MAGNETICAL INSTRUCTIONS. 15 



-f — sin 8' = c cos 8 cos £ + d sin 8, to be used when the Inclination is large. 

 A <p 



-j? — cos 8' sin f ' = (1 — D) cos 8 sin £ to he used when the Inclination is small. 

 A <p 



This coefficient A', which is the X (l+£)), or (l + «) of the "Admiralty Compass Manual," can 

 also he simply determined by observations made with a small vibrating needle, in the manner directed 

 at pp. 69, 70, 71 (3d edition), for the determination of the directive force and X. In these directions it 

 will be seen that if the coefficients B, C, D are known, and the directive force of the small vibrating 

 needle on board (H'), — found by dividing the square of the time of a fixed number of its vibrations on 

 shore by the square of the time of the same number of vibrations made on board, and the product 

 multiplied into the directive force of the needle on shore (•!!), which for convenience may be con- 

 sidered unity — then on any azimuth of the ship's head — 



, _ II' cos S 



A, — r X 



H ' 1 + 83 cos ? - 6 sin f + 2> cos 2 f ' 



a tabular form is given in the " Admiralty Manual," p. 71, for computing X when made on several 

 magnetic azimuths as the ship swings round. 



[Xote. — It is probable that X in the " Challenger " will be found of a value so near unity as to be 

 assumed = TO.] 



In the correction of the Intensity observations, the arithmetical mean of the sixteen or eight 

 determinations (as observed with the ship's head placed successively on each of the sixteen or 

 eight principal points, as indicated by the Fox position compass), may be regarded as a result in 

 which the disturbing influences on the several points may be considered to have balanced each other. 

 and as a true measure of the force at the locality. 



A table of corrections for the several azimuths can be formed by means of the equation — 



i- = A'c ( - tan 8 + cos t ) cos 8 cosec 8', 

 f \c J 



8 and £ being obtained from the tables for correcting the Dips and Declinations. 



Method of calculating the Intensity Results. Fox's Circle. 



With Weights. — Presuming the magnetism of the needle to be constant, the intensity of the 

 magnetic force in different localities is inversely as the sines of the angles of deflection, with a con- 

 stant weight, or 



I sin v 



I' = 



sin v 



when I is the value of the Intensity, v the angle of deflection produced by a constant weight at a base 

 station, and- 1' and v the Intensity and angle of deflection at any other station; or if we express by <p 

 the absolute value of the Force at a base station, and q>' the corresponding value at another station — 



sin v 



r sin v 



