7G GAUSS AND WEBER ON TERRESTRIAL MAGNETISM. 



If we divide the equation (II.) by (III.) we obtain 



mM _ FB?. ian^v 



'mT ~ 2F ' 



whence the independence of the deflection v, both of the mag- 

 netism of the needle m, and of the moment of rotation F, is evi- 

 dent of itself, and we have the following simple result : 



« The determination of the intensity of the magnetism of the 

 globe is therefore reduced to two principal operations. 



" I. To observe the time of vibration of a needle N S, and to 

 deduce from thence the moment of rotation which the terrestrial 

 magnetism exerts on it." 



This moment of rotation will be expressed by the product M T, 

 and calculated by the equation (I.) 



in which C represents the moment of inertia of the bar, multi- 

 plied by the number, tt^, or 9'8696 . . . and divided by the double 

 of the space of the fall of a heavy body in the unit of time. 



" II. A second needle, n s, being suspended : its position is 

 observed ; first, when subject to the influence of the earth's mag- 

 netism alone; and secondly, after N S has been placed at a con- 

 siderable distance, as represented in the figure. Then calculate 

 from the difference between the two positions, or from the de- 

 flection, what fraction of the force of the earth's magnetism, the 

 magnetic force of the needle N S, corresponds to at the selected 

 distance. An equal fraction of the moment of rotation, found in 

 (I.,) gives the moment of rotation which the needle NS at that 

 distance would impart to a similar one ; this result, multipUed 

 by the cube of the distance, gives the reduced moment of rota- 

 tion ; the square root of this gives the force of the needle N S 

 in absolute measure : and finally, the number found in (I.) 

 divided by this square root, gives the expression for the absolute 

 measure of the earth's magnetism." 



