72 
MR. F. E. SMITH ON THE ABSOLUTE MEASUREMENTS OF A 
dimensions of the coils and discs differ from these values by small amounts dA for 
the radius of the coils, da for the radius of the discs, and dx for the length of the 
coils. Small corrections to the calculated values in Table IX. have therefore to be 
applied. These corrections are obtained by application of the increment formula 
dM 
M 
dA da , 
— q ~T~+r - 1-5 
A a 
dx 
x 
which gives the change in M due to small changes in dimensions, A being the radius 
of the coil, a that of the disc, and x the axial length of the coil; q, r, and s are 
coefficients which are given by the expressions 
«=T A { F+ ^ (F - n) }’ 
r — 
Qch 
A—a 
2A 
s — — 1 — 
Qck 
~M~ 
(A+a) ■{( 1— p)F—j-j 
The sum q + r + s is always equal to unity. 
In Table IX. we give in columns 1, 2, and 3 the constants employed for the 
calculation of nine mutual inductances ; in column 4 the values of the mutual 
inductances ; and in columns 5, 6, and 7 the values of q, r, and s, which are required 
in our work. Table X. gives the difference values Mj. 
Table IX.—Calculation of Mutual Inductance. 
A = radius of coil, a = radius of circle (disc), x = length of coil. 
The number of turns per centimetre length of the coil is 12. 
A. 
a. 
X. 
M. 
?• 
r. 
s. 
cm. 
cm. 
cm. 
cm. 
17-9419 
26-7870 
23-2650 
52702-37 
2-1003 
-0-5737 
-0-5265 
17-9419 
26-7870 
7-2635 
23682-39 
2-4007 
- 1-2626 
-0-1381 
17*9419 
26-7870 
23-3150 
52755-93 
2-0998 
-0-5724 
-0-5274 
17-9419 
26-7870 
7-3135 
23822-74 
2-3991 
- 1-2596 
-0-1396 
17-9419 
26-7870 
23-2900 
52729-18 
2-1000 
-0-5731 
-0-5270 
17-9419 
26-7870 
7-2885 
23752-65 
2-3999 
- 1-2611 
-0-1388 
17-9419 
26-7870 
19*2851! 
47883-64 
2-1404 
17-9419 
26-7870 
11 *1678 8 
33534-20 
2-2880 
17-9419 
26-7870 
15-2572 s 
41656-11 
2-2001 
In Table X. the first difference values are the mutual inductances of a coil 
16'0015 cm. long and a circle of radius 267870 cm., when the mean diametral plane 
