MAGNETISM DISTRIBUTED THROUGH THE EARTH. 109 



every magnetic particle. For summing the effects of 



the whole, let F= Su. -: then the total forces 



J P 

 upon the particle x, y, z in the directions x, y, z, which 



we may call X, Y, Z, are respectively 



dV dV dV 

 dx' dy' da' 



The symbol V will be recognized here as denoting the 

 Potential of the forces acting on the particle x, y, z, 

 affected with the negative sign : it is a physical quan- 

 tity whose numerical value is independent of the 

 directions- of the ordinates x, y, z t provided they are 

 rectangular. 



Now instead of denning the place of the experi- 

 mental needle by a?, y, and z, it is convenient to define 

 it by u the colatitude of the place or its angular 

 distance from the terrestrial pole, A, the longitude of 

 the place as measured from a fixed meridian towards 

 the east, and r the distance of the place from the 

 Earth's center. And it is convenient to estimate the 

 magnetic forces in directions opposite to the directions 

 of those coordinates as they are seen at the locality: 

 namely as a force N towards the north, as a force W 

 towards the west, and a force C in the vertical along 

 the radius towards the Earth's center (the Earth being 

 considered spherical). These three directions are at 

 right angles to each other; and therefore they can be 

 Considered as the x } y, z of the last paragraph, and the 



dV 



expressions -r- &c. can be employed, provided that we use 

 dx 



