COEFFICIENTS OF MAGNETS. 281 
axis at right angles to that of the suspended magnet in its deflected 
position, the axes of the two magnets being in the same horizontal 
plane, and the centre of the unifilar in the prolongation of the axis of 
the deflector. 
Also let r be the distance between the magnetie centres, 
w the angle of deflection, 
X the horizontal component of the force. 
‘The relation between m, 7, uv, and X is given by the formula 
m — f(r) X sin uw, (where f(r) is some function of 7) 
and that of their simultaneous small changes by 
An fO AX 
aif) Ar + cot u Au+ TT 
Now, if an be the increase in the magnetic moment due to a 
decrease of (¢—Z,) in the temperature, and g that due to a decrease 
of 1°, so that an = g (¢—+,), the preceding equation will become 
LANE WAND) AX 
=~} ve Ar+coty Au+ a 
It is customary to assume that Ar=0, or that the magnetic centre 
occupies a fixed position in the magnet during the changes of temper- 
ature. Such will probably be the case if the magnet be strictly 
homogeneous throughout ; but if its molecular condition be not 
uniform, it is at least conceivable that a change of temperature will 
affect differently the different parts of the magnet, as it is already 
known to affect the general magnetism of two different magnets. 
Suppose, then, the north end of the deflector to be directed to- 
wards the suspended magnet, and that a decrease of 1° in tempera- 
ture causes the magnetic centre to recede from the north end by the 
small quantity (a), so that Ar=(¢—+,)o. Also, suppose g, to be the 
_ value of g determined in this case on the supposition that ” is con- 
stant or that Ar=0. 
We shall then have 
+ aft) 
I(r) 
Similarly, if g, be the value determined on the same hypothesis 
when the south end of the deflector is presented, 
Coa ay 
