200 SYSTEMS COMPOSED OF MOLECULES. 



that is, 



da = O + PI* ft*-? ^ _ a - fa _ s 2i dai (525) 



Since equation (503) gives 



the preceding equation may be written 



dQ, ILd 2 vid/xi 2 2 l da lt (527) 

 Again, equation (526) gives 



c?Q + Sjiie^i + S vi cZ/*! de = dH + Hc2. (528) 

 Eliminating <#fl from these equations, we get 



de = rfH + 2/x^i - S^j rfoj. (529) 



If we set * = e + H, (530) 



d* = de + dH + H d, (531) 



we have d* = H d + 2 ^ d^ - S -^ e?^. (532) 



The corresponding thermodynamic equations are 



de = Tdy + 5 ^dmi S -4i ^ , (533) 



(534) 



/xi cZm! SA <?% . (535) 



These are derived from the thermodynamic equations (114) 

 and (11 7) by the addition of the terms necessary to take ac- 

 count of variation in the quantities (m v m v etc.) of the 

 several substances of which a body is composed. The cor- 

 respondence of the equations is most perfect when the com- 

 ponent substances are measured in such units that m v m 2 , 

 etc., are proportional to the numbers of the different kinds 

 of molecules or atoms. The quantities p v p 2 , etc., in these 

 thermodynamic equations may be defined as differential coeffi- 

 cients by either of the equations in which they occur.* 



* Compare Transactions Connecticut Academy, Vol. Ill, pages 116 ff. 



