ASSOCIATION UNIT OF RESISTANCE IN ABSOLUTE MEASURE. 
675 
coefficient of mutual induction without regard to the number of turns. Lj and L 3 
may be calculated from the formula 
L = 47 Td 
10&7+ 
1 
12 
cot 2d—J7rcosec20—-Jcot^log^cos d—■g-tan s dlog lS sin d 
in which r is the diagonal of the section, and d the angle between it and the plane of 
the coil. With this formula and with the dimensions as measured when the coil was 
wound, we get 
Lj. (for A) =1029‘3 centims. 
L 3 (for B) =1031'9 centims. 
It would not be difficult to calculate an approximate correction for the curvature of 
the coil, but this is scarcely necessary. (See p. 119 of former paper.) Adding the 
above, we have 
L 1 +L 3 = 2061*2 centims. 
The value of M was found from the tables given as Appendix I. to § 706 of the new 
edition of Maxwell’s f Electricity.’ If we suppose each coil condensed into the centre 
of its section, we find M= 47?X 33*061. A more exact calculation by the formula of 
interpolation explained in Appendix II. gives M=47 tX 33*140, so that 
2M= 832*88 centims. 
The final result is accordingly 
L=16 3 X 18 3 X 2894*1 = 2*4004X 10 8 centims. 
These calculations of the coefficients of induction have been made independently by 
Mr. Niven and myself, and are so far reliable; but we must not forget that the 
accuracy of the result depends upon the accuracy of the data, and that in the present 
case the diagonal of the section (r) on which the most important part of L depends is 
an element subject to considerable relative uncertainty. It is probable that the 
effective axial dimensions of the section is somewhat less than the width of the 
groove, and therefore that the real value of L may be a little greater than would 
appear from the preceding calculation. 
Theory of the ring currents. 
If the circuits are conjugate, the currents in the wire and in the ring are formed in 
complete independence of one another, a circumstance which simplifies the theory very 
materially. In the same notation as was used in the former paper (p. 105), and with 
dashed letters for the ring circuit, we have as the equation determining the angle of 
deflection (f) when the wire circuit is closed. 
