510 PROFESSOR W. E. AYRTON, MR. T. MATHER AND MR. F. E. SMITH: 

 Similarly for reversal of 1 ampere in left-hand set we get 



m, = 7'49987 grammes . , . ... (7), 



and for right-hand set 



m r = 7 '49942 grammes (8). 



Further, we may express the current in amperes in terms of the mass to halance 

 change of force on reversal as 



Amperes = v/m/14'99928 (9), 



when both sets of coils are used (secondary effects eliminated), or 



Amperes = v / m/7'49987 for left-hand set . . . . (10) 

 and 



Amperes = \/m/7 '49942 for right-hand set. . . . (11). 



Again, by taking the sum of the balancing masses obtained in a D + S observation 

 and a D S observation* with the same current passing, and calling this m', we have 



Amperes = v/m729-99856 ........ (12), 



the formula employed in the great majority of the measurements. 



SECTION 10. CALCULATION OF MUTUAL INDUCTION OF HELIX AND CIRCULAR 



END OF COAXIAL CURRENT SHEET. 



The formula employed is 



...... (13), 



where 



= angular length of helix, A = radius of helix, a = radius of circle, 



x = axial length of helix, 



e 2 = 4 Ao/( A + a) 2 , c' 2 = 1 - c 2 , 



F = 4 Aa/( A + a) 2 + a 2 , V = 1 - F, 



and F, E and II are complete elliptic integrals of the 1st, 2nd and 3rd kinds 

 respectively ; F and E are to modulus k, and 



f 2 ( ty 



= J l-c 2 sin 2 l-Fsin 2 T 4 



* See p. 508. 



t J. V. JONES, 'Roy. Soc. Proc.,' vol. 63, p. 198, 1898. 



