74 APPLICATION OF THE PRECEDING RESULTS 



And hence, by differentiation, we immediately obtain the value 

 of the forces acting on any particle situate without the sphere, 

 which arise from its rotation ; but, if we would determine the 

 total forces arising from the sphere, we must, to the value of 

 the potential function just found, add that part which would be 

 produced by the action of the constant force upon this sphere, 

 when it is supposed to conduct electricity perfectly, which will 

 be given in precisely the same way as the former. In fact,/ 

 designating the constant force, and 6" the angle formed by r and 

 a line parallel to the direction of/, the potential function arising 

 from it, for the point JP, will be 



- r/cos 0", 



and consequently the part arising from the electricity, induced 

 by its action, must be 



+fr cos 0", 



seeing that their sum ought to be equal to zero. The cor- 

 responding value for the point p ', exterior to the sphere, is 



therefore 



fa 3 cos 0" 



this added to the value of V, before found, will give the value 

 of the total potential function for the point /?', arising from the 

 sphere itself. 



It will be seen when we come to treat of the theory of 

 magnetism, that the results of his theory, in general, agree very 

 nearly with those which would arise from supposing the mag- 

 netic fluid at liberty to move from one part of a magnetized body 

 to another; at least, for bodies whose magnetic powers admit of 

 considerable developement, as iron and nickel for example ; the 

 errors of the latter supposition being of the order 1 g only ; 

 g being a constant quantity dependant on the nature of the body, 

 which in those just mentioned, differs very little from unity. 

 It is therefore evident that when a solid of revolution, formed 

 of iron, is caused to revolve slowly round its axis, and placed 

 under the influence of the earth's magnetic force / the act of 

 revolving, combined with the coercive force fi of the body, will 



