708 TEKRESTRIAL MAGNETISM. 



If r and 7\ be the two distances between the centres of the 

 magnets, and u, Wj, the deflections, then combining thetwo formulae 

 we get 



^P- 



f\^ sin u^ — 



r^^^'S gin 



w 



r2 



,.^5 



sm 2/j 



-- r^ sin z^ 





sin 

 sin 



U 



-(f.)* 



.-f3 





sin 



Uj_ __ 



fry 



-.-f5 





sin u 



\rj 







so that 



M 

 X 



: i r^ sin u ^ ~" ^^ 





where 



P = 



— and( 



^ _ sin z^j 





r^' sm 2^ 



These were the formulae employed in discussing the observations 

 of Dr. Kane and Dr. Hayes in the Arctic regions ; and the values 

 of M and X determined by Dr. Kane in 1854-55 at three stations, 

 and by Dr. Hayes in 1860-61 at six stations, are given on p. 699. 



[The great differences in the value of ^, obtained by Dr. 



Hayes at Port Foulke in the course of one week's observations in 

 July, differences which range from + 0*0044 to —0-0851, would 

 seem to show that if this method is employed to determine the 

 Earth's magnetic force, it will be necessary to take the more exact 

 formula, and to determine the deflections for three different dis- 

 tances between the centres of the magnets. 



In the neighbourhood of the magnetic pole the results obtained 

 by this method are liable to large errors because of the smallness 

 of the Earth's horizontal force, and hence one of the methods with 

 the dipping needle should be adopted. The early Arctic voyagers, 

 Sir John Ross, Sir James Ross, Sabine, and Parry, all made use 

 of a dipping needle to determine the Earth's force as compared with 

 its value in London, determined by the same needle before starting 

 and after returning.] 



[For methods of using the dipping needle see Admiralty Manual 

 of Scientific Inquiry, p. 103 to 106.] 



The absolute value of the Earth's magnetic force may be deter- 

 mined by observing the inclination of the dipping needle, 1st, 

 under the action of the Earth's magnetism alone ; and 2nd, under 

 the combined action of magnetism and gravity, by attaching a 

 weight to the needle as in Fox's dip circle. (See Lloyd's 

 Magnetism, p. 95). 



If F stand for the dipping needle employed to determine the 

 Earth's force ; if 6 be the inclination of the needle F without the 

 weight, vj the inclination of the needle F with the weight, and tj^ 

 the inclination of another needle which is deflected by the 

 needle F, and r the distance between their centres, R the Earth's 

 force, W the weight on the axis of radius «, then 



R2 sin (d — 7j) sin (0 - ^i) = UW a 



whereU = ?3(l+| + i,). 



