Currents by means of a Tangent-galvanometer or a Multiplier. 531 



it is equal to 1 when - =5-828426, that is to say, when the length 



of the needle is nearly one-sixth the length of the axis a. It 

 then rapidly decreases; and as it has to be multiplied with 

 sin 2 3r#, it exerts but little influence on the measurements by means 

 of a tangent-galvanometer, the needle of which has usually only 

 one-seventh or one-eighth the length of the axis a. The needle 

 of multipliers being very long, the influence of the term c sin 2 ^ 

 becomes increased in such a manner as to prevent the possibility 

 of measuring according to the law of tangents. For that reason 

 I proposed to use multipliers consisting of an elliptic metal band 

 or coil of copper wire with a single needle (made astatic by means 

 of a magnetic bar approached to it with the same pole) ; the 

 needle may then be taken of any length, and it may be made 

 perfectly astatic if required. The needle being very long, c 

 becomes so increased that it can be omitted in the equation 



S:S' = l+csin 2 i6':l + csin 2 i^=l + sin 2 ^:- + sin 2 i^ 



S:S'=sin 2 i0:sin 2 i0>. 



We find, in conformity with the law of tangents, 



S' = H tan and S = H tan 0(1 + c sin 2 \9) t 



S : S' = (1 + c sin 2 \6) tan : (1 + c sin 2 \&) tan &. 



The needle being very long, we find with sufficient approximation, 



S : S'= sin 2 \0 tan : sin 2 \& tan 0'. 



To convey a clear idea of the accuracy to be attained by the 

 formula of Mr. Johnstone Stoney and mine, I applied each of 

 them to a series of observations made by means of a tangent- 

 galvanometer, the needle of which had (with regard to the dia- 

 meter of the circular metal band of 202'5 millims.) the enormous 

 length of 190 millims. I observed the intensity of currents of a 

 constant electromotive apparatus when 01, 0*2, and ultimately 

 the whole length of the metal plates was immersed. 



Immer- 

 sion. 



Deflections. 



Average. 



Immer- 

 sion. 



Deflections. 



Average . 



North 

 pole. 



South 

 pole. 



North 



pole. 



South 

 pole. 



01 

 0-2 

 0-3 

 0-4 

 0-5 



150 

 172 

 20-0 

 22-5 

 240 



1955 

 197-5 

 200-4 

 202-5 

 204-5 



15 15 

 17 21 

 20 12 

 22 39 

 24 15 



06 

 0-7 



0-8 

 0-9 

 10 



25-2 

 26-2 

 275 



28-5 

 29-8 



205-4 

 206-7 

 208-0 

 2090 

 210-2 



25° 18 



26 41 



27 45 



28 45 



29 54 



