TO THE THEORY OF MAGNETISM. 105 



are not very great and of the order . If F t represents what 



& ' 



F becomes by changing u into u + 2t, we have 



^ ^r-!.W^F)L^ st '*"" ; 



and consequently 



which, by effecting the integrations and rejecting the imaginary 

 quantities, becomes 





Suppose now j? is a perpendicular falling* from the point p 

 upon the surface of the plate, and on this line, indefinitely ex- 

 tended in the direction Op, take the points p^ p# p a , &c., at the 

 distances 2, 4, 6^, &c. from p ; then F v F z , F B , &c. being the 

 values of F, calculated for the points p^ p# p s , &c. by the for- 

 mula (a) of this article, and r' l9 r' 2 , r' 3 , &c. the corresponding 

 values of r', we shall equally have 



and consequently 



F= | (1 - g) (, + - + -*- + &c. in infinitum) ; 



seeing that J^ = 0. 



From this value of F, it is evident the total action exerted 

 upon the point p, in any given direction pn, is equal to the sum 

 of the actions which would be exerted without the interposition 

 of the plate, on each of the points p, p v p# &c. in infinitum, 



in the directions pn t p^ p z n z , &c. multiplied by the constant 





 factor - (1 g) : the lines pn, pji^ p^ &c. being all parallel. 



Moreover, as this is the case wherever the inducing point P 



