USE OF THE BALANCE. 619 



1191. USE OF THE BALANCE. The director-couple of a magnet 

 may be counterpoised by a weight, by means of the ordinary balance. 

 If a bar magnet is fixed vertically to the arm of a balance made of 

 brass, so as to avoid any perturbing action,* and which oscillates in 

 the magnetic meridian, the couple MH tends to incline the arm on 

 one side, and the direction of its action changes when the magnet is 

 reversed end-wise. The balance is counterpoised, in the two cases, 

 by the weights P 1 and P 2 . The semi-length of the arm being /, 

 and the weights being expressed in grammes, the product (P l - P 2 ) gt 

 is equivalent to twice the director-couple, and we have 



(i) 



This is- a kind of double weighing, in which the induced mag- 

 netisation has no appreciable influence, because its action is in 

 the same direction in both cases ; the difference of the induced 

 magnetisations alone comes into play. 



When the magnet is placed horizontally in the direction of the 

 arm, two observations are made in the same way, turning the magnet 

 end for end, or by turning the support of the balance through 180. 

 The difference of the tares Q l and Q 2 counterbalances twice the 

 couple due to the vertical component, and we have 



(2) 



Dividing equation (i) by equation (2), we shall have the ratio 

 of the components H and Z, and therefore the value of the in- 

 clination (1167). 



1192. Von Helmholtzf has pointed out another mode of utilising 

 the balance. A vertical bar is suspended from one pan, and on the 

 other a horizontal bar is directed towards the centre of the first. Let 

 Mj be the magnetic moment of the horizontal bar and 2L X the 

 distance of the poles, M 2 and 2L 2 the same quantities for the 

 vertical bar, R the distance of the centres, D the distance of the 

 centre of the bar M l from the pole of the bar M 2 , w the angle 

 between the directions D and R. 



* A. TOPLER. Wiedemann's Annalen, Vol. XXI., p. 158. 1884. 



f VON HELMHOLTZ. Ber. der Akad. der Wissens. zu Berlin, Vol. xvi. 1883. 



