654 Mr. Shizuwo Sano on the Tliermodynamical 



reaction equations, and the 2n + l unknown quantities 

 Pi, pJ, • • • Pn, Pi", P2", • • • Pn", %"— "¥'/ are determined by 

 2n + l unknown quantities pi, p 2 ', . . . p n ', pi', p 2 " , . . . p n " y 

 W "-W/ are determined by 2n+ 1 equations (9), (10), (11), 

 and 



tqip/ = 0, Xqipi" = 0. ..... (14) 



Hence, if we write 



£— + qi(W e -W e ') = Gi, p = l, 2, . . . n ], . (15) 



-■F + S/i<|^ ■=(*»+!, (16) 



then the constants Gr are determined quantities. Solving 

 the w + 1 equations (15) and (16), the n + 1 quantities 

 — (M^— WJ), /Oi, f>2 5 • • . /o» and also the right-hand side of 

 the equation 



|H=s^ P i en) 



become functions of D and a only. Differentiating •qrj — 'qr e 

 with respect to x and making use of the equation 



B =S' (") 



and then eliminating D, we get an equation in the form 

 / da d 2 <F\ 



from which we deduce a solution of the form 



o=f 2 (x + A,B), (19) 



where A and B are constants of integration. 



During the process of reaching the final solution of a as a 

 function of x, we have differentiated WJ — W e with respect to 

 A", so that we cannot expect (19) to satisfy the condition that 

 W e ' — W e vanishes at P', unless the arbitary constants in (19) 

 are so chosen as to satisfy the condition. All the solutions 



of (17) satisfy the condition -^-- =0 at <j = ct', but not D = 



at the same point. Hence, in order that equation (19) may 

 be our solution, it must satisfy the three conditions that 

 W e — W e ' and D vanish at P' and a becomes a' at the same 



