of Force between Electric Currents. 461 



tial between the shell and current is 



x 2 +y 2 



the symbols having the same meaning as before. 



If, now, the potential of positive magnetic matter on one 

 face of the area A relative to the infinite current be fjbA.i$(x 7 y), 

 that of the negative matter on the opposite face will be 



-M**fa y) -M* (^ l + c ^ m } ] h 



where h is the thickness of the shell ; and the resulting poten- 

 tial is 



^ I dx dy J 



dy 

 But this has been shown to be equal to 



. ,, t ly—mx 

 ar-ry* 



Therefore these expressions must be equal for all values of I 

 and m; 



* ' ^dx ~ a?+f> ^dy " + x*+tf > 





and 



*(*,y)=^tan x 



/xA^(^y)=-^-tan- 1 | ? 



giving the law required. 



We have here shown in detail that these two results are 

 deducible from the law of F. E. Neumann; but it is evident 

 that we might have inferred this without further proof from 

 the fact that we are throughout dealing with complete circuits, 

 for which it has been already shown that the mutual potential 

 is in all cases the same as that given by Ampere's law. 



17. The adoption of the above law for the potential of two 

 elementary currents, viz. 



V= mi' ds ds f . 



v 



agrees perfectly with Maxwell's treatment of the subject, 

 although Maxwell nowhere distinctly states the existence of 

 the law, perhaps on account of its conflict with canon III. 

 mentioned at the beginning of this paper, the validity of which 

 Phil. Mag. S. 5. Vol. 11. No. 70. June 1881. 2 L 



