Horizontal Component of the Earth's Magnetic Field. 485 



where b is the length of the magnetometer-needle ; but it is 

 one of the merits of the method here described that the mag- 

 netometer-needle is made so short that its magnetic length 

 may be neglected, and the resulting equation thus much 

 simplified. 



The positions adopted in these determinations were, for the 

 line joining the centres of the deflector and the magnetometer- 

 needle, the magnetic meridian and a line at right angles to it ; 

 and for the direction of the magnetic axis of the deflector, a 

 line at right angles to the magnetic meridian. We then have 

 for the former of these positions, 



(V 2 — <7 2 Y 2 

 /(2a 1 ,,)=^ll; (2) 



and (or the latter position, 



/(2a 1 ,r) = (^ + a?) f (3) 



From equation (1) we obtain, by (2) and (3), 



M_ <V 2 -a 2 ) 2 



and 



- tan ^ w 



|=0l + «?) f taii^ (5) 



Now, besides M and H, the value of a^ is also unknown ; but 

 when O and d 1 are determined at nearly the same time, we 

 can calculate a x from the above equations. We have clearly 



(r*-a\y = tan^ 

 2r(r? + a*)* tan0 o ' 



Expanding the numerator and denominator on the left-hand 

 side of the above equation, and neglecting small terms, we 

 readily obtain, as a close approximation, 



V-i^r! (7) 



1 20«r+30 1 r L " ' 



There is in the method here described a departure from the 

 usual practice — namely, determining the effect of the length 

 of the deflector and deflected magnets, by double and triple 

 experiments with the deflector placed at different distances 

 along a line through the centre of the deflected magnet. In 

 j the first place, the third experiment is rendered unneces- 



Phil. Mag. S. 5. Vol. 20. No. 127. Dec. 1885. 2 M 



