548 Royal Society : — Prof. W. G. Adams on the Forms 



adduced reasons, which are not altogether satisfactory, for em- 

 ploying the equation (a) for that purpose. The use of that 

 equation I consider to be completely justified by the argument 

 contained in the present communication. 



Again, supposing X to be the north latitude and the longi- 

 tude west from Greenwich of any particle of the ocean distant by 

 t from the earth's centre, the above-mentioned solution is effected 

 by assuming that 



<£ = F(r)cos 2 \sin2(0-/*O. 

 Having been led to adopt this form of <j> by indirect considera- 

 tions, for verification I substituted it in the equation (a), and 

 thus obtained a differential equation containing only F(r) and r, 



C 



the integration of which gave Y(r) = Cr 2 + -j. Thus the truth 



of the above expression for (f> was proved by an argument a pos- 

 teriori. The proper course for arriving at the same expression 

 directly would be to obtain a solution of (a) suitable to the given 

 circumstances by means of Laplace's coefficients. 



To these remarks relative to the above-mentioned problem I 

 have only to add that I consider the mathematical details of 

 the solution contained in pp. 261-266 of vol. xxxix. of the 

 Phil. Mag. to be quite correct, excepting that the expressions 

 for X and Y in p. 262 should have included the terms afx 

 and co 9 y respectively, on account of centrifugal force. 



Cambridge, November 20, 1875. 



LXV. Proceedings of Learned Societies. 



ROYAL SOCIETY. 



[Continued from p. 152.] 



February 25, 1875. — Joseph Dalton Hooker, C.B., President, in 



the Chair. 



HPHE following communication w T as read : — 



" On the Forms of Equipotential Curves and Surfaces and 

 Lines of Electric Force." — The Bakerian Lecture. By Prof. "W. 

 G. Adams, M.A., F.E.S. 



Tbis paper contains an account of certain experimental verifi- 

 cations of the laws of electrical distribution in space and in a plane 

 conducting sheet. 



The potential at any point of an unlimited plane sheet due to a 

 charge of electricity at any other point of the plane at distance r 

 from it is proportional to the logarithm of the distance ; and the 

 potential due to two or more charges at different points of the 

 plane is the sum of the potentials due to the several charges ; so 

 that when there are two points in a plane conducting sheet con- 



