ITS ERRORS AND CORRECTIONS, ETC. 471 
11. The results from the angle of torsion are always too little, though 
approaching the truth, for platinum wires with light weights. The result by 
vibrations shows the insufficiency of this method, without some better system of 
correction for arc. On the whole, it appears that by weights and deflections the 
same mean result is obtained very nearly ; and both methods should be employed 
in the case of an instrument intended for a fixed observatory. The experiments 
by weights should, however, always be made first, as there is some danger in 
laying on and taking off the weights of an accident (the smallest shock producing 
a change of position in the magnet). When an instrument is closed up, and the 
line passing through the centre of the bifilar at right angles to its magnetic 
axis is marked, the deflections can always be made without disturbing the 
instrument. 
12. Temperature Corrections.—Having satisfied ourselves that we have obtained 
the true value of the unit coefficient, it is desirable to consider what causes may 
influence the members of equation (3). The quantities may evidently all vary, 
but the variations of W and 7 may be neglected, since the only known causes 
which can make W to vary are the moon’s attraction, producing a variation in all 
of less than 0:000002 of the horizontal force, and therefore inappreciable in our 
instruments; and the varying density of the atmosphere, producing for a varia- 
tion of three inches of mercury no greater change than 0:00002 of the horizontal 
force X; the variation of 2 appears in equation (4) as tan 2 d 7, a quantity of the 
second order; m, a, b, 1, and p, however, all vary with temperature. If we 
differentiate with respect to temperature, we shall obtain as corrections to 
equation (4) 

dm da db dl 
+ el 
m a b l 
+2 sin & <P. : 4 ‘ F (15) 
The variation of m, the magnetic moment, has been usually obtained by Mr 
ae da db dl é D 
Christie’s process; —*, i and 7 are the expansion coefficients of the metals 
separating the wires above and below, and of the wires themselves. These co- 
efficients have been usually taken as obtained from the expansion of solid bars of 
these metals. My own experiments show that this is not accurate; the expansion 
coefficient of a wire stretched by a weight is considerably greater than for a bar of 
the same metal; this error, however, bears a small proportion to the whole 
temperature coefficient: 2 is the correction due to the variation of the elasticity 
of the wires with temperature. 
13. If, then, we allow that the temperature coefficient obtained by placing a 
magnet in water of different temperatures is the same, or very nearly the same, 
as should be obtained when placed in air of different temperatures, we have still 
the effects of temperature on the wires undetermined, It is also by no means 
VOL. XXII. PART III. OF 
