412 MAGNETIC CONDITION OF THE GLOBE. 



We have 



At the point P , e Q ^ = ^ + . 1 ; 



*!. 2 = ^ + 1. 2; 



' 2 1 = 2 ~^~ * ' 1 ' 



2>3 = 8 a + 2.3; etc. 



On the side PoPj the horizontal component H is not constant either 

 in magnitude or in direction ; nevertheless, if this side is very small 

 compared with the dimensions of the terrestrial globe, we may 

 assume that the value of H is constant, equal to the mean of the 

 values which it has at the points P and P 1? and put 



H cose = -(H cos^.j + Hj cose 1<0 ). 



The theorem expressed by equation (2) gives then 







We shall have then, for the closed polygon, 



cos + O.l + cos 



+ 2 [ Hl cos (S, + 1 . 2) + H 2 cos-(5 2 + 2 . 1)] 



+ ? [H n cos (8 n + n . 0) + H cos (8 + . )]. 



Applying this equation to the triangle formed by the stations at 

 Paris, Gottingen, and Milan, and taking as unknown the value H 

 at Paris, Gauss found by calculation the value H = 0.5i7, while 

 observation gave 0.518. 



