74 MR BROUN ON THE BALANCE MAGNETOMETER, 
would probably not be altogether in the vertical, the portion resolvable to the ho- 
rizontal would affect the position of the needle. 
14. From these considerations I was induced, about two years ago, to endea- 
vour to obtain the temperature correction from the usual daily observations of 
the instrument. To most persons acquainted with the irregularities in the mag- 
netical variations, from the changes of the magnetic intensity or its direction, this 
might appear to some extent chimerical, and as at best only capable of giving a 
rough approximation to, or verification of, the determinations by deflection. It 
will, however, I think, be shewn, that a better coincidence of partial results, and 
a better correction, may be obtained from this than from the usual method. 
It will not be necessary to point out the methods which were at first tried; 
I shall proceed at once to those which have been ultimately adopted. 
15. Having selected a series of days during which the readings of the instru- 
ment seem regular, and in which the changes of temperature from day to day 
are considerable, rejecting any day of marked disturbance, the hourly or two- 
hourly readings for the position of the needle and for its temperature are summed 
for each day. Let us designate the sum of the micrometer readings for the first 
day of the series y,. for the second day y,, and so on to Ys; the corresponding 
sums of the thermometer readings being ¢,, ¢,, . . . . ¢,,;, the number of the days, 
from the beginning to the end of the period, being 2 +1. 
The most simple and probable hypothesis that can be formed, is, that the 
mean vertical force increases or diminishes gradually throughout the period; let 
the mean daily change be a. 
If g be the temperature correction for 1° Fahr. in micrometer divisions, we 
may form the following series of equations: 
N=Hyt+atrh—-h)¢g Y=¥st+ A+(h-—&)G 
Al = Yn+1 +nQ + (4 id +1) Yo = Yni2 af 2G (t, as nae (7.) 
Yns2 = Yass + A + (nse — tags) g 
There will be breaks in each series, as there are no sums for the Sundays. As 
t, may be greater than ¢, and ¢,, the result of the comparison of y, with y; is not 
equivalent to the comparison of y, with y, and y with y;. 
From these equations the most probable values of a and g might be obtained 
by the usual methods; but the labour which they demand is probably much be- 
yond the greater accuracy to be attained. The following, it is conceived, will be 
found sufficient. 7 
First classing the equations in which t,> or ~¢,,,, and considering each 
class separately. 
