MAGNETISM SUPPOSED NOT COLLECTED IN POLES. 37 

 or c~ m ~ 1 .zx$x.{3ySy 



/ 

 ( 



This is to be integrated through the whole length 

 of A, from x a to x = + a, and through the whole 

 length of B, from y = btoy = + b. Now, remarking 

 that x and y are absolutely independent, and that the 

 limits of the integrations are absolutely independent, it 

 will be seen at once that the double integral of each 

 term is simply the product of the two single integrals 

 related to the two variables x and y in that term, and 

 thus the double integral becomes 



We shall call the definite integral / ax "the magnet- 



J x 



power of A," and shall put the symbol A for it : and 

 similarly, we shall call the definite integral / /3y "the 



J y 



magnet-power of B" and shall use the symbol B for it. 

 For the whole of the bracket, which is a function of 

 definite integrals, we shall put K. (It is to be re- 

 marked that every one of these terms has a real valu, 

 inasmuch as, when the sign of x is changed, that is 

 when we consider the other half of the magnet, the 

 quality of the magnetism is changed, and therefore the 

 sign of a is changed : and therefore the sign of ax or of 



