CHANGES OF EARTH'S HORIZONTAL FORCE. 197 



Now conceive E to be variable, and < to vary in con- 

 sequence. The equation of variation is 



cos 



Dividing this equation by the last, 



$ -rt 



cotan <f>.$(f> = -^. 



Thus the ratio in which the Earth's horizontal mag- 

 netic force (E or H) varies is inferred at once from 

 B<p', that is, from the angular change, in the horizontal 

 plane, of the position of the magnet. To make this 

 measurable, let a concave mirror, or a plane mirror 

 assisted by a lens, be attached to the magnet so as to 

 partake of its angular vibration in the horizontal plane : 

 let light from a fixed lamp fall on it; and let it form 

 an image of the light upon a rotating barrel covered 

 with photographic paper at distance n inches. A 

 motion of the spot through 1 inch corresponds to an 

 angle in the position of the reflected ray represented 



by -, and therefore to an angle in the position of the 



mirror represented by ; therefore, for a motion 

 2tfi 



1 inch in the spot, &<j> = , and 

 SE BH I 



