and its Application to the Molecular Motions of Gases. 199 

 side then represents the total ergal U, and we get 



U=Nw-£[- + - + ±]n>— (109) 



n \c l c 2 c 3 / 



We multiply the second equation by ^, and then subtract 

 J log (4mf from both sides. The left side then represents, 

 according to (95), the quantity log il, and consequently there 

 comes 



log U = log (2V*%)- — Z/Sf- + - + iW». (110) 



W \ C l C 2 C 3/ 



In referring these equations to the particular parallelepiped 

 with the sides a, b, b, we have to substitute \a, \b, \b for the 

 quantities c v c 2 , c 3 , and then to bring into use equations (81), 

 whereby we obtain 



2 3 c l c 2 c 3 = ab* = Y-e, 

 1112 4 S 

 Cj c 2 c 3 a b V— e 



that the preceding equations will be : — 



Z S 7 lz± 

 U = Nw -ft ^ — tt> » ; 

 n v — e 



log U = log (V - e) - ^ Z/3 ~- ttT «. 



(Ill) 



(112) 



If we denote, as before, the total vis viva of the system by T, 



then 



2 T 

 T = i N3wiW, and hence it) = - 1 r r -> 



by which the equations are changed into : — 



If by V we understand specially that volume which contains a 

 unit weight of the gas, so that the masses of the molecules con- 

 tained in it together form a unit of mass, we have to put Nm = l. 

 .For this case we will, for simplification, introduce the symbol y, 

 the meaning of which is determined by the equation 



(o\n-i 7 



