ON PHYSICAL LINES OF FOECE. 495 



We assume the axis of z to be in the direction of maximum variation of 

 the pressure among the particles, and we have to determine the relation 

 between an electromotive force R acting on the particles in that direction, and 

 the electric displacement h which accompanies it. 



PKOP. XIII. To find the relation between electromotive force and electric 

 displacement when a uniform electromotive force R acts parallel to the axis of z. 



Take any element 8S of the surface, covered with a stratum whose density 

 is p, and having its normal inclined 6 to the axis of z ; then the tangential 



force upon it will be 



P R8Ssmd=2T8S .............................. (99), 



T being, as before, the tangential force on each side of 'the surface. Putting 

 p = -- as in equation (34)*, we find 



'2.TT 



R= -2irma(e+2f) ........................... (100). 



The displacement of electricity due to the distortion of the sphere is 



ZSS^pt sin taken over the whole surface ............ (101); 



and if h is the electric displacement per unit of volume, we shall have 



f7ra% = fa j e ............................... (102), 



or h= ae ................................. (103); 



27T 



so that # = 47r j m /t ........................ (104), 



6 



or we may write R = irE 2 h .............................. (105), 



gi ^f 

 provided we assume E*= -rnn - -3L ......................... (106). 



6 



Finding e and / from (87) and (90), we get 



1..... 1 ...................... (107). 



The ratio of m to p. varies in different substances ; but in a medium whose 

 elasticity depends entirely upon forces acting between pairs of particles, this 

 ratio is that of G to 5, and in this case 



JS'-vm (108). 



* Phil. J%. April, 1861 [p. 471 of this vol.]. 



