110 Magnetic Field diie to an Elliptical Current. 



for any values-of (j> and % may be readily calculated by finding 

 their arithmetico-geometrical mean (v. Cay ley, 'Elliptic 

 Integrals,' chap. xiii.). 

 - § 5. In the case of my standard coil 



a = 10*5419 inches, 

 6 = 10-5340 inches, 



and the angle made by the radius of brush contact with the 

 major axis is approximately 55°. 



I have calculated the values of H c - and H e for points on 

 this radius distant 1 inch, 2 inches, 3 inches, &c, from the 

 centre, with the following results : — : 



r. 



H c -f 2*r. 



H e -f2^. 



(T-r2^. 



rv-i-2'Gr. 







•094896 



•094896 



•oooooo 



•oooooo 



1 



•095542 



•095542 



•oooooo 



•oooooo 



2 



,•097551 



•097552 



•oooooi 



•000002 .-_. 



3 



•101142 



•10U44 



•000002 



•000006 



4 



•106764 



•106768 



•000004 



■000017 



5 



•115252 



•115260 



•000008 



•000040 



6 



•128235 



•128250 



•000015 



•000089 



■ 7 



•149170 



•14919& 



•000028 



•000199 



ff = He — He. 



§ 6. We are now in a position to calculate the value of B. 

 In the apparatus I used 



a = *0585, 



a 1= 6*4949. 



By numerical integration between these limits we have 



ra 



and 



Also we have 



f 



^=•000163, 



j" 



J a a 



B = 2<sr r<7dr= '00643. 



%= 6-4949, 

 c= 10-5377, 



M c = 94-014, 



and 



and hence 



and therefore 



B~M C = -0000684, 



or the required correction is -00684 per cent. 



And by the argument contained in § 2 this may "be taken 



