262 Prof. W. Stroud. [June 19, 



magnetic moment of the magnet, H the horizontal component of the 

 earth's magnetic field, and 6 the azimuthal deflection of the magnet. 

 The couple exerted by the weight W attached to the bifilars is 



- sin 0, where d, d' are the distances between the upper and lower 

 4il 



ends of the bifilars, and I is their length. Hence we get 



At the centre of the circular magnet there is suspended the little 

 needle, which will be deflected from the magnetic meridian through 

 an angle 0. In its position of equilibrium the couple exerted by H 

 is equal to the couple exerted by the magnet. The former couple is 

 mH sin where m is the magnetic moment of the needle. Let us 

 imagine for the moment that the whole of the magnetism of the circu- 

 lar magnet is concentrated at two points, one at each end of a hori- 

 zontal diameter, and let each pole have a strength fi. The intensity 



of field at the centre is -4- from each pole, or together , where r de- 



,f'2 ipi 



notes the radius of the circular magnet ; so that, neglecting the distance 

 between the poles of the needle, the couple exerted on it by the 

 magnet will be 



2m ^ M?n 



2 cos (0 0) or 3- cos (0 0) 



M 



. ' . -g- cos (0 0) = H sin ; 



M r 3 sin 



' H cos (00)' 



,_.. Wdd' tan cos (00) 



whence H 2 = -- -- : ~ - - 



sin 



If the distances between the bifilars and their length be so ad- 

 justed that = 0, i.e., that the magnet and the needle turn through 

 approximately the same angle in the same sense, then 



_ Wdd' tan 

 4Zr 3 sin 



Or, if the deflections 0, be read off in the usual way with telescope 

 or lamp and scale, then, to a certain degree of approximation, 



4Z/- 3 



