416 



PROCEEDINGS OF THE AMERICAN ACADEMY. 



Professor J. J. Thomson solves the following problems, which are most 

 concisely stated by diagrams. The sign co at the end of a line, denotes 

 that the line is to be considered to extend to infinity in that direction. 



Every line represents the intersection with the plane of the paper of 

 planes perpendicular to the paper and extending to infinity in both direc- 

 tions, above and below. So that figure (a), for example, represents a 

 semi-infinite plane, near and parallel to another infinite plane. 



In all the diagrams these planes are to be considered conductors of 

 electricity. 



co- 



oo 



• oo 



00 - 



co- 

 oo 



(a) 



oo 



(b) 



oo 



oo 

 co- 

 co ■ 

 co- 



■ oo 



■ oo 



oo- 

 oo 



(c) 



oo 



(d) 



■ oo 



-00 



CO 

 00 



CO 



00 

 CO 



(f) 



The last two cases have special reference to the correction for the slit 

 in a guard ring electrometer. 



For further work on the electrometer from this point of view see the 

 French translation of Maxwell, Vol. II, p. 568, et seq., where M. Potier 

 has worked out more general cases. We can immediately extend these 

 results of Thomson's by the method of electrical images. We thus 

 obtain the solutions for the following cases, where v represents the 

 potential : 



