RESISTANCE BY A METHOD BASED ON THAT OF LORENZ. 
73 
of the coil is distant from the circle 15'2642 s cm., 15‘2892 5 cm., and 15'3142 5 cm. 
respectively. In these three positions an increase in the radius of the coil of 10 /u. 
increases the mutual inductance by 3‘001, 2'995, and 2'988 respectively, and an 
increase in the radius of the circle of 100/* increases the mutual inductance by —0'125, 
— 0'099, and — 0'072 respectively. If we have two such coils, one on each side of the 
circle, the intensity of the magnetic field at the circumference of the circle will be 
zero when the mean planes of the coils are about 30'656 cm. apart and the circle is 
Table X.—Difference Values of Mutual Inductance. 
A = radius of coil .... 
17*9419 
17-9419 
17-9419 
17-9419 
17-9419 
17-9419 
a = radius of circle .... 
26-7870 
26-7870 
26-7870 
26-7870 
26-7870 
26-7870 
x = Axial length of coil . 
23-2650 
7-2635 
23-2900 
7-2885 
23-3150 
7-3135 
M = mutual inductance . . 
52702-37 
23682-39 
52729-18 
23752-65 
52755-93 
23822-74 
Difference value = Mi. . . 
29019-98 
28976-53 
28933-19 
dM for dA = 10/x .... 
+ 6-169 
+ 3-168 
+ 6-172 
+ 3-177 
+ 6-174 
+ 3-186 
Difference value. 
+ 3-001 
+ 2 
995 
+ 2 
988 
dM for dA = 100/x .... 
- 11-288 
- 11-163 
- 11-281 
- 11-182 
- 11-274 
- 11-202 
Difference value. 
-0 
125 
-0-099 
-0 
072 
midway between them. The same result is of course brought about by a slight 
reduction in the diameter of the brush contact circle, an inevitable result of wear and 
re-turning of the surface of the segments. However, exact realisation of this condition 
is unimportant since for the positions of the coils dealt with in the calculations, the 
maximum change in the mutual inductance is only 4 parts in 1,000,000 for a change 
in the diameter of the circle of one-fifth of a millimetre. Exact centering of the 
circle between the coils is also unimportant as will now be shown. 
When the distance of the circle from each of the mean diametral planes of the coils 
is exactly 15'2892 s cm. the total mutual inductance of the two coils and the circle is 
57953'0 7 . If the circle is moved so as to be 0'25 mm. nearer one of the coils the 
total mutual inductance is increased to 57953'1 7 , i.e., about 1 part in 600,000 greater 
than before. Hence with a brush half a millimetre wide the variation of potential 
from wire to wire will not exceed 1 part in 600,000. In practice the brushes 
commonly used consisted of three parallel wires, the extreme width being about 
0'5 mm. 
VOL. CCXIV.-A. 
L 
