Mn MAXWELL, ON FARADAY'S LINES OF FORCE. 43 



By this assumption we find that if V be the potential, 



dV = Xdoo + Ydy + Zd% = - dp, 



or since at an infinite distance V =0 andp = 0, F = —p. 

 In the electrical problem we have 



In the fluid p = 2 ( ] ; 



p-.f^). 



_ 47r , 

 .•. .y = — dm. 

 k 



If A; be supposed very great, the amount of fluid produced by each source in order to 

 keep up the pressures will be very small. 



The potential of any system of electricity on itself will be 



^{pdm)= ^,-E{pS)^-^W. 

 47r 47r 



If 2 (dm), S (dm') be two systems of electrical particles and pp' the potentials due to them 

 respectively, then by (32) 



2(pdm') = — , 2(p5') = — , 2 (p'^ = 2 (p'dm), 



47r 'tir 



or the potential of the first system on the second is equal to that of the second system 

 on the first. 



So that in the ordinary electrical problems the analogy in fluid motion is of this kind : 



r=-p, 



X=-^ = Am, 

 dx 



k 

 dm = — S, 

 47r 



k . 



whole potential of a system = - '2Vdm = — W, where W is the work done by the fluid in over- 



coming resistance. 



The lines of force are the unit tubes of fluid motion, and they may be estimated numerically 

 by those tubes. 



Theory/ of Dielectrics. 



The electrical induction exercised on a body at a distance depends not only on the distri- 

 bution of electricity in the inductric, and the form and position of the inducteous body, but on 

 the nature of the interposed medium, or dielectric. Faraday * expresses this by the conception 



* Series XI. 



6—2 



