AND RATU) OK THEIR ATOMU; WKICHTS. 93 



When the gases are miugled, it is obvious that tlie constants li and b will 

 each enter into botli equations; whether the same is ti-ue of A, and how, are 

 [)erhaps uucei'tain. First supposing that it should not ; when 



V = 3, and 



V = -^—, we have approximately 



2 



P = ^ , and 

 3 



2 

 P = -• 



3 



We may therefore wi'ite 



(P + "^ ) (3 - B - 2b) =-- C, and 

 9 



(p + 4a) ( 3 _ b - :B^) =: ,, 

 92 2 



Neglecting products of the constants, we get 



P = ^ + -^- (A - B + b), and 



3 9 



p =^ + A(a-b + B). 



3 9 



The sum of these gives the pressure of the mixture, supposing that the oxygen and 

 hydrogen were originally measured at unit pressure and then mixed without 

 change of their joint volume; therefore 



P + p =. I + — (A + a). 

 9 



This is on the supposition that no nuitual attraction acts between the unlike 

 molecules. If such attractions exist, and if they follow the law f — . , we can 

 take notice of them by wiiting 



(P+4^)(3-B-2b) = C,and 



o 



(p + 4a^ A)(^_^_ B)^^_ 

 9 72 2 2 



Reducing as before, we get 



P + p r= I + ^ A + -'- a. 

 36 9 



The value of A seems to depend on the temperature, so that it must be deter- 

 mined from observations of pressure and volume at 0°. The experiments of 

 Amagat* serve to determine A and a. Sarrau f has discussed the first series, but 

 with some modification of Van der Waals' formula. If we reduce the constants 



* Annales de Cliiink et de Physique (5), 22, 353. t Coiiipks Raidiis, 94, 844. 



