360 Comparison of Methods for observing Small Rotations. 



of homogeneity of the transmitted light. If the shutters be 

 nearly closed, so that light finds entrance through a narrow 

 slit only, a better judgment can be formed, which may be 

 tested by prismatic analysis. 



In an otherwise dark room, lighted by a powerful soda- 

 flame, it is interesting to remark how very slight a change in 

 the critical colour manifests itself in the general appearance 

 of surrounding objects seen through the preparation. When 

 the ray of maximum transmission corresponds closely to that 

 of soda, the powder is almost invisible, and objects are seen 

 as through a clear medium. But so slight a change of tem- 

 perature brings with it a hazy appearance, that it requires 

 some care to obtain the best effect. It is desirable also to 

 exclude by absorbing media the blue light which usually 

 attends a soda-flame in very sensible degree. 



XLII. Optical Comparison of Methods for observing Small 

 Rotations. By Lobd Kayleigh, F.R.S* 



IN order to measure very small rotations, e. g. of the sus- 

 pended parts of a galvanometer or magnetometer, two 

 methods are commonly employed. We may either observe 

 with a magnifier the motion of a material pointer; or, follow- 

 ing Gauss, cause the rotating parts to carry round a mirror 

 in which a scale is seen by reflection. In a modification of 

 Gauss's method, well known from Sir W. Thomson's galva- 

 nometers, the image of a dark or bright line is thrown ob- 

 jectively upon the scale. In deciding which arrangement to 

 adopt in any particular case, various circumstances would have 

 to be taken into account, but still a comparison of capabilities 

 from a purely optical point of view is not without interest. 



In the mirror method the optical limit depends upon the 

 horizontal breadth of the mirror itself. The easiest road to 

 the desired conclusion, as well as the most instructive, is by a 

 direct application of the principles of the wave theory. To 

 take the simplest case, we will suppose the mirror rectangular. 

 Consider, then, aluminous point, and its image after reflection, 

 whether in the focal plane of a telescope, or formed directly 

 upon a scale. The optical work being perfect, the secondary 

 rays from every part of the mirror agree in phase at the focal 

 point. Now suppose that the mirror rotates through such 

 an angle that one vertical edge advances a quarter of a wave- 

 length (J X), while the other retreats to the same amount, and 

 consider the effect on the phase-relations at the point in ques- 



* Communicated by the Author. 



