in the Neighbourhood of the Polarizing Angle. 13 



and for cos 7, 



cos J7r(l + Sy/y ) = — i w ^Y/7o- 



Hence the condition of achromatism is 



or by (15), 



^S\±i7rM o a 7 / 7o =0; 

 dT _7tM 



(/A-o 2A.Q 



Thus if M be of the right magnitude, the colour will be 

 compensated when 7= \tt, and doubled when 7= — i 73 "? or 

 vice versa. 



When the colours were but little dispersed in the plane of 

 incidence, there could usually be observed on sufficiently 

 contaminated surfaces a dispersion laterally, indicating a 

 variation of M with X. It was to be expected that M should 

 be proportional to X -1 . Not much more could be done expe- 

 rimentally than to verify the direction and order of magnitude 

 of the effect. Thus it appeared that on a greasy surface the 

 difference of readings corresponding to /3= +30° was greater 

 when the settings were made for the brown than for the blue 

 side of the spot. Of these the former, due to the absence of 

 bine, represents the setting proper to blue light. 



The angles +30° were found suitable for /3. It was at 

 first supposed that advantage would accompany a smaller /3 ; 

 but in this case the spot was too diffused in a horizontal direc- 

 tion to suit the dimensions of the bright field employed. The 

 adjustment of the spot to centrality (right and left) by varia- 

 tion of a was then less certain. On the other hand, a too 

 great increase of /3 throws excessive stress upon the readings 

 of a. 



The delicacy of the apparatus may be measured by the 

 smallest error of ot visible on simple inspection. When the 

 light was bright and the reflecting surface steady, a setting 

 for ft — +30° was visibly wrong on going over to {3= —30°, 

 when the change afterwards found necessary in the setting of 

 a exceeded about 2'. Less than this could hardly be recog- 

 nized on simple inspection ; but the error of a single setting, 

 arrived at by trials backwards and forwards, appeared to be 

 less than V. Thus the same readings, taken to the nearest 

 minute, were often recovered many times in succession ; but 

 on other occasions larger differences were met with, and it 

 was often difficult to judge whether they were due to imper- 

 fect observation or to real changes in the condition of the 

 rehVctino; surface. In any case it will be a modest estimate 



