636 SUPPLEMENTARY. 



gas in contact with the condenser produces an external work pdv, 

 when its volume increases by dv. If the gas and the condenser 

 return to their original condition, the change of energy of the system 

 is null, and we have 



(16) 



which requires that the expression within the parenthesis shall be 

 an exact differential. 



The volume v of the gas in question is a function of the pressure 

 /, and perhaps also of the difference of potential x ; we shall 

 therefore write 



(17) dv 



and the course of the reasoning will show whether the coefficient 

 a differs from zero. As this expression is also an exact differential, 

 we deduce from it 



Substituting in the expression (16) the values of dv and of dm, 

 we get 



( 

 [(O - op) dx + (hx -bp)dp~\ = Q. 



The condition of integrability is then 

 (19) 



(JJJ UA 



Taking into account equations (15) and (18), this condition 

 reduces to 



a= -h. 



The coefficient a is thus different from zero, and negative. It 

 follows then, from equation (17), that, at a constant pressure, the 

 volume of a mass of gas surrounding a condenser should diminish 

 proportionally to the difference of potential of the armatures. This 

 result seems to have been verified by Quincke at any rate for 

 carbonic acid. 



