214 ROSA, DORSEY AND MILLER! INTERNATIONAL AMPERE 



believed to be known to three parts in a million. On this basis, the abso- 

 lute value at the current balance is 980.091 cm. per sec. per sec, and is 

 probably correct to five or six parts in a million. 



As seen before, the constant K is the rate of change of the mutual 

 inductance with the displacement of one circuit in that direction in 

 which we wish to determine the force. In the present case then, K 

 is the rate of change of the mutual inductance of two coaxial circular 

 coils, with the displacement of one coil in the direction of the common 

 axis. The calculation can be simplified by first considering the actual 

 coils to be linear circular circuits of radii equal to the mean radii of the 

 coils. Then in various ways corrections for the finite sections of the 

 coil can be applied. Maxwell has derived an exact formula for the mu- 

 tual inductance of coaxial circles, and by differentiation obtained the 

 expression for the force between them acting along the common axis. 

 The force is given by the equation, 



F= SB = V37, t 2 *'- (1 + " rfT) M 



where A and a are the radii of the two coaxial circles, B is the distance 

 between their planes, Fy and Ey are the complete elliptic integrals of 

 argument y and » 



2VZa 

 sin 7 = — 



V(A+a) 2 +S 2 



, . . a B 



This expression for F can be put in a form where only the ratios — and — 



enter, hence F is a function of these ratios alone. Furthermore, at a 

 certain distance B the force is a maximum, and the coils of the Bureau 

 of Standards current balance were spaced so that this condition was 



a 

 satisfied. In this case the force becomes practically a function of ~ 



alone; in other words is determined solely by the ratio of the radii of 

 the two circles. 



The determination of this ratio is then the important point in the 

 determination of the constant of the instrument. It was determined 

 experimentally by methods which admit of extreme accuracy. The 

 principle of the method was identical with that given by Bosscha and 

 used by Lord Rayleigh, but was modified to increase the precision. The 

 coils to be compared were adjusted concentric and coplanar, with their 

 planes vertical and in the magnetic meridian. Most of these adjust- 



