486 Mr. F. Twyman on Improvements 



edges of the rhomb being 70° (which makes the angle 

 of incidence of the beam upon the face of the rhomb 55°). 

 With these values we find that the intensity of the light 

 transmitted by the rhomb, if that light be polarized after 

 transmission in the plane of incidence, would vary from 1 

 to 0*732: the partial polarization due to the rhomb in a plane 

 at right angles to this being negligible. 



Thus if the beam after passage through both rhomb and 

 dispersion prism be polarized, it will vary from 0*732 to 0*651 

 as the analyzing nicol is turned. 



This variation in the intensity of the top beam produces 

 errors of the following amounts: — 



Density of the absorbing 



medium under test Percentage error in the density, 



(s. e. log ln *1, I, being the to be added or subtracted 



I according as the first nicol is set 



intensity of the incident beam and Avith its plane of polarization 



I that of the transmitted beam). vertical or horizontal. 



0*054 11*5 



0*231 9*4 



0*602 6*4 



1*521 3*3 



The errors of reading are considerably less than the errors 

 in the above table, so that it is very important to get rid of 

 the latter. This is done in the more recent instruments by the 

 simple and obvious plan of making the rhomb of the same 

 glass as the prism, and of such angles that the angles of 

 incidence of the beam on its surfaces equal those on the sur- 

 faces of the dispersion prism. 



The following table will show the effect of this in several 

 actual instances. A piece of neutral-tint glass was retained 

 as a standard, and its density measured on various instru- 

 ments, some with the old form of rhomb and some with the 

 new. The plane of polarization of the front nicol was 

 sometimes vertical, sometimes horizontal. 



It was in the testing of Nos. 2 and 3 that we first became 

 fully aware of the magnitude of the error. 



Having calculated the amount on the hypothesis that the 

 arror was caused in the manner I have described, the front 

 nicol was rotated through 90°, and an altered reading of the 

 expected amount was obtained. On replacing the Hiifner 

 rhomb by a fresh one of the same glass as the dispersion-prism 

 and of corresponding angles, a reading was obtained exactly 

 the mean between the two former ones. (See No. 3 below.) 



Several instruments were made before readings on a test 

 density were taken, and instrument No. 4 was one of these 



