16 THE VOYAGE OF H.M.S. CHALLENGER. 



With Deflectors. — In the case of employing " deflectors " for " weights " (a measure which must 

 often be resorted to at sea, where manipulation of the weights wovdd catise undue exposure of the 

 needle), the ratio of the Intensity in different localities is inversely as the sines of the angles of 

 deflection, and directly as the weights equivalent to the deflecting force of the deflector on the needle 

 at the respective angles ; or 



T , _ w' . sin v 

 w . sin v 



where v and w are the angle of deflection and equivalent weight at a base station, and I', v', and w, 

 the Intensity, angle of deflection, and equivalent weight at any other station ; or 



sin v iv a sin v 



<p = —■ t • — or, <l = - ,w . co . v . 



r sin v iv T w 



A table of equivalent or coercing weights is usually formed at a base station, for each of the 

 deflectors on each of the needles, at the different angles which are likely to occur in the course of the 

 observations with them. The table is formed in the following manner : — 



The plane of the circle being perpendicular to the magnetic meridian, and the needle in its 

 natural position of rest (which in such case is a vertical position), the deflector is placed successively 

 at angles from the vertical, each differing one degree from the preceding; the needle is thereby 

 deflected to an angle on the side of the vertical opposite to the deflector, and is brought back to its 

 natural position of rest by weights applied to the grooved wheel on the axle. These weights are 

 called the equivalent weights corresponding to the angle from the vertical at which the deflector was 

 successively placed, and which ought to include all the angles likely to occur in the course of the 

 observations. For greater accuracy the table is formed from results obtained by placing the deflector 

 successively on either side of the needle. 



If time or other circumstances prevent the table being formed in the manner just described, 

 there is no other resource for reducing the observations made with the deflectors than to form a table 

 from the observations of the weights and deflectors — when both methods have been employed at the 

 same station — which shall answer the same purpose as a table of coercing weights. 



The table may be thus formed : — For the primary or base station, let V be the angle of deflection 

 with a constant weight W, and v the angle of deflection produced by the deflector placed at the dip, 

 then is — 



w = W sin v cosec V , 



w being the weight equivalent to the deflecting force of the deflector at the angle v. If several 

 constant weights were used at the primary station, the value of w may be obtained from each 

 separately, and an arithmetical mean taken. 



Then at another station (of which there would be many at sea if very fine weather is experienced) 

 at which the angles of deflection have been observed both with the deflector and with constant 

 weights, the equivalent weight w' to the angle v produced by the deflector may be obtained from 



, I' w sin v' -r, • , 



iv = — = — ■. or, w = xv. cosec v. 1 sin v , 



Isinn 



