GAUSS AND WEBER ON TERRESTRIAL MAGNETISM. 73 



" Let N S he a fixed magnet in a horizontal position ; it is 

 required to find its influence on a second needle, n s, suspended 

 to a thread ; the relative position of the two needles being shown 

 in the annexed figure : 

 N 



n. ^« 



S 



The action of the first needle upon the second will consist in 

 imparting to it a tendency to turn in the direction indicated by 

 the arrows, the letters N, n designating the North poles, and S, s 

 the South poles. The moment of rotation is exjDressed by a num- 

 ber, exactly in the same way that the action of terrestrial mag- 

 netism on a needle vibrating freely has been indicated above. 

 The magnitude of the moment of rotation depends, however, on 

 the distance, and on the magnetic force in both needles. Thus 

 for example (supposing the distances to be sufficiently great), at 

 equal distances it would be augmented six-fold, by doubling the 

 magnetism of one of the needles and trebhng that of the other. 

 " The effect depends on the distance in such manner, that, 

 at twice the distance the effect wiU be ^th, and at three times 

 the distance gyth of the effect produced at the simple distance ; 

 bearing in mind, however, that this law is correct only for very 

 great distances, and cannot be extended to small ones. As all 

 distances, when referred to a selected unit, can be exj^ressed by 

 numbers, this law maybe expressed thus : ' the moment of rota- 

 tion, multiplied by the cube of the distance, is constant for very 

 great distances.' This product may be termed with propriety the 

 moment of rotation reduced to the unit of distance ; remembering 

 that, according to the remark above made, the actual moment 

 of rotation at the unit of distance, when the distance is small, 

 may differ considerably fi'om the reduced moment. This, how- 

 ever, does not prevent us from employing the reduced moment 

 of rotation as a measure of the magnetism of the needles, and 

 from considering as unity, the magnetism of that needle, which 

 imparts to another needle, {of equal magnetism, and in a given 

 position) a reduced moment of rotation equal to the effect of the 

 unit of weight on the arm of a lever whose length is the unit of 

 distance.'^ 



