On the Distribution of Electricity on Spherical Surfaces, 193 



But MM'T = NMP, and MTM'=180°-MNS, and also 

 sin NMP 1 

 — : — mxTo =T^> whence 

 smMNS N' 



n _ sinMM'T _ sin NMP _ 1 

 A ~ sinMTM' ~ sin MNS ~ n' 

 or 



n2=A, 

 which was to be proved. 



I have said above, that the law of density here assumed con- 

 ditions also the hypothesis that the vibrations of light are per- 

 pendicular to the plane of polarization. If, however, instead of 

 the above supposition that the earth is at rest, we had considered 

 that, as is actually the case, the surrounding aether is unmoved 

 while the earth has the velocity c, the result is obviously the same ; 

 the absolute velocity, however, with which the sether moves in 

 the prism is now equal to the velocity of the prism itself, less the 

 velocity it would have had in the prism at rest on the opposite 



supposition, or c— •t-=c( — T~]'' ^^^*' ^^ to say, the sether is 



carried along with the prism, though not at the same rate. 



This result was confirmed latterly by Foucault by direct experi- 



n^— 1 

 ment with water, where — -^ — is nearly \. 



XXX. On an Analytical Theorem connected with the Distribution 

 of Electricity on Spho'ical Surfaces. — Part II. By A. Cay- 

 ley, Esq. 



[Continued from p. 127.] 



THE theorem is certainly true ; but its existence gives rise to 

 a difficulty to which I shall advert in the sequel. I pi-o- 

 pose, in the first instance, to give a demonstration which starts 

 from the expression for fz given by Plana's equation (115), 

 instead of the deduced equation which was the basis of my former 

 proof. It will be proper to explain the origin and meaning of 

 the formulae. We have two conducting spherical surfaces, radii 

 1 and b, in contact with each other (so that the distance between 

 the centres is 1+b). And then, if x is the distance from the 

 centre of the sphere radius 1 of an exterior point, and /u,(= cos 6) 

 the cosine of the inclination of this distance to the line from the 

 centre to the centre of the other sphere, the potential ^(/it, x) of 

 the sphere radius 1 at the point whose coordinates are {x, fj,) is 

 deduced from the potential fx of a point in the axis ; that is, if 



fx = Ao+AiX + Aa*^ + &c., 

 Phil. Mag. S. 4. Vol. 18. No. 119. Sept. 1859. O 



