fig Prof. A. Gray on the Calculation 



where 



K.,= - \ { £* (4*,'-3««)- J(4^-3« 2 ) } , 



K 6 = - | { ^(W-6^V+ £*)- ^(4V-6%V+ i« 4 )} , 



_ 1J 



K ' =_ 8\, 



If one of the coils, say that of radius a, have its centre at 

 the origin, % 2 = — #1, and the terms of even order all vanish 

 since k 2 , & 4 , &c. vanish. If, besides, the other coil have its 

 centre at the origin, ? 2 =— fi, and the even terms doubly 

 vanish. 



Further, if besides being so placed the second coil be con- 

 structed so that its length 2f 2 = v /3a, the third term of the 

 series in (13) will vanish ; and similarly the fifth term will 

 disappear if the first coil fulfil the relation 2«£ 2 = y / 3a. Thus, 

 under the conditions specified, all the terms in (13) between 

 the first and seventh disappear. 



The first term will give T to a sufficient degree of approxi- 

 mation for all practical purposes if a ^> 2a/3, as then the coeffi- 

 cient of Z 7 (0) does not amount to more than 1/4500 of that of 

 Zi(0) , and the terms of higher order are relatively unimportant. 

 If a. -jp> a/2 the seventh coefficient in (13) is, at most, only 

 about 1/26,000 of that of the first. 



