On the Distribution of Electricity upon Spherical Surfaces. 119 



The average error for T being 0-036 millim., the probable 

 error 0-024 millim., which, in the determination of h — h', is 

 quite inappreciable. 



In order, finally, to compare the calculated errors {h — h') m 

 the scalar division with those observed, numerous experiments 

 were made with the four instruments above mentioned, the 

 results of which are put together shortly in the following 

 Table:— 



It appears from this Table that the difference between the 

 observed and calculated values of h—h' only twice reached -13, 

 which on the scale answered to about '2 millim,, a degree of 

 accuracy which must be pronounced to be perfectly satisfactory. 



XXII. On an Analytical Theorem relating to the Distribution of 

 Electricity upon Spherical Surfaces. By A. Cayley, Esq.^ 



THERE is contained in Plana's Memoire sur la distribution 

 de I' electricite a la surface de deux spheres conductrices com- 

 pletement isolees {Mem. de Turin, vol. vii. 1845), an identical 

 relation which is remarkable, as well in itself as because by means 

 of it the author corrects an error into which Poisson had fallen 

 in his researches on the same subject. The development of a 

 certain definite integral is obtained in the form (equation 165) 



j/=-2.3 



Mj/i 



21.^3.4. 

 ^2^+TT2 



sm*^^+ &c. 



IF"" 2^ 1.2 b^ 

 Poisson had in effect shown that M, =0; and be thence inferred 



* Communicated by the Autiior. 



