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re-arrange themselves when the suspended load is withdrawn.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 \?,v-u; 

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

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

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

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

 brium is 



H{v - «) = mXu. 



Hence 



The value of the coeflBcient, -7^"+ 1' is determined expe- 

 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 Vi and ug denote the values of v in the 

 two positions ; Ui and U2 the corresponding values of u ; then 

 denoting the coefficient for abridgment by p, 



Vi^pUi, V2=pU2. 



Whence, subtracting and dividing, 



V1-V2 



P 



U\ - U'2 



' Intensitas Vis Magnetica Terrestris ad mensuram absolutam revocata. 



