Endosmose and other Allied Phenomena. 65 



The details of the process may be illustrated by the case of 

 a spherical particle. If r denote the distance from the centre, 

 the angular distance from the lowest radius, the stream- 

 function for the relative motion is of the form 



y=/ J ±+Br-±vAsm 2 6, .... (32) 



where V is the velocity of the sphere. The relative velocity 

 of the fluid over the surface is therefore 



°--jg=(ff-i +v )*"' • ^ 



if R be the radius. In consequence of the slipping, the zone 

 bounded by and + d0 gains electricity at the rate 



-pj^(27rRsin0.0)d0. 



Dividing by the area 2ttW sin . dO of the zone, we find that 

 each point of the spherical surface is, in regard to the sur- 

 rounding conducting mass, a source of electricity of strength 



2 / A B T7 \ a 



-n\W-R +Y )P cosd 



per unit area. Now 



A/R 3 =-iV/(l + 3//B) "I m% 



B/R=fV(l + 2Z/R)/(l + 3?/R)J ' ' 

 whence, for the strength of the source, 



- g ^lpcos0, (35) 



approximately. The corresponding potential at any point of 

 the fluid is therefore of the form 



^ = CcosJ +cong ^ 



* " 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 overlooked. Allowing for this I now find, in the nota- 

 tion there employed, 



P = 6naV . (1 + 2/t//3o)/(l +3/*//3a) . 

 If fi/^a(=l/a) be small, this is equal to the resistance which would be ex- 

 perienced by a sphere of radius a — I in the absence of slipping. 



Phil. Mag. S. 5. Vol. 25. No. 152. Jan. 1888. F 



