TERRESTRIAL MAGNETISM. 199 



Local deviations, indeed, may well be supposed to exist. Mag- 

 netic masses near the surface, though producing no sensible 

 effect at any considerable distance, may obscure and even obli- 

 terate the regular progress of the terrestrial magnetic force in 

 their immediate vicinity. In the simplest case the system of 

 lines in such a district might take the form represented in 

 Figure 2. 



14. 

 After this geometrical representation of the relations of the 

 horizontal magnetic force, we proceed to develope the mode of 

 submitting them to calculation. On the surface of the earth V 

 becomes a simple function of two variable magnitudes, for which 

 we will take the geographical longitude reckoned eastward from 

 an arbitraiy first meridian, — and the distance from the north 

 pole of the earth ; we will designate the first of these, or the lon- 

 gitude, by A, and the second, or the complement of the geogra- 

 phical latitude, by u. Considering the earth as a spheroid of re- 

 volution, of which the greater semi-axis = R, and the lesser semi- 

 axis = (1 — e) jR, an element of the meridian is 



^ ^ 3_' 



(1 — (2 6— e^) COS W-) -' 

 and an element of the parallel is 



R sin u . d\ 



-v/(l-(2e-e*)cos«2) 



