395 



the law expressing the variation of the rotation corresponding to the 

 deviation of the refracted ray, when the inclination of the planes of 

 polarization to the plane of incidence is 45 ; namely, that the co- 

 tangent of the inclination of the plane of polarization to that of re- 

 fraction, is equal to the cosine of the difference between the angles 

 of incidence and refraction. This formula represents the experi- 

 ments so accurately, that when the analysing rhomb of calcareous 

 spar is set to the calculated angle of inclination, the extraordinary 

 image completely disappears ; a result which is the strongest test of 

 the correctness of the formula. 



In order to determine the quantity of polarized light in the re- 

 fracted pencil, the author follows a method similar to that which he 

 employed for the reflected rays, and which he has explained in his 

 former paper. He deduces as a general result, that the quantity of 

 light polarized by refraction can never be mathematically equal to the 

 whole of the transmitted pencil, however numerous be the refractions 

 which it undergoes ; or, in other words, refraction cannot produce 

 rays truly polarized, that is, with their planes of polarization parallel. 

 The same conclusions as were deduced in a preceding paper, respect- 

 ing the partial polarization of light by reflexion, hold good with re- 

 gard to similar changes produced by its refraction. Each refracting 

 surface produces a change in the position of the planes of polarization, 

 and consequently a physical change upon the transmitted pencil by 

 which it has approached to the state of complete polarization. This 

 proposition the author illustrates by applying the formulae to the re- 

 sults of actual experiment, and showing their coincidence. 



By prosecuting this investigation, the author arrives at the follow- 

 ing important laws, namely, that at the first surface of all bodies, 

 and at all angles of incidence, the quantity of light polarized by re- 

 fraction is equal to the quantity polarized by reflexion ; and also that 

 the reflected is equal to the transmitted light when the inclination of 

 the planes of polarization of the reflected pencil to the plane of the 

 reflexion is the complement of the inclination of the planes of polari- 

 zation to the same plane. 



On the Action of the Second Surfaces of transparent Plates upon Light. 

 By David Brewster, LL.D. F.R.S. L.% E. Read February 25, 

 1830. [Phil. Trans. 1830, p. 145.] 



M. Arago had conceived that he had proved by an experiment, 

 that at every possible angle of incidence the quantity of light pola- 

 rized by reflexion was precisely equal to that of the light at the same 

 time polarized by refraction. Dr. Brewster shows in the present 

 paper, that the experiment does not warrant this conclusion ; as the 

 phenomena observed from it are the complicated effects of various 

 refractions and reflexions from both surfaces of the glass, each affect- 

 ing the position of the planes of polarization. By varying the form 

 of the experiment in a way which allowed of the observation of these 

 effects when separate, he is led to the following general law ; namely, 



