﻿182 Mr. J. Trowbridge on Electrical 



(2) The radial-pressure gradient falls off in steepness both 

 nside and outside the altered layer, making up for this by 

 ncreased steepness in the layer itself. 



(3) The change of volume — whether expansion following p 

 nternal pressure, or contraction following external pressure 



— is reduced in the material both inside and outside the 

 altered layer. 



(4) The altered layer itself suffers greater change of volume 

 than if the entire sphere or shell were composed of the same 

 material as the layer. 



(5) The alteration of compressibility only throughout a 

 layer of given volume is equally effective for all positions of 

 the layer, but the alteration of rigidity only is more effective 

 the nearer the altered layer to the centre. 



(6) The stress-difference vanishes at every point of a simple 

 solid sphere ; but, if the compressibility of a layer be altered, 

 the stress-difference attains a finite value both outside the 

 layer and in the material of the layer itself, becoming of 

 importance in the layer itself however thin that may be. 



XIX. Electrical Resonance and Electrical Interference. 

 By John Trowbridge*. 



[Plate VII.] 



THE solution of the differential equations which express 

 the distribution of electricity on conductors of various 

 forms and varying magnetic permeability is not always 

 simple ; and many assumptions have been made in regard to 

 the constants which enter these equations. Thus Poincare t 

 assumes that the spark of a vibrator is dampened more 

 readily than that of the oscillator. This has been shown 

 independently by Bjerknes to be true when the oscillating 

 circuit is not closed by a spark-gap %. Stefan §, by making 

 the assumption that the oscillations are confined to the outer 

 layer of the conductor, reduced his differential equation to 

 the form treated by Lord Kelvin, in periodic heat move- 

 ments. Analysis leads him to suppose that the formula 

 t = 27r VL C applies only to a special case; and he gives a 

 more general law. 



With the conviction, therefore, that the experimental side 



* Communicated by the Author. 



f Electricite et Optique. 



% Ann. der Physik und Cliemie, xliy. 1891 ; xlvii. 1892, 



§ Ibid. xli. 1890. 



