230 
MESSRS. R. T. GLAZEBROOK AND J. M. DODDS ON THE 
It was noticed, however, that two of these rods had been slightly bruised at the 
end, thus producing a small lump at one point; when the rods were placed so that 
this lump came between the jaws of the calipers an increase of ’002 inch was observed 
in the length. In the calculations this greater length has been used as the true 
length of these two rods. In the shortest rods, series A, the difference in length, 
arising from a slight lump on the end of one of the rods, was somewhat greater, being 
about '003 inch. 
Another series of measurements made in an entirely different manner by placing 
first the rods and then the beam-compass beneath a pair of reading microscopes gave 
very closely concordant results; these measurements made the rods appear about 
'001 inch longer than the measurements with the calipers. Some difference of this 
kind was to be expected from the difference which exists between the contact length 
and the sight length of a rod. 
In our calculations we have taken the values given by the calipers. 
iteclucing them to centimetres we have for the lengths of the rods 
centims. 
Series A. 12'182 
Series B. 15 '416 
Series C. 23'85G 
We have thus obtained all the dimensions requisite for the calculation of the mutual 
induction between the coils in the three series. 
Let us call b the distance between the mean planes; 6, of course, is slightly different 
in each of the four positions included in each series. 
The calculations of M have been conducted as follows :— 
If all the windings are supposed to be coincident with the mean windings, and M 0 
be the mutual induction on this hypothesis 
M n = iirnn '\/Aal (c ——\ F+ —E 
where 
c= — 7 ======== and n, n are the number of windings ; 
V(A + «.) 2 + & 3 
and F, E are complete elliptic integrals to modulus c (Maxwell, vol. ii., § 701). 
Appendix i., ch. xiv., to the second edition of Maxwell’s ‘ Electricity’ contains a 
table in which the logarithms of M 0 /47r v / Aa are given for values of sin -1 c from 
60° to 90°, proceeding by intervals of 6'. 
The proper value of y— sin -1 c is most easily obtained from the equations 
r*= (A +V t£— (A - cr)*+ ¥ 
COS y = '?’ 2 /r 1 . 
