TO THE THEORY OF MAGNETISM. 103 



which, as c is perfectly arbitrary, must be the part due to the 

 term Q (i} -^ in the potential function arising from the inducing 

 bodies. If then this function had been 



V jf " V^ ya V r /a V r / 4 



where the successive powers c, c 1 , c 2 , &c. of c are replaced by 

 the arbitrary constant quantities k , & x , & 2 , &c., the correspond- 

 ing value of the total potential function will be given by making 

 a like change in that due to P', Hence if, for abridgement, we 

 make 



fc \7 s + r4^7 3 +&c. ) 



the value of this function at the point p will be 



Now, if the original one due to the point P be called F, it is 

 clear the expression just given may be written 



where the symbols of operation are separated from those of 

 quantity, according to ARBOG AST'S method ; thus all the difficulty 

 is reduced to the determination of F. 



Kesummg therefore the original supposition of the plate's 

 magnetic state being induced by a particle of positive fluid con^- 

 centrated in P, the value of the total potential function at p 

 will be 



as was before shown. 





Let = m : we shall have 



