300 Variations of the Terrestrial Macrneti^m 



or by putting for the cosines their values : 

 F {x -a) F {x + a) 



and as we have 

 we shall have also 



tang. /3 = -^, 



// (D'"! - D*) 



X (D'-^— D3) — a (D'- + D»); 



and putting for x, ij, and a, their values, r cos, u ; r sin.?/ j 

 Krj 



tang. /3 = 



D'3 + D^' 



COS. M — K ^-7 -— I 



D'- = r'^ (1 + 2 K cos. u + K'^) ; 



D^ = ?•' (I — 2 K COS. u + K'^); 



which gives the system of the two equations, 



sin. u 

 tang. |3 = 



D'^ +D' 





(l+'iKcos,M+K2)"?_(l_2Kcos.M + K)^ 

 These equations determine the direction of the niagnt^tic 

 needle in regard to each point M, the distance of which 

 from the magnetic equator is known ; but it is seen that 

 this direction depends on the quantity K, which represents 

 the distance of the magiietic centres from the centre of the 

 earth : this distance being expressed in parts of the terres- 

 trial radius, we must therefore first determine this quantitv 

 from observations. 



To do it in the manner of approximation, and thus ac- 

 quire a first idea of the value of K, I have chosen an obser- 

 vation made by M. Humboldt at Caricliana in 7'2978° (6° 

 34' b") of north latitude counted from the terrestrial equa- 

 tor, and 78-111° (70" is') west longitude reckoned from 



the 



