AND THE LINES OF FORCE OF A CIllCULAR CURRENT. 



13 



which is given at once from the dimensions and configuration of the 

 coils. Instead of finding r, we shall have to calculate 



where 



_ 1-V^' 



of which the first term is generally sufficient,'^ as the following short 

 table for q—~Tr "^'i^l show. For practical purposes, a single calculation 

 according to formula (25) or (27) gives at once the value of M. In or- 

 der to shew the rapid convergence of the ^-series, it will be sufficient 

 to indicate the smallness of the corrections £ and £i, £/ entering in 

 the above tM'o formulae. For this purpose, the following short 

 tables of corrections have been calculated. 



I 



Table of c = 3g*-4g« + 9g«-12(7i° and q- 



2 



1) For the table of 7, see Jacobi, Crolle's Journal Bd. 26, p. 93: Gesammelte Werke, 

 Bd. 1, p. :^63. 



