THE SMITHSONIAN INSTITUTION. 



391 



assume a position nearly at right angles to the magnetic meridian, 

 when the horizontal force acting upon it at right angles small changes 

 of force will produce proportional changes of direction, and the former 

 may be measured by the latter. Figure 4 shows the instrument in 

 outline. The framework is the same 

 as in the declinometer above de- 

 scribed. The magnet and attachments 

 are suspended by a silk suspension 

 skein attached to two hooks, and 

 passing at the top over a glass roller, 

 which turns on pivots in bearings sup- 

 ported by the torsion-circle. The 

 compound bar above the magnet, to 

 which the hooks are attached, effects 

 the compensation for changes of tem- 

 perature, as will be specially described 

 below. The force of the torsion-bal- 

 ance depends upon the wp-per and 

 lower distance between the threads, 

 their length I. the weight iv, of the sus- 

 pended mass, and the angle 0, by 

 which the plane of the threads is 

 twisted. If we designate, as is cus- 

 tomary, the earth's horizontal force 

 by X, the magnetic moment of magnet 

 by ???, and half the upper and lower 

 distance between the centres of the 

 threads by a and b, respectively, we 

 have the following equilibrium of 

 forces: 



ml=j W, sin 6. 



From this equation is readily de- 

 rived the simple and accurate method C 

 of ascertaining the scale value of the 

 instrument proposed by Mr. Brooke. 

 Observing that any variations in the 

 quantity Jmay be balanced by pro- 

 portional Variations in W, he observes Horizontal force instrument or bifilar magneto- 



the change of scale-reading produced 



by adding to the suspended mass a small weight equal to its one 

 hundredth part, and the same change on the scale, of course, corres 

 ponds to a variation of one-hundredth part of the force. This space 

 on the scale is divided into one hundred parts, in order to have as a 

 convenient unit the ten-thousandth part of the whole horizontal force. 



Since the magnetic force ra of the magnet is diminished by increase 

 of temperature, and vice versa, the indications of the instrument 

 would be affected by this cause if some arrangement were not intro- 

 duced to counteract and precisely balance its effect. 



Mr. Brooke's compensating apparatus consists of a glass rod clamped 



