6l8 CONSTANTS OF MAGNETISATION. 



When the bars M and M', arranged on the common frame, make 

 an angle with each other, the resulting magnet R sets in the plane 

 of the magnetic meridian ; and if a is the angle which the bar makes 

 with the meridian, we have 



R M M' 



sin sin (0 - a) sin a ' 

 The value of the directive couple of the system is 



. 



sm (9 - a) sm a 



The ratio of the magnetic moments M and M' is defined by the 

 angles 6 and a, for we have 



M' sin a 



M sin (0- a) ' 



if the bars are at right angles, we have simply 



M' 



This method, which was used by Bouty,* enables us to compare 

 rapidly the magnetic moments of the bars. 



1190. METHODS OF TORSION. The methods of torsion also 

 give the director-couple of a field on a magnet. They even pre- 

 sent this special advantage that, if the deflection is near 90, the 

 director-couple only depends on the rigid magnetism. 



In merely comparing two magnetic moments, and working in the 

 same field, the angles o> and 0, w' and 6', relative to the magnets M 

 and M', give, according to the mode of suspension, 



M' a)' - 0' sin 6 



M <o - sin 0" 



M' C' sin (to' - 0') sin 



M"~~C sin(<o-0) sin0'' 



With a bifilar suspension, the ratio of the coefficients C and C' is 

 equal to the ratio of the corresponding weights P and P' of the total 

 system. 



* BOUTY. Annales.de VEcole Norm. [2], Vol. iv., p. 9. 1875. 



