506 REroKT — 1887. 



per unit area. Now 



A/R--'=-iV/(l + 3?/R) ^ 



whence, for the strength of the source, 



3V 



— -ry^lp cos ..... (35) 



approximately. The corresponding potential at any point of the fluid is 

 therefore of the form 



, C cos^ , ^„,.. 



<ji= .2 + const. .... (3o) 



with the condition that at the surface 

 1 J.^ 3V 



whence 



C=-?,aYRIp (37) 



If we neglect the slipping, the hydrodynamical theory gives 



^=1 /aVE. . — 2 +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 connection 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 distinguish- 

 ing 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 dissipation of energy is 



2F = PU-1-VJ .... (39) 



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



P=KU + .J1 .^Q. 



whete 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. 



' Motion of Fluids, § 185. I take occasion to correct the final result (46) of the 

 article referred to. The dissipation of energy by sliding friction has been over- 

 looked. Allowing for this I now find, in the notation there employed, 



P = 6fiaY . (1 + 2fil$a)l(l + Sfij^a). 



If njPa ( = Z|a) be small, this is equal to the resistance which would be experienced 

 by a sphere of radius a — Z in the absence of slipping. 



