220 



re-arrange themselves when the suspended load is withdrawn. 

 It is also subject to changes, although to a much smaller ex- 

 tent, arising from hygrometric variations in the atmosphere. 

 It is important, therefore, that we should possess a simple and 

 accurate method of determining its amount. 



Let us conceive, with Gauss,* two horizontal diameters 

 of the suspension thread, — one at the lower extremity, pa- 

 rallel to the magnetic axis of the suspended magnet, and there- 

 fore moveable along with it ; the other at the upper extremity, 

 parallel to the former in the state of detorsion. The angles 

 contained by these lines with the magnetic meridian being 

 denoted, respectively, by u and v, the angle of torsion is v-u; 

 and the moment of the force of fl" torsion is {v - u), H being 

 a constant coefficient. This is resisted by the earth's mag- 

 netic force, the moment of which is mJYsin u, or mXu, q.p-, 

 the angle u being small ; and therefore the equation of equili- 

 brium is 



H {v - u) = mXu. 



Hence 



mX 

 The value of the coeflBcient, -^^+ 1, is determined expe- 



£1. 



rimentally, by observing the readings of the scale attached to 

 the magnet, corresponding to two positions of the arm of the 

 torsion circle connected with the upper extremity of the sus- 

 pension thread. Let i\ and v-i denote the values of v in the 

 two positions ; U\ and Me the corresponding values of m ; then 

 denoting the coefficient for abridgment by p, 



t'l = pui, v-i = pu-i. 



Whence, subtracting and dividing, 



^•l - V2 



/>= ; 



* Intensitas Vis Magneticce Terrestris ad ynensurain absolittam revocata. 



