152 Intelligence and Miscellaneous Articles. 



is joined to earth : then A is insulated. If the pressure p of the 

 gas in the receiver is now increased, it can be demonstrated that the 

 quantity of free electricity on A is diminished. The insulation 

 remains perfect, and the plate A has not moved ; but the capacity 

 of the condenser has become greater by the introduction of the gas 

 into the previously exhausted receiver. The effect is virtually the 

 same as if the distance between the plates had become D times less. 

 The gas possesses, then, the property of making the capacity of 

 the receiver D times greater by its presence, D being what is called 

 the dielectric power of the gas under pressure p. M. Boltzmann 

 has proved that D varies for different gases, and for any one gas 

 varies proportionally with the pressure p. 



Such is the phenomenon given by experience, and to which we 

 will apply equation (a). For this end let us take for independent 

 variables the potential x of the plate A, and the pressure p of the 

 gas. Let us write 



dm=c dx-\-h dp, 



where dm is the quantity of electricity received by the plate A when 

 x increases by doc and p by dp, and where c is the capacity of the 

 condenser when the gas is maintained at pressure p, and h a coeffi- 

 cient which, according to Boltzmann's experiments, is positive. 

 Equation (a) becomes here 



d^> " Vx (a ; 



This equation expresses the principle of the Conservation of Elec- 

 tricity. 



In order to complete the study of Boltzmann's phenomenon, we 

 must apply to equation (a) that equation which expresses the prin- 

 ciple of the conservation of energy. "When the piston of the 

 air-pump in M. Boltzmann's experiment is displaced through an 

 infinitely small distance, the volume v of the air contained in the 

 apparatus varies by an amount dv. If we lay down the following 

 equation, 



dE =p dv — x dm, 



dE will represent the differential of the energy : and it can be de- 

 monstrated easily that the principle of the Conservation of Energy 

 will be expressed by the condition that dE be an exact differential. 

 To write down this condition, we must express dv as a function of 

 x and of p. Let us put 



dv = adx+bdp, 



a being a coefficient about which we will make no hypothesis, b being 

 a function of p and perhaps of x also. We have consequently the 

 relation 



ba _"db .... 



d^ ~~ ^x ^ } 



Substituting for dv its value in the expression of dE, we have 

 dE = (ap — cx)dx -\-(bp — hx)dp. 



