THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



— — 4? 4> \ 



[SIXTH SERIES.] 



MARCH 1916. 



J * 4' 



XXVI. On the Electrical Capacity of Approximate Spheres 

 and Cylinders. By Lord Rayleigh, O.M., F.R.S* 



MANY years ago I had occasion to calculate these 

 capacities f so far as to include the squares of small 

 quantities, but only the results were recorded. Recently, 

 in endeavouring to extend them, I had a little difficulty in 

 retracing the steps, especially in the case of the cylinder. 

 The present communication gives the argument from the 

 beginning. It may be well to remark at the outset that 

 there is an important difference between the two cases. 

 The capacity of a sphere situated in the open is finite, being 

 equal to the radius. But when we come to the cylinder, 

 supposed to be entirely isolated, we have to recognise that; 

 the capacity reckoned per unit length is infinitely small. 

 If a be the radius of the cylinder and b that of a coaxal 

 enveloping case at potential zero, the capacity of a length I 

 is J 



¥ 



log (&/«)' 



which diminishes without limit as b is increased. For clear- 

 ness it may be well to retain the enveloping case in the first 

 instance. 



* Communicated by the Autbor. 



t " On the Equilibrium of Liquid Conducting Masses charged with 

 Electricity," Phil. Mag. vol. xiv. p. 184 (1882); ' Scientific Papers/ 

 vol. ii. p. 130. 



X Maxwell's ' Electricity,' § 126. 



Phil. Mag. S. 6. Vol. 31. No. 183. March 1916. 





