We then have 



the Gas-equation, 



p«=J-*p, 



878 



(5) 



or 



That is, the deviation from the ideal gas-equation is propor 

 tional to the pressure. This relation can be written 



PV-Rfl P' 



pv-RrF" .... 



(6) 



where P' and v are referred to one case and P" and v" to 

 another at the same temperature. 



The equation (6) includes no quantity characteristic for the 

 gas, and therefore can be regarded as a general gas-law in 

 the second approximation if Boyle-Mai iotte-Gay Lussac's law 

 is regarded as the first approximation. 



It will be of some interest to see what form the expression 

 of the expansion coefficient & p will take as a series in powers 

 of P and 6. 



We have dv 7T > 7/1 



— = k r cW. 

 v 

 and get from (4) 



+ P 3 (lO0 3 -9</)6 2 +6(/) 2 6-4^) + . . . . 1. 

 From (3) we get 



-L = I + Pc/) + P 2 (2</> 2 - 6 2 ) + P 3 (5</> 3 - 5<fo& 2 - V) + . . . 



As 

 we finally get 



o = a — 6, 



3<V-h<9 2 6> 2 + 26> 4 



F= i_[ 1+ p(^! a _ 6 ) +p2 (^±^ 



or if 



P-°=v 



46> a +(V6> + 46> 3 

 <9 3 



1 /Q * 

 a 2Jtf-=P> 77 =7, 



C7C7 (7 



a£ + 6 2 J...~] 



- (40 O 3 + Of 6 + 40 3 )/3 7 4- 7 2 # 2 } + ...], 



