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' = X sin u. 



"Now let the two components of the earth's force undergo 

 any small changes, 8X and 8 Y, and let V8 Y and V'8 Ybe the 

 changes of U and U' produced by the latter. Then, 8u de- 

 noting the corresponding change of the angle u, in parts of 



radius, 



(V+V')8Y=X cos u8u + 8X sin u. 



Dividing by the equation Y = X tan 9, in which 9 denotes the 

 magnetic inclination, there is 



(V + V) tan 9 -= = cos u8u + sin u — - ; 



or, making, for abridgment, (F+ V) tan 9 = - , 



8Y ( 8X\ 



-^r = p I cos ubu + SlllU -=r 1 . 



The angle u, 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, 8u, are the 

 differences between the observed changes of position, mea- 

 sured from a fixed line, and the corresponding changes of de- 

 clination. 



" In order to correct for the effect of temperature upon the 

 iron bars, we have only to substitute (8u - a8t) for 8u, 8t 

 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- 



b 2 



