1881.] On the Refraction of Plane Polarised Light. 



31 



been turned. There is some difficulty in determining with certainty 

 the angle between the edge of the prism, from which 6 is measured, 

 and the principal plane of the polarising prism in any given position. 

 We, therefore, cannot compare a series of observed and calculated 

 values of with accuracy ; we can, however, compare the differences 

 between consecutive values of 6 given by theory with those differences 

 as produced by the known rotation of the polarising Nicol, or that 

 due to the sugar cell. 



Similar observations were made for the case in which only the 

 extraordinary ray traverses the crystal ; in this case, if a and b be the 

 principal refractive indices, we have, according to the same theories, — 



, a , a , A . ,„s ,„n . ar — b~ sin 2/3 sin(\. + 0") sin 2 



tan 6 = tan /3 cos (\ + ) cos (0- 0") + — — v y ; ^ , 



2 or sm(0-f-0 )cos^0 



where 6" is given by 



tan e" = tan (3 cos (X + 0") . 



Two series of observations are recorded in the paper, the one made 

 in November, 1880, the other with new and improved apparatus in 

 August, 1881. 



The two series lead to practically identical results. Taking first 

 the case in which the ordinary wave only is transmitted; for high 

 angles of incidence the rate of change in the values of 6 as given by 

 theory is considerably greater than that given by experiment. When 

 lies between 40° and 55° (about), the two agree closely, and as the 

 angle of incidence decreases still further, there is a tendency for the 

 experimental value of the difference to become the greater. 



The differences between theory and experiment amount to 6 per 

 cent, of the quantity measured when the ordinary wave is transmitted, 

 and to 15 per cent, when the extraordinary wave only passes through 

 the prism. 



When only the extraordinary wave is transmitted the reverse is the 

 case, the theoretical value is for large values of too small ; for 

 angles between 40° and 55° the two agree fairly, and for smaller 

 angles the experimental value becomes too small. Other series of 

 experiments lead to the same conclusions. Tor details as to the 

 arrangements of the apparatus, the method of determining exactly 

 when one ray is quenched, the probable accuracy of the results, and 

 the effects of small errors in the constants of the formulas or the 

 adjustment of the apparatus, reference must be made to the paper. 



The experiments were conducted by Lord Rayleigh's kind per- 

 mission in one of the rooms of the Cavendish Laboratory, at 

 Cambridge. 



