THE SMITHSONIAN INSTITUTION. 323 



and so that the tangent of the angle of deflection iv is exactly double 

 the tangent of deflection v, which the same magnet, at the same dis- 

 tance, would have produced in the position Fig. 4 ; hence, under cir- 

 cumstances otherwise the same, we have — 



tang. V = ^^"g- '' 



2 



By making the experiment, not in the position Fig. 4, hut that of 

 Fig. 5, we get — 



M=: "T r^ tang, iv 

 2 ' 



The relation of the circulating current, which traverses the ring of 

 the tangent compass, in the magnetic meridian, to the terrestrial mag- 

 netism, as well as to the magnetic needle, may now be compared 

 with the effect of the magnetic bar placed in the position of Fig. 5. 



If the circulating current of the tangent compass deflects the 

 needle w degrees, we have — 



tans:, to = 



^^9 

 r T 



denoting by g the force of the current, and by r the radius of the 

 ring : thus we have for the reduced moment G of the deflection of the 

 circular current, which corresponds to the moment of deflection M 

 of a magnetic bar 



Tr^ang. 1(7 (3.) 



ix= 2 = 7rr^g. 



This G is the force with which, under the relation stated above, 

 the circular current would be deflected from the plane of the mag- 

 netic meridian, if the force of the terrestrial magnetism were =1. 



Making ;r r^ = 1, we will have G =. g; 

 hence g is the moment of a circular current which circulates in unit 

 of surface. 



From equation (3) we get for g the value — 



a T r t ang, w (4) 



^ - 2~7r 



thus we obtain a value for the force of the current g, measured by the 

 moment of deflection of a current traversing around the unit of sur- 

 face, expressed in absolute measure, by substituting for T its absolute 

 value. 



§5. Comparison of the different current units. — Theoretically these 

 three units of force are determined with perfect exactness, and if the 

 matter were considered only in a scientific point of view, each of them 

 would seem acceptable, though the preference would be due to Weber's 

 unit. 



But the selection must be different when practical wants are also 

 considered. 



The galvanic battery enters so multifariously into a process of art, 

 that it is of great importance to have methods by which the constants 



