440 THE THEORY OF TERRESTRIAL MAGNETISM. 



over the Earth's surface, otherwise the coefficients of the neglected terms 

 on the left-hand side of these equations will not vanish, and each equation 

 may have other terms which are too important to be neglected, and so it 

 will not be so easy to separate the magnetic constants from one another. 



Suppose a,, + /3,, = k n and (n+l) a n - n/3 n = k n ', 



then ( 2 n + 1 ) a n = nk n + k,' , 



and (2n +!)& = (n+l) k n -k n ', 



which are expressions analogous to those of Gauss (Werke, 1867, Vol. v. 

 p. 173), and a n , ft n , k n and k,' correspond to P', p', n' and Q' respectively*. 



Determination of Special Points on the Earth's Surface. 



25. At the Magnetic Poles, we have X=0, Y = 0, two equations 

 which determine the colatitude 6 and the longitude X. 



For a line of equal magnetic declination, we have -^ = a constant, 

 hence for such a line the equation 



.dY v dX\. ./-dY tr dX\ 



gives the relation between 80 and SX at any point. 



On a Mercator's chart the tangent of the angle which the tangent 

 to this line at any point makes with the equator is 



y d Y ^, dX 

 80 d\~ d\ 



-jff- 



do 



jrdY 

 d\ 



v ' where /" = cos ft 



2 

 I p. v dY 



A- j ~ * ~r~ 

 dp. dp. 



* In Taylor's Scientific Memoirs, vol. n. p. 233, there are some misprints, and the values 

 of 3P', &c. there given should have been as follows : 



3^ =: H' +Q', 3/=2IT -Q', 



5P"=2H"+Q", 5p" = 3H"-Q", 



7 P" = 3IT" + Q'", l p '" = 4 n'" - Q"', 

 fee- &c. 



