496 ON PHYSICAL LINES OF FORCE. 



When the resistance to compression is infinitely greater than the resistance to 

 distortion, as in a liquid rendered slightly elastic by gum or jelly, 



E t = Zirm ................................... (109). 



The value of E 1 must lie between these limits. It is probable that the substance 

 of our cells is of the former kind, and that we must use the first value of E 1 , 

 which is that belonging to a hypothetically "perfect" solid*, in which 



5m = 6/x. ................................. (110), 



so that we must use equation (108). 



PROP. XIV. To correct the equations (9)f of electric currents for the effect 

 due to the elasticity of the medium. 



We have seen that electromotive force and electric displacement are 

 connected by equation (105). Differentiating this equation with respect to t, we 

 find 



dR n, dh 



shewing that when the electromotive force varies, the electric displacement also 

 varies. But a variation of displacement is equivalent to a current, and this 

 current must be taken into account in equations (9) and added to r. The three 

 equations then become 



(112), 



r = 



where p, q, r are the electric currents in the directions of x, y, and z ; a, y8, y 

 are the components of magnetic intensity; and P, Q, R are the electromotive 

 forces. Now if e be the quantity of free electricity in unit of volume, then the 

 equation of continuity will be 



* See Rankine "On Elasticity," Camb. and Dub. Math. Journ. 1851. 

 t I'hil Mag. March, 1861 [p. 462 of this vol.]. 



