RESISTANCE BY A METHOD BASED ON THAT OF LORENZ. 
75 
57955'4, the temperature being 20°'0 C. For an increase in the distance apart of the 
mean planes of Nos. 1 and 2 by 250 fx the mutual inductance diminishes by 43'43, and 
for a decrease in the distance by the same amount the mutual inductance increases 
by 43'32. The corresponding values for cylinders Nos. 3 and 4 are practically 
identical, being 43'48 and 43'37 respectively. 
Table XII.—Giving the Mutual Inductance Mj of the Coils and Contact Circles on 
the Assumption that the Radius is at all Points Equal to the Mean Pmdius and 
that the Pitch is Uniform. 
Coils on cylinder No.— 
1. 
2. 
3. 
4. 
Differences. 
Correc¬ 
tion 
to Mi- 
Differences. 
Correc¬ 
tion 
to Mi. 
Differences. 
Correc¬ 
tion 
to Mi. 
Differences. 
Correc¬ 
tion 
to Mi. 
y. 
dk = - 15-3 
dx = + 3 
da = +40 
For number \ 
of turns n J 
Total 
correction J 
-4-58 
+ 0-58 
-0-04 
-3-26 
-7-30 
/a. 
dk = - 11 
dx = — 1 
da —— + 40 
-3-29 
-0-19 
-0-04 
-2-54 
-6-06 
/X. 
dk = + 8 
dx = +39 
da = - 7 0 
+ 2-40 
+ 7-57 
+ 0-07 
-9-78 
+ 0-26 
/X. 
dk = +14 
dx = +39 
da = — 7 0 
+ 4-19 
+ 7-57 
+ 0-07 
-9-78 
+ 2-05 
Mi = 28969-24 
Mj = 28970-48 
M 2 = 28976-80 
Mj = 28978-59 
Sum = 57939-7 
Sum = 57955-4 
With change of temperature the mutual inductance varies owing to the expansion 
of the coils and discs. If the distance apart of the mean diametral planes of the coils 
is kept constant, the temperature coefficient of M : is readily calculated to be 1'06 x 10 -5 
for an increase in temperature of 1° C. 
AVe have previously stated that it is not necessary to know the axial length of a 
coil with great accuracy. From the data given on page 74, it is clear that if the 
coils increase in length by 1(V, the change in M : for the coils on any one cylinder is 
+ 1'94. But this supposes the number of turns to increase in the ratio 16'0010/16'0000. 
Since the number of turns is constant the real change is P94 + 28970 — 28970 x 
(16'0010/16'0000) = 0'13. That is, a change of 10/x in the axial length of the coils 
produces a change in the mutual inductance of the coils and discs of about 5 parts in 
1 , 000 , 000 . 
