ELECTRICAL DILATATION OF GLASS. 637 



653. ELECTRICAL DILATATION OF GLASS. A Leyden jar dilates 

 when it is electrified, and contracts as soon as it is discharged. 

 This phenomenon, foreseen by Volta, was demonstrated by M. Govi, 

 and M. Duter has shown that the expansion of gas is proportional 

 to the square of the difference of potential of the armatures. 

 Let us consider the phenomenon in the form given to it by M. 

 Righi, that is to say, a condenser formed of a glass tube whose 

 two faces are covered with tinfoil; let / be its length, and let us 

 suppose that at the same time the tube is exposed to a strain in 

 the direction of its length, which is represented by the weight /. 



As the length is a function of the difference of potential x, 

 and of the stretching weight /, we have 



(20) dl=adx + bdp. 



The coefficient a is positive, and measures the electrical elon- 

 gation, and b is the coefficient of elasticity of the tube. 



If we assume that the tube undergoes no permanent defor- 

 mation, it follows that 



(21) S* = S~- 



op ox 



On the other hand, it is to be presumed that the charge of 

 the condenser is also a function of the stretching weight, so that 

 we may put 



(22) dm 



C being the capacity of the jar, and h a coefficient which we do 

 not know a priori to be different from zero. 



The principle of the conservation of electricity gives 



DC M 



(23) = 



The variation of energy of the jar, for an increase dm of the 

 charge, and an elongation dl, is 



xdm +pdl= (Cx + ap} dx + (hx + bp)dp. 



