3 
moment is MX sin u,— X denoting the horizontal component, 
and u the angle of deflection of the magnet from the magnetic 
meridian. Hence the equation of equilibrium is 
U+ U'= Xsinu. 
“‘ Now let the two components of the earth’s force undergo 
any small changes, 6X and 3 Y, andlet é Y and Vd ¥Y be the 
changes of U and U’ produced by the latter. Then, du de- 
noting the corresponding change of the angle w, in parts of 
radius, ‘ 
(V+V)8Y=X cosudu + dX sinu. 
Dividing by the equation Y = X tan @, in which @ denotes the 
magnetic inclination, there is 
oY | 
ae et ne + sinu—> 3 
l 
or, making, for abridgment, (/ + V’’) tan 0 4% 
oY 
1 OA 
+7 (cos uou + sinu X ). 
The angle zw, in this formula, being the deviation of the sus- 
pended magnet from the position which it would assume 
under the action of the earth alone, its changes, du, are the 
differences between the observed changes of position, mea- 
sured from a fixed line, and the corresponding changes of de- 
clination. 
‘Tn order to correct for the effect of temperature upon the 
iron bars, we have only to substitute (du — ad¢) for du, de 
being the actual change of temperature, and a the change 
of angle (in parts of radius) corresponding to a change of one 
degree. ‘The effect of an increase of temperature upon a soft 
iron bar, in all my experiments, has been an increase of its 
induced magnetism,—the reverse of its effect upon the per- 
manent magnetism of an artificial magnet. The amount of 
the change is, however, very small. With the bar which has 
been most used in the Dublin Magnetical Observatory, an in- 
B2 
