308 LORD RAYLEIGH AND MRS. H. SIDGWICK ON THE ABSOLUTE 
made to the standard scale. Two independent measurements gave 83"580 and 83-579, 
mean 83'5795 centims., as the aggregate length. This was further verified by measuring 
each piece separately with callipers, the sum of the lengths thus found being 83'582. 
For the mean length of these distance-pieces we take 
27"8598 centims. 
As has been already explained, the rings were used in two positions relatively to 
the distance-pieces, with the view of eliminating any uncertainty as to the situation 
of the mean planes, and of rendering the final result independent of all measurements 
of thickness except that of the total thicknesses of the rings. Thus the mean distance 
of mean planes in the two positions is 
27*8598+£(2*8625+2*8067) = 30 , 6944 centims. 
To compare the partial results for the two positions separately, we must use the 
thicknesses of the rims which were in contact with the distance pieces. In the first 
position these were the marked rims, and thus the distance of mean planes 
— 27-860+-478 +-446 +1-897 = 30-681 centims. 
In like manner for the second position we find 
27-860 +‘488 +-465 +1-897 = 30-710 centims. 
The induction coefficients. 
§ 25. Series I. and II. The distance (h) of the mean planes of the coils from the 
middle plane of the disc is 
h=l‘637 centim. 
The extreme distances, required to be known for the quadrature, are 
h-\-l j = 2• 585 centims., h — A- = *689 centim. 
The extreme and mean radii are 
A—A = 24'805 centims., A=25"760 centims., A + A=26'715 centims. 
while a=15"536 centims. 
The coefficient of induction between the disc and the middle turn of the coil, 
denoted by M(A, a, h), is equal to 4v v /(A«) v /'(y), where f(y) is a function of y given 
by tables.* The angle y itself is defined by 
. _ 2+ (A a) 
S1U y y/{(a+<x) 2 +& 2 } 
* Maxwell’s ‘ Electricity and Magnetism,’ 2nd edition, § 706. 
