before, that heat consists in a vibratory motion, 

 various phenomena can be analyzed from that point of view. 



1. With bodies in the solid state the ordinary specific heat is sen- 

 sibly equal to three times the absolute specific heat. Let us see 

 what indication is furnished in regard to this by the above-stated 

 theory. 



The quantity of heat necessary to increase the temperature of the 

 body by dT is then 3MKdT. A part of this heat, MKdT repre- 

 sents the increment of the heat really existing within the body ; so 

 that the heat expended in work is 2MKdT. We have therefore 



<ZT=2t4-. 



This relation amounts to the following — 

 — = constant. 



Substituting for i and T their values deduced from the preceding 

 relations, we find the condition /= constant. 



Therefore, in bodies in the solid state, when the vulgar specific 

 heat is equal to triple the absolute specific heat, the molecular forces 

 have a sensibly constant value, independent of the temperature. 

 We thus rediscover a property enunciated in a previous memoir*. 



* Comptes Rendus, vol. lxxi. p. 934 ; Annates de Chimie et de Physique, 

 S. 4. vol. xxiv. p. 306. 



