Tempekature Coefficient of the Balance Magnet. 
xlvii 
number of days compared are too few to give good results* It is obvious, however, 
that if we consider the equation 
2 A y, r a 
4 = , 
A t r 
that the value of q f deduced from the quantity ^ ^ Vr alone will be too much or too 
little according as the sign of a t, is positive or negative ; whence, if a period of 
moderate length be selected, throughout which the mean daily temperature increases 
and diminishes considerably, we may neglect the sign of a t r and the quantity a, as 
in the summations the coefficients of the latter will nearly destroy each other. For 
periods of moderate length, and free from disturbances, it is the fact, as may be 
seen from the previous Table (with the exception of one day), that the signs of a y r 
and a t r are always opposite. The latter method, then, will be found the easiest, 
and, it is conceived, in general the most accurate. The mean results obtained for 
the series, June — July, when t p )> and t p+ „ are indeed exactly the same, and 
the partial results seem to indicate that the sign of a is itself so variable as to render 
its total effect nugatory. The same remark applies to the series August — Septem- 
ber 1844. 
The following Table contains a series of results obtained according to the latter 
method. In each series each day is compared with every day following it to the 
end of the series for the differences a y and a t : — 
Table 16. — Determinations of the Temperature Coefficient for the Balance Magnet 
from Comparisons of the Daily Observations. 
Period. 
2 A (0 
2- A GO 
</ 
Observed 
Time of 
Vibration. 
Remarks. 
1843. 
Jan. 16— Jan. 21 
Jan. 23 — Jan. 28 
Jan. 30— Feb. 4 
Feb. 6— Feb. 11 
June 1 — June 30 
Sept. 6— Sept. 16 
525-3 
817-7 
576-0 
609-9 
14320-4 
1083-7 
Mic. Div. 
4315-3 
5723-5 
4151-5 
4080-6 
114646-9 
8730-4 
Mic. Div. 
8-21 
6- 99 
7- 21 
6-69 
8- 006 
8-04 
s. 
9-7 
9-7 
9-5 
9-4 
9-7 
10-8 
In 1843 there were 9 daily obser- 
vations, made at two-hourly in- 
tervals, from 18 h till 10\ 
Sept. 2, the needle was removed in 
order to determine its tempera- 
ture correction by the method of 
deflections. 
1844. 
May 9— May 24 
Aug. 3— Sept. 6 
For the series in) 
1843, . . • j 
For all, . . . 
8415-4 
21696-9 
17933-0 
48045-3 
66621-7 
171460-5 
141648-2 
379730-4 
7-93 
7-902 
7-898 
7-903 
8-6 
8- 5 
9- 8 
8-5 
In 1844 there were observations 
made at every hour of the day. 
The needle was removed between 
September 1843 and February 
1844 for temperature experi- 
ments. 
The mean value of q from the series in 1843 is 7*90, and from the tempera- 
* Such as these results are, however, their disagreement with the result obtained by deflection ex 
periments and vibration, is, in each case, even more than that of the adopted result. 
