482 



REPORT 1867. 



together at right angles, -with a short magnet hung in their centre, having 

 a long light index pointing at a fiducial mark when the needle is in the 

 magnetic meridian. Let the battery and coils be so joined that the current 

 shall divide in the ratio of the resistances in the two coUs, and shall pass in 

 such a direction as to tend to turn the needle in opposite directions. 



The clotted lines show the position of coils when the current is passing. 



Let one coil with a resistance E at the beginning of the experiment stand 

 in the magnetic meridian, and the other coil with a resistance R^ in a plane 

 perpendicular to the meridian ; and when the current is passing in such a 

 direction that R tends to turn X S in the direction of the arrow, let the coiLs 

 be turned till the needle is again brought to the fiducial point and the coD. R, 

 makes an angle with the magnetic meridian, then we have R = tan R, ; 

 for the force exerted by the coil Rj to deflect the needle in the direction of 

 the arrow will then equal m sin ^ ; the force exerted by the coil R^ to deflect 

 the needle in the opposite direction will be i)?^ cos ; and we have m sin 



<j>=m^ cos (p, or — =tan 0, where ni and m^ arc the couples experienced by 



the magnet under the action of the two coUs, but as we have supposed these 



in R 

 coils to have equal magnetic moments with equal currents, "~=t|' '> there- 

 fore R=:tan f Rj. R and Rj need not be the resistances of the galvano- 

 meter-coils only, but may consist of two parts, G 4 »' and Gj -f- i\, where 

 G and Gj are the resistances of the galvanometer-coils, but r and r^ are 

 added resistances. Thus, when G G^ and r are known, ',\ can be obtained by a 

 simple observation. 



If G -|- r be one, one hundred, or one thousand units, the resistance of r^ 

 will be equal to the tangent of (p, or to one hundred or one thousand times 

 that tangent respectively minus in cacli case a constant = G^. 



If the range of the instrument were not required to be very great, the coils 

 Woidd betiu-ned by the pushing of a straight slide, equal divisions on which 

 would correspond to equal increments of the tangent of 0, and the scale would 

 be numbered, so that the resistance r^-^-shoiild be read oif dii'ectly, as in 

 Mr. Siemens's instrument. 



The tangent coils should be made of German-silver wire, and might be 

 arranged as pi-actised by Helmholtz and Gaugain. Theoretically, the range 

 of each instrument would be infinite, i.-eTanj instrument would be capable 



