Construction of a Standard Galvanometer. 



417 



tion was the expansion in ' Spherical Harmonics ' used by 

 Maxwell, part 4, chap. xiv. The tangent law was found to 

 be practically true, i. e. the deviation from it would never 

 introduce an error of more than about *5 per cent. The error 

 was greater the less the deflexion, and was negligible for 

 the accuracy required, which was of course not very great. 

 The error arising from partly neglecting the torsion of the 

 silk fibre was also investigated and found to be without 

 influence : the fibre was seven inches long. 



The divided scale was one of Elliott's scales, in which 360 

 divisions correspond to 229 millimetres. The distance from 

 the mirror to the scale was 1095'7 scale-divisions, or about 

 seven hundred millimetres. The problem of finding the form 

 of the curve into which it is necessary to bend the scale of 

 equal parts so as to read direct currents was solved by Mr. 

 Adair ; as we could find no previous record of this solution, I 

 will give it here. 



Let A B be a portion of the 

 curve required; let OA=/ 

 the apsidal distance, 6 the polar 

 angle subtended by A B, OB 

 = r the distance of the light- 

 spot from the mirror. The 

 incident light falls along A 0. 

 AB = s. 



The form of the curve, assuming that the galvanometer 

 obeys the tangent law, is 



6 



or 



s = 2/tan^j 



dd -/ seci 2 ; 



and the differential equation giving r in terms of 6 is 



(l) 2 —/ 2 -1 



This is insoluble in general terms : but if the range of 6 is 

 small we can develop in powers of 6, and assume r=f+\, 

 wmere X is the addition to the radius of the circle whose centre 

 is and radius /. Thus the differential equation for X 

 becomes, by retaining terms in 6 i J 



Phil. Mag. S. 5. Vol. 28. No. 174. Nov. 1889. 2 H 



