A NEW CURRENT WKK1HKR, ETC. 509 



in formula (1), p. 507, was determined as follows: The mutual induction of one of 

 the two helices on CD, the lower half of the fixed cylinder, and the circle a,, was 

 calculated by finding M for the circle a, and helix BC (half of CD) and doubling it. 

 To find M, two mutual inductions were calculated, viz., that between a/ and a helix 

 of length JD, and that between a,' and a helix of length JC, and taking the 

 difference. It was therefore necessary to calculate three coefficients of mutual 



v 



induction ; these, for convenience of reference, are designated by M , M S| , and M, f 

 respectively. The value of (M a M,) for both helices* on CD is given by 



M,-M 1 = 2{2M.-(M e .-M ei )} ....... (2). 



For the current sheet OK, a/ and the helices on GH the value of (M s MI) was 

 determined from M,, M ei , and M Si by the increment formula 



'/M M '/A da , dx . 



- = - + '' + t ........ 3 



which gives the change in M e due to small changes in dimensions, A being the radius 

 of the helix, a that of the circle, x the length of the helix, and q, r, and s coefficients 

 determined as shown on pp. 200, 201 (Ibid.). 



The sum of the two values of (M a M,) thus obtained gives the total for the left- 

 hand set of coils, and is designated by M,.. 



As the dimensions of the right-hand set of coils are very nearly equal to those of 

 the left-hand set, the increment formula was employed for finding the two values of 

 (Mj M,) for this side of the current weigher and their sum called M,,. The " direct " 

 force between the fixed and suspended systems when arranged to assist each other 



may therefore be written 



.......... (4), 



and the mass required to balance this force is given by 



Taking the values of M L and M H determined on p. 514, and assuming g to be 

 981 '20, we get for both sets of coils (neglecting secondary forces) 



m 



0-1x184 51922-471 

 (for I ampere) = VI x -^^ x -^^- 



= 7'49964 grammes; 

 or change of mass on reversal of 1 ampere = 14*99928 grammes ...... (6). 



* As previously mentioned, each cylinder has double-threaded screw grooves. 



t 'Roy. Soc. Proc.,' vol. 63, p. 197, 1898. 



\ There are 184 turns on each suspended cylinder, the axial length of which is 12'983o centinw. 



