Dr. Tyntlall on tlie Laws of Magnetism. 287 



ball of steel thus independently magnetized; and to make the 

 matter easier, we will suppose it charged with one of the fluids 

 only, say the north fluid. Let the force witli which the south 

 pole of a magnet attracts the ball when placed at the unit of 

 distance be a ; then, according to the common law of magnetic 

 attraction (where the pole is supposed to be contracted to a point), 



the force of attraction at any other distance, r, would be -^ . If 



the force with which the north pole of another magnet repels the 

 ball at the unit of distance be a', then at any other distance r' 



a 

 the repulsion will be -^ . If the two poles act simultaneously upon 



the ball from the same side of it, the ball vnW be in equilibrium 

 when attraction and repulsion are equal, or when 



from which we derive 



r : ?■' = \/a : \^a' ; 



that is to say, the distances between the point of equilibrium 

 and the respective poles are directly proportional to the square 

 roots of the strengths of the magnets. 



28. This is the law when the poles are points, and the mag- 

 netism of the body operated upon is independent. But in our 

 case the poles are planes, and the magnetism of the body ope- 

 rated upon is not independent. Let us conceive two flat poles, 

 charged with opposite magnetisms, to be placed parallel, one 

 underneath the other ; the upper one, however, being supposed 

 to offer no obstruction to tJie passage of the force from the one 

 beneath it. Let the force of attraction between the lower pole, 

 acting by itself, and the sphere of soft iron at the unit of distance 

 be A ; the attraction of the same pole at any other distance, R, 

 would, according to the law established in the last section, be 



A 



p-. The attraction of the upper pole for the ball, when acting 



on it singly at the unit of distance, being A', its attraction at 



A' 

 any other distance R' will be-^,. But when both act simulta- 

 neously upon the ball, that which causes attraction by the one 

 will cause repulsion by the other; and when tliese two forces are 

 equal, the ball will be in equilibrium ; that is to say, when 



A_ iV 

 R ~ R" 



or when 



R:R' = A:A'; (2.) 



from which we might be disposed by analogy to infer that the 



