Q6 Prof. H. Lamb on the Theory of Electric 



with the condition that at the surface 



whence 



0=-|o-VR?/t) (37) 



If we neglect the slipping, the hydrodynamical theory gives 



p=^YU.^+ const,, .... (38) 



so that the relation (29) is verified. 



6. It is to be noticed that a comparison of the results of 

 § 1 with those of § 4 indicates the existence of a Dissipation- 

 Function ; and from this point of view the connexion between 

 the various classes of phenomena discussed in this paper may 

 be very concisely exhibited. Considering, for instance, the 

 case of a porous diaphragm, and distinguishing the two sides 

 of it by the letters A and B, let P be the excess of pressure, 

 and V that of electric potential, in the fluid on the side A. 

 If U be the quantity of fluid, J that of electricity, which is 

 transferred per second from A to B, then the rate of dissipa- 

 tion of energy is 



2F = PU + VJ (39) 



Now P and V are obviously linear functions of U and J, say 



P=KU + «J| 



V«XU + BjJ' (40) 



where K is the hydraulic and R the electric resistance of the 

 system of channels. In the case of § 1 we have P = 0, and 

 therefore 



whilst in § 2, U=0, and therefore 

 P=*J. 

 Again, in the case of § 4 we have J = 0, and therefore 



V=\U=g.P. 



The results we have obtained show that 



ic=\=-Kapj^ (41) 



