TEMPERATURE COEFFICIENT OF THE BIFILAR MAGNET. xlv 
whence 
Let a series of such values be obtained by comparing the mean scale reading, and 
mean temperature of the magnet for each day with those for each day following in 
the period selected : if we consider the differences a ¢ positive, when the succeeding 
day’s mean temperature is less than that for the preceding day, and sum the whole 
number of differences for which a ¢ is positive,* then 
TAR 3AxX 
mia en Laas 
If we neglect the last member, the whole error of the determination of ¢ will 
depend on the sum of variations of the mean horizontal force 2 4 X ; asin a sufficient 
number of determinations, it is probable that these variations will be as much posi- 
tive as negative, and, therefore that the numerator will nearly vanish, the last mem- 
ber may be neglected in the determination of q’, and this with the more accuracy 
the larger the sum of the differences of temperature 3 aé. Again, if the differences 
for which a # is negative are summed, we shall have 
TAR Zax 
NE A 
, 
I= 
The sign of the first member on the right remains as before, since a R also 
changes sign. Reasoning as in the previous case, ¥ a X may be supposed nearly 
zero, and the last member of the equation negligible. If, however, the supposition 
that the sign of A X varies positively and negatively with reference to the sign of 
« t be inaccurate, it must be supposed either that the horizontal component remains 
constant, and therefore, that 4 X = 0, or that it varies in one direction only, in- 
creasing continuously, or diminishing continuously, throughout the period selected, 
and, therefore, that the sign of « X is the same for both equations. In the latter 
case, it is evident that by taking the mean of the values of g' from the two equations, 
the last members will nearly destroy each other. It has been supposed that the 
variations of X are altogether independent of the variations of the temperature, a 
supposition which is borne out by every method of examination of the results. The 
details of a series of comparisons are given, pages li, lii., and hii., Introduction, 1843, 
from these it appears : 
70. Ist, That the value of q’ is the same, when a sufficient number of compari- 
* If the scale readings increase with increasing horizontal force, A R will generally be negative 
when A ¢ is positive, and vice versa. The sign of A tis used as the argument, so that if A R be 
positive when A ¢ is positive, that value of A R will be subtracted from the sum of differences 2 A R. 
MAG. AND MET. oBS., 1845 anp 1846. m 
