198 Prof. J. V. Jones. Calculation of the Coefficient of 

 8: For the values of A, a, x given in 6 we find 



W = 0-8890325, 



T = 0-0443163, 



2V = 0-1036138, 



log de = 2-9667036, 



8 = 0-0997, 



q = 1-2467, 



r = +2-3464, 



or cZM/M@ = l- 



Let us suppose that after re-winding the coil mentioned in 6, 

 and regrinding the disc, the diameters become 



2A' = 21*02459, 2a' = 13'01499. 

 Then rda/a 0'000899, 



qdA/A. = +0-000127, 

 and e?M@/M = 0'000772 or dM. 6'97 inches = I7'70cm. 



Therefore M' = 9021-21 inches = 22913*47 cm. 



9. I now pass on to the second and more general method of deal- 

 ing with the expression 



Integrating by parts we have 

 M e = 



16A 2 a 2 



, -. , 4A.a 



C 



Hence by simple changes we have 



; ..... (6), 



where F and E are complete elliptic integrals of the first and second 

 kinds to modulus fc, 



