ACTION OF A COIL AT A GREAT DISTANCE. 99 



The action of a coil will be again obtained by a double 



ci b c 



integration. If we neglect the fourth powers of the ratios - , - , - , 



x x a 



and consequently the ratio , we get 



oc 



zmra? f c 2 26* 3 a* 



i i + -T---i 



T a x 2 x 



3-4-5.6 /T < 2 7.8 



( 2 . 4 ) 2 



This action tends to become inversely as the cube of the distance, 

 as could be seen directly by comparing the coil to a magnet. 



742. ACTION OF A LONG COIL. In the centre of a coil of a 

 great length, the field in the interior is sensibly uniform (495) ; 

 the examination of this problem presents accordingly a particular 

 interest. 



We may observe, in the first place, that the action exerted in the 

 interior by a coil of length 2^, which only contains one layer of wire, 

 and therefore is equal to the induction of the equivalent magnetic 

 cylinder, has a component parallel to the axis 



an expression in which X a and X & denote the absolute values of the 

 components in respect of the two bases of the cylinder, where the 

 density is n v 



We have further (739) 



du j 



with 



*2 = r 2 + ( + *)*. 



H 2 



