22 Mr. Holmes on 



dC dC ^ 



sm?nz--r + cos7Uz-j-~ = 

 az dz 



^f dC . dC\ dF,^ 



Ficosmz-^ - smmz-^ j + — (Ccosw^r - Csinmz) = 0. 



Now F = kD ; we have therefore to consider the value of the 



dF 

 differential coefficient -^. 

 dz 



As stated above P is the pressure at some point^between 

 the planes A,+i A^+g in the actual state of the gas, from 



dF 

 which we immediately obtain — =^D. 



Thus our equations for C and C become, writing y 

 for 7/1^, 



. dC dC ^ 



cosy^sinj;^ + //(Ccosy - C'sinj) = 0, 



or 



where /i = ~. 

 mk 



If in these equations we put 



C = r sinj/ + C0SJ1/--J- 



^, ^ . dF 



C = rcosy - sinjK , 



the first is satisfied identically, while the second becomes 



d^F dF _; . 



dy^ dy 



the solution of which is 



P = e^y (^k.Q.o'-^vy + BsinrjF), 

 where ju + v ^" - i are the roots of 



X^ + //jv: + I = 



and J^ is supposed for the moment less than 4. 



The values of B and B' differ only from those of C and 

 C^ by containing different constants. If then we substitute 

 the values found in the expression for \, noticing that 



