Dr. Tyudall on the Latvs of Magnetism. 291 



or positive according as the two poles are of the same or of op- 

 posite names. This may be called the fmidamcutal law of mag- 

 netism. We have already assmned the magnetism of the soft 

 iron sphere to be proportional to that of the magnet. By aid of 

 this assumption, the law of Lenz and Jacobi can be immediately 

 deduced from the above fundamental principle. Let m-^ be the 

 magnetism of the magnet, and m^ the corresponding magnetism 

 of the sphere at a given distance. The attraction will be 



Supposing the power of the magnet to be increased n times, the 

 sphere will receive a proportionate increase, and the attraction 

 will then be 



wrtij X nm^, 

 or 



nhn-^iUQ. 



In like manner, for any other multiple, n', the attraction M'ill be 



n'hn^viQ ; 



hence the attraction in one case is to the attraction in the other as 



which expresses the same as the law of Lenz and Jacobi. 



34. Li (29.) it was asserted, that the attraction of a soft iron 

 ball at the unit of distance was not proportional to the strength 

 of the magnet. We now learn that it is proportional to the square 

 of the stre)igth. Calling A and A' the attractions exerted by any 

 two magnets of the strengths M and ]\I' at the unit of distance, 

 we have 



M2:M'2 = A:A'. 



Substituting M'^ and M'^ for A and A' in equation (2.), we shall 

 have for the position of equilibrium 



R:R' = M2:M'2, 



which is exactly the same result as that established in (30.) by 

 direct expc'riment. 



§ 9- 



35. Table VIIL shows us that a distance of ^j^th of an inch 

 between the ball and i)ole entirely changes the law of attraction. 

 In contact, a double current will support a double weight ; but 

 at jj-yth of an inch distance-, a double cuireiit will support four 

 times the weight. Lidec.dj it is not until the ball is within 

 j^^jjdtli of an inch of the pole that any remarkable deviation 



