474 PROCEEDINGS OP THE AMERICAN ACADEMY. 



N _Nd\nT 

 T~ dT ' 



hence by simply subtracting the equations we obtain 



d rV %2"=/2"'= ... ) dT ~ RT- RT'' 



Simplifying, and noting that — C + N R T =^ X, the heat actually ab- 

 sorbed in the reaction, we may write 



_^, Px"^p\"'^ ... _ - A 



dT p."2p'/2...- RT^' ^^^ 



Here — X signifies heat given out when the reaction takes place un- 

 der constant gas or osmotic pressure, because X signifies heat absorbed, 

 or latent heat. The equation states that when pressures are being com- 

 pared, the latent heat under constant pressure is the term to be used in 

 calculation. 



Hence at constant outside pressure the heat observed in any reaction 

 bears a very simple relation to the acting pressures which take part in 

 that reaction, just as at constant volume the concentrations are similarly 

 related to the observed evolution of heat. This equation may be called 

 the " Reaction-isobar," on account of the fact that constancy of total 

 pressure is the condition essential to its immediate application. The 

 equation of Clausius is a special case of this law. 



Evidently these reactions isobar and isochor may now be combined 

 into one, for the obstacles to this union are now removed. Before com- 

 bining them, it is advantageous to examine into the meaning of 



d\n(R7y=d\n T'' , 



which constitutes the only puzzling difference between them. 



The physical meaning of this important factor in the equation is inter- 

 esting. From its mode of introduction into equation (2), this term is 

 clearly the representative of the pressure caused by an addition to the 

 total number of molecules in a given space. Wheu the total pressure is 

 artificially maintained at a constant value, In T^ disappears from the 

 equation, just as it does when the pressure remains constant because the 

 total number of molecules present is not increased by the reaction. This 

 is equivalent to defining N in its present situation as a direct function of 

 the increase in the total pressure of the reacting svhstances during the 

 reaction. In order to avoid conflict with the original definition of N, we 



