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 0° 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 AB. Calling the total intensity W, and the magnetic 
moment of the needle m, the following condition for equilibrium is obtained}, 
the line ZM indicating the horizon: 
mW sin (AON) = P.r.cos (LOQ). 
Now the angle of deflection 
AON = LON—c— LOA=I'—c—I=—c—4 
and the angle LOQ = I’ +a. We then get 
siOaee] ae cos (= ale 
and when we put sin (¢ + 4)=(c¢+ 4) sin 1’, and the constant quantity 
is signified by p, 
=— 6+ 400s (I + 2). (1) 
Thus the index-error consists of a constant and a variable term, and 
r 
— m.sin 1’ 
this equation contains 3 constants, c, p, and «, 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: 
Needle B Needle B! 
af 4 Ws 4 
67°49 | 68°27 | —20°7' | 68° 5 | —98! 
67 475] 68 08 | —133 
Hamburg, June, 1893 . . .| 047842 
Wilhelmshaven, April 20, 1897} 0:47630 
Mean 04774 
67° 44°8'] 68° 1:8! | —17-0' 
1 Liznar. Anleitung zur Messung und Berechnung der Elemente des Erdmagnetismus, 
Vienna, 1883, p. 44. 
17 
