GAUSS AND WEBER ON TERRESTRIAL MAGNETISM. /S 



tion of the earth's magnetism. But this very circumstance 

 affords the means of an easy solution. Let us suppose that in 

 our figure the straight line, from the centre of the magnet N S, 

 through the needle n s, coincides with the magnetic meridian ; 

 in this position the terrestrial magnetic force will not act at all 

 on the needle n s. As soon, however, as the moment of rota- 

 tion which NS exerts on ns begins to act, ti s will be deflected 

 from its original position, and set in motion ; but the more it 

 deviates on account of this movement from its first position, the 

 more strongly does the earth's magnetism tend to bring it back 

 to its former position. The needle consequently performs vibra- 

 tions about a line, which is no longer in the direction of the 

 magnetic meridian itself, but is more or less inclined to it. 

 This line is the position of equilibrium of the needle n s, wliich 

 it assumes when the vibrations have ceased. This direction is 

 evidently that of the resultant of the two forces, ^^z. the earth's 

 magnetism, and the magnetism of the needle N S. According 

 to the well-known laws of statics, the proportion of the strength 

 of these forces, which is also the proportion of the moments of 

 rotation produced by them, may consequently be determined from 

 the angle of deviation, i. e. from the difference between the two 

 positions of repose of ns, when it is subjected to the action of 

 both the forces ; and when N S is removed. 



" Here then arises another important remark ; namely, that the 

 angle of deviation of the needle n s is quite independent of its 

 magnetism ; as any increase in that respect e\'idently causes both 

 moments of rotation to increase in the same proportion. We are 

 thus freed from the necessity of fulfilling the difficult condition 

 of equaUty in the magnetism of the two needles." 



If we represent the deflection by v, — the greatest moment of 

 rotation exerted by the earth on the needle (according to the 

 measure fixed for the terrestrial magnetism) by m T, — and by 

 F, the moment of rotation exerted by the magnetism of the 

 bar {M) on the magnetism of the needle (y») at the distance 

 R ; the forces exerted by the earth, and by the bar, on the needle, 

 are to each other in the proportion of the cosme to the sine of 

 the deflection v ; and the moments of rotation, m T and F being 

 also in the same relation to each other, 



m T: F:: cos v : sin v, 



i.e. niT=--^. (III.) 



tang V ^ 



