owing to the Rotation of the Plane of Polarization. 139 



nature of the substance forming the prism, and upon the thick- 

 ness of the rotating plate. For a prism made of crown glass the 

 following propositions may be deduced from the measurements : — - 



1. The dark bands of the spectrum are equidistant. 



2. The distance between two contiguous bands is inversely 

 proportional to the thickness of the quartz plate employed. 



3. The bands move regularly and correspondingly on turning 

 the analyzer. 



Since the dark bands answer to colours of which the angles 

 of rotation differ by a constant quantity, it follows that the 

 distances of the colours in the spectrum are proportional to the 

 differences of their angles of rotation. 



By the refractions in the prism, the directions of propagation 

 of the coloured rays, and by rotation in the quartz, their direc- 

 tions of vibration are spread out so as to form a fan. The ar- 

 rangement of the colours follows the same law in both fans. 



On calculating the refractive indices of the individual dark 

 bands, the following law is arrived at : — Equal differences of re- 

 fractive index correspond to equal differences of rotation. Angle 

 of rotation and refractive index are therefore in linear con- 

 nexion ; consequently both are similar functions* of the length of 

 the undulations. 



Making the reciprocal squares of the lengths of the undula- 

 tions abscissae and the indices of refraction ordinates, then, ac- 

 cording to Cauchy's law of dispersion, the terminal points of the 

 latter will lie in a straight line. The dispersion through rota- 

 tion in quartz follows therefore the same law. Biot's law, that 

 the angle of rotation is inversely proportional to the square of 

 the length of the undulations, cannot be maintained. The line 

 drawn for the angles of rotation cuts the axis of ordinates, 

 not at the origin, but on the negative side. If this line is also 

 correct for the ultra-red rays, then for rays of a certain length of 

 undulation, a right-rotating quartz may become left-rotating, 

 and vice versa. 



The investigation of the spectrum of flint glass led to the same 

 laws. For the spectra of water and quartz, it was found that 

 the dark bands lay nearer to one another towards the violet end. 

 A corresponding departure of the refraction produced by this 

 substance from Cauchy's law was therefore inferred, and found 

 to be supported by direct observation. 



Moreover a direct way was devised for finding the depen- 

 dence of the angle of refraction upon the length of the undula- 



* If by " similar functions " be meant functions differing merely by a 

 constant multiplier, as the reasoning in the next paragraph seems to imply, 

 the statement is clearly wrong. The author seems to have forgotten the 

 necessity of introducing an arbitrary constant after integration. The ex- 

 perimental results stated are in perfect harmony with Biot's law.— G. G. S. 



