GAS CONDENSERS. 635 



From these two equations (n) and (13) we deduce 

 dA c) 2 A 



;, Q 



= - S dx- -d= -d S 



The capacities X and Y are therefore functions of the capillary 

 tension. It follows from this that if this tension is a function of the 

 difference of potential, as experiment shows, this capacity cannot be 

 null. If the surface is deformed, while the difference of potentials is 

 kept constant, there should from equation (10) be a production or 

 absorption of electricity ; and, if we work at a constant charge, we 

 modify the difference of potentials. These two orders of phenomena 

 are therefore correlated, which is what experiment confirms. 



652, GAS CONDENSERS. Boltzmann has proved, in conformity 

 with Maxwell's theory (634), that the capacity of a condenser, whose 

 two coatings are separated by a layer of gas, varies proportionally 

 with the pressure. The converse must follow, that the pressure of 

 a definite mass of gas, placed between the coatings of a condenser, 

 is a function of the difference of potential. 



The two independent variables on which the phenomenon here 

 depends, are the difference of potential x, and the pressure p of 

 the gas. When the positive armature receives a quantity dm of 

 electricity, we have 



(14) dm = Cdx + hdp. 



The factor C represents the capacity of the condenser at constant 

 pressure, *h a coefficient which experiment shows is positive, for 

 the capacity increases with the pressure, and which is determined 

 by Maxwell's theory. The principle of the conservation of elec- 

 tricity gives 



ac M 



Let us now consider a closed cycle, without change of tempera- 

 ture. The work required to increase by dm the charge of the 

 positive coating is equal to xdm ; on the other hand, a mass of 



