NO. 7.] 



INCLINATION. 



129 



the geometrical axis of the needle, an angle NOQ, which we will call a, and 

 which is reckoned as positive from the north end of the needle through the 

 nadir from to 360. Let the weight of the needle be indicated by P. This, 

 acting in the centre of gravity Q, will divert the needle from its position 

 with its magnetic axis in the direction of the total intensity, indicated in the 

 figure by the arrow A B. Calling the total intensity W, and the magnetic 

 moment of the needle m, the following condition for equilibrium is obtained 1 , 

 the line LM indicating the horizon: 



m W sin (AON') = P.r.cos (LOQ) . 

 Now the angle of deflection 



and the angle LOQ = 



We then get 



sin (c -f- J) = 



P r 



cos (/' + a) , 



and when we put sin (c -f- 4) = (c -f- J) sin 1 ', and the constant quantity 



P.r . . . 

 in. sin 1' 1S S1 8 mfied b y P> 



4 = c + ^ cos (I' + a) . (1) 



Thus the index-error consists of a constant and a variable term, and 

 this equation contains 3 constants, c, p, and or, which can be determined 

 when inclination-observations have been made with the needle in question 

 in at least 3 different places, of which the inclination and total intensity are 

 known. 



Observations such as these, however, were only taken in Hamburg in 

 1893, and at Wilhelmshaven in 1897, in Hamburg with both needles, at 

 Wilhelmshaven only with needle B. The result was as follows: 



1 Liznar. Anleitung zur Messung und Berechnung der Elemente des Erdmagnetismus, 

 Vienna, 1883, p. 44. 



17 



