Intelligence and Miscellaneous Articles, 153 



In order that dE may be an exact differential, we must have 



~d(ap — ex) _ d (bp — hx) 

 dp dx 



or, developing and comparing with equation (1), 



— (!-£)-* ;■«> 



This equation (/3) expresses the principle of the Conservation of 

 Energy. Comparing it with equation (a), equation ((3) reduces to 



a=-ft. . (fi) 



Such is, then, the result of analysis. The two principles of the 

 Conservation of Electricity and of the Conservation of Energy are 

 expressed by the system of equations (a) and (/3 ; ). According to 

 experiment, h is a positive quantity ; and a is, by equation (/3'), 

 always different from zero, and negative. Now a is the partial 

 derivative of v with respect to the potential x. Hence the follow- 

 ing phenomenon — that if, while the pressure is constant, the plate 

 A is more and more electrified, the circumambient gas will contract 

 under the influence of this electrification. The application of equa- 

 tion (a), then, makes us foresee a new electric property of gases. 

 I say equation (a) ; for equation (/3) alone does not permit us to 

 conclude that a is different from zero. The electric contraction of 

 gases has recently been perceived by an able German experimenter, 

 M. Quincke, in an experiment upon carbonic acid. 



M. Boltzmann has verified by experiment that 



7 being a specific constant of the gas, and n its refractive index. 

 Introducing this result into our preceding equations, it follows 

 easily that 



Av=-^yc x\ 



Av being the electric contraction of the gas, and c Q the capacity of 

 the condenser in vacuo. And since we have 



l + yp=n 2 , 

 it follows that 



p 

 or, in other terms, that what we call the " coefficient of electric con- 

 traction " of a gas is equal to its ref racting-power for light. 



In the accompanying memoir (presented to the Academie des 

 Sciences) I have applied the same kind of analysis to various elec- 

 tric phenomena — the expansion of the glass of a Leyden jar during 

 charge, the electrification of hemihedral crystals by compression, 

 pyroelectricity of crystals. I find, amongst other results, the 

 existence and the magnitude of the following phenomena, which 

 have not yet been verified by experiment : — (1) The dielectric power 



Phil. Mag. S. 5. Vol. 12. No. 73. Aug. 1881. M 



