46 LECTURES AND ESSAYS [1869- 



of electric currents of his beautiful theory of the motion of 

 an immaterial incompressible fluid in a resisting medium, 

 but does not appear to have developed the suggestion. 1 



The object of this paper is to show that, by regarding, 

 in accordance with Maxwell s suggestion, every point of 

 exit or issue as a source or sink, spreading or absorbing 

 electricity, independently of all other sources, Kirchhoff s 

 general equations may be deduced by easy geometrical 

 processes, and extended to certain cases of flow in curved 

 surfaces. We shall, by this method, be naturally led to 

 look mainly at the function u, which in the analytical 

 investigation is subordinated to v. The equation u = 

 will receive an obvious physical interpretation, and we 

 shall then proceed to consider in detail the nature of the 

 flow in certain special cases apparently not yet examined. 



If a source P, in an infinite uniformly resisting plate, 

 steadily give forth a quantity of electricity E per unit of 

 time, the flow per second over the whole circumference of 

 all circles with P as centre is equal. Hence the rate of 

 flow at each point of the circumference of such a circle is 



jr 

 inversely as the radius and = . The potential due to P 



satisfies the equation 



dr~ 2irr 

 or, E 



The potential due to any number of sources P l P 2 etc., 

 and sinks P/ P 2 etc., all of equal power, is got by simple 

 superposition. If E be equal for all points, 



v = C - 2 log r + 2 log /, 



2ir 2TT 



where r corresponds to a source, and r to a sink. Hence 

 the equipotential lines are 



r^fe = c (5)&amp;gt; 



1 Cambridge Phil. Trans, vol. x. 



