530 Prof. Zenger on the Measurement of the Intensity of Electric 



angle of deflection from the magnetic meridian, and 2\= the 

 length of the needle. 



Though this equation is very similar to my formula of correc- 

 tion, yet both are not identical, and do not afford the same 

 approximation to real intensity. As M. Gaugain's arrangement 

 considerably lessens the sensibility of tangent-galvanometers, and 

 as it cannot be applied to the construction of multipliers, it may 

 perhaps be of use and interest to call to mind the formula of 

 correction which I gave in 1855. 



Conceive a circular or elliptical band of metal to be placed in 

 the plane of the magnetic meridian, together with a magnetic 

 needle, the centre of which coincides with the centre of the 

 baud ; imagine now the action of an element A of an electric cur- 

 rent to be p at the distance 1, and pj at a distance 8 ; then 



P'=PA*)> 

 and the total action of the current 



s=,/(S){i + ? + f^... + /f}=,/(wa } (1) 



2/'(S) being a constant as long as the needle does not deviate 

 from the magnetic meridian. The action of two different cur- 

 rents on the same galvanometer would be 



S : S>=pf(8)Zf(8) .y/(S)2/'(S)=i> :p>, 



if the needle remained in the plane of the band. 



The poles of the needle being deviated, the distances 8 . . . 8 n 

 become increased, and the magnetic action of the current de- 

 creases at the rate 



S:S' = AN' 2 :AN 2 , 



S : S'= p~ — - y sin 2 i 



6 being the angle of deviation from the 

 magnetic meridian, 2X = the length of 

 the needle, and 8 = the distance AN. 

 We find AN + NO = AO, or 8+\=a, 

 2a being the axis of the circular or ellip- 

 tic band, and 



S'= T^ • 



4a\ -21/3 



The constant c = - ( ^T2 rapidly increases when a nearly equals X; 



a. 



