﻿464 Mr. W. M. Hicks on the Self-induction 



flux functions (and therefore forces) and self-induction of 

 large tores of any size may be calculated to any desired 

 degree of approximation directly from the formulae obtained. 

 AY hen, however, the rings are of smaller cross section, and k 

 small, it is more convenient to have the formulae expressed 

 directly in terms of k. 



6. Putting in the values of P, Q given in [T. F. ii. 9, 10], 

 and remembering that djdu= —kd[dk, it will be found that, 

 L denoting log e 4/&, 



&^,{ 4 L- 6t (, L -l> + (- L -i|>}, 

 &_ _24 



7T ~ 35 ' 



and that the self-induction 



7rR ,„ „ N . 47rRcos 3 « 



= -f(l + 2 cos«) +( ^^{4L- 6 + (14L-18)^} 



when a is very small this is 7rR(4L — 7), and not 7rR(4L — 8) 

 as usually assumed. 



Taking Professor Minchin's example, R= 1 cm., r=*l cm., 



sin«=-l, cosa=*995, A 2 = 10025, 



and self-induction = 33'36 C.Gr.S. units. The formula 

 47rR(L — 2) gives 29*9. The numerical values given by 

 Prof. Minchin appear to be doubled, as if he had used the 

 diameter instead of the radius. 

 Similarly, 



Hence, for space outside the ring. 



