8 



On the Constitution of Matter^ 



If (T be the specific heat at the absolute zero 

 = ^ (1 



,, ^ 21 At ,^ . 



s = a- (1 + -^— )= (7 (1 + er) 



Where A - ,,. 

 The expansion is 



21Jg(T 

 4 m'h^ 



Jo_ 



zdt 



= 5ap 



And the rate of expansion 

 Bap ^fh 

 a ~ 2i u 



(1 - 2^ + 

 (1 + 9 A t) 



147y\ 



16 ; 



= e T (1 + Cj t) 

 which is in accordance with the known laws of expansion, e and 

 Ci being constants. 



Suppose a solid body consisting of oi equal atoms, and let 

 X y z represent a very small displacement of an atom. There will 

 be 3;i linear differential equations for the determination of such 

 quantities as a; ^ 2; ; and it may be shewn that 

 a? = 2 a cos (ja^ + O5 y = 2 S cos (^u,^ + Z), 2 = 2 c cos {ij,t + Z) 

 where ^ and I have Zn different values which are the same for 

 all quantities, such as a? y s. The displacement being small, and 

 no change in the constitution of the body being supposed to take 

 place, terms involving e* or e~* cannot, from the nature of the 

 case occur. The whole heat for this atom is proportional to 



-J 2 ijr (a- + 6- + C-) ; 

 and the heat developed as temperature is proportional to one-half 

 the non-periodic terms in 



m - ty ^ (rjy 



It foUows therefore, that for every atom, at very small tem- 

 peratures, one half the heat is developed as temperature, and the 

 remainder is latent. If then, there be two bodies, the masses of 

 whose atoms are M and Mj respectively ; at the same small tern- 



