108 OX MAGNETISM. 



of red and of blue magnetism in the Earth are equal. 

 And it is supposed that the attraction or repulsion is 

 inversely as the square of the distance. The magnet- 

 ism of every point of the Earth will be supposed, in the 

 algebraical investigation, to be red : blue magnetism 

 being included in the same investigation by conceiving 

 its sign to be negative. As regards the experimental 

 magnet or compass-needle, whose dimensions are ex- 

 ceedingly small in proportion to the distance of the 

 magnetic parts of the Earth, it will be sufficient to 

 consider the terrestrial action upon its red end only. 



Let a, b, c be the coordinates of an attracting point : 

 BJJL the amount of magnetism there (its unit being 

 that quantity of red magnetism which at distance 1 

 exercises on a similar mass the moving force represent- 

 ed by 1) : and let x, y, z be the coordinates of the red 

 end of the needle. The magnetic force on the end 



r\ 



of the needle is 7, in the direction of the line join- 



ing the attracting and attracted points, wherep = 

 *j{x a) 2 + (y 6) 2 + (z c) 2 J. Resolving this in the 

 directions of x, y, z, the several forces are 



Bfi . (x a) Sfj, . (y b) B/J, . (z c) 



~T~ ~?~ ~^~ 



It is easily seen that those forces are the same as 



A similar system of formulae applies to the effects of 



