Changes in Temperature and Distribution of Magnetism. 279 
III. CALCULATING OF BESULTS. 
The formula for the ballistic galvanometer is 
Q = k sin 
where Q is the quantity of electricity; k, a constant factor; and 5 the 
angular throw of the needle. The observations were made with telescope 
and scale. Calling d the observed throw and r the distance of the mirror 
from the scale. 
tan 2 5 = — 
r 
5 
Expanding sin we have • 
this formula was used in reducing the large readings. 
The earth inductor readings were taken frequently and were sub¬ 
stantially the same throughout the experiment. The throw of the nee¬ 
dle due to the earth inductor when both magnets were at 14° C. was 39.5 
scale divisions; when one magnet was at 99.°5 C. and the other at 14° C., 
it was 37.8. The average throw due to slipping the exploring coils over 
a certain portion of the magnets when one was hot and the other cold, 
was multiplies by ff f = 1.045 to reduce to the scale of readings taken 
when both magnets were cold. Corresponding readings were then sub¬ 
tracted, giving the change in distribution in terms of the scale divisions. 
The reduction to absolute measure was as follows: The effective area of 
the earth inductor as determined by previous observers is 20,716 sq. cm. 
The value of the horizontal component of the earth’s field at and near 
the position in which the earth inductor was placed has been determined 
by numerous observers, and by various methods, and may safely be 
taken as within 1 per cent, of 0. 2 C. G, S units. The total number of 
lines of induction cut by turning the earth inductor was 2 H A = 8,286.4. 
As the throw was 39.5 scale divisions, each division correspouded to 
8,286.4-r- (39.5 X 150) = 1.398 C. G. S. lines of induction. The factor 150 
is due to the 150 turns of the exploring coils. The change in distribu¬ 
tion in scale divisions obtained above was then multiplied by 1.398 
giving the change in linear distribution in C. G. S. lines of induction 
per 2.17 cm., that being the distance the coils were moved at each step. 
