368 FOURTH REPORT 1834. 



This ingenious theory seems open to an objection ah-eady 

 noticed, — namely, that the light resulting from the union of 

 two oppositely polarized pencils cannot, in all respects, be 

 taken as the physical representative of common or unpolarized 

 light. It also involves this further difficulty, that the positions 

 of the planes of polarization of the two oppositely polarized 

 portions are entirely arbitrary ; and that if they be dift'erently 

 assumed, the results will be physically different. Thus, for ex- 

 ample, if the two planes be taken, one coincident with the plane 

 of reflexion itself, and the other with the perpendicular plane, 

 neither of these planes will be changed by reflexion, although 

 the intensities of the corresponding pencils will. 



Sir David Brewster has also investigated experimentallj'^ the 

 eff"ect of refraction upon the plane of polarization of the refracted 

 ray ; and he has found that the law of the change may be ex- 

 pressed by a very simple and elegant formula *. This formula 

 is a necessary consequence of Fresnel's theory, although he does 

 not seem himself to have observ^ed it. Its discovery by Sir 

 David Brewster adds one to the many instances of rare saga- 

 city by which this philosopher is guided in his experimental 

 inquiries. The partial polarization of light by refraction has 

 been considered by Sir David Brewster in the same memoir. In 

 the investigation of the quantity of polarized light in the refracted 

 pencil, he employs a principle similar to that which he had 

 already applied to the reflected ray ; and he arrives at the result 

 that the quantities of polarized light in the reflected and refracted 

 pencils are precisely equal, whatever be the incidence, con- 

 formably to the law of M. Arago. The effects produced by suc- 

 cessive refractions are accounted for on the same principles. 



Sir David Brewster seems to have been the first who studied 

 the effects produced by total reflexion upon polarized light, and 

 he observed in particular the complementary colours which the 

 light thus reflected furnished when analysed with a rhomb of 

 Iceland spar f. At this time both he and Dr. Young concurred 

 in thinking that these phenomena arose from the interference of 

 two portions of light which were reflected at unequal depths ; 

 one portion, according to Dr. Young, beginning to be refracted, 

 and being then turned back by the continued exercise of the 

 same power J. 



* a and a' being the azimuths of the planes of polarization of the incident and 

 refracted rays, estimated from the plane of reflexion, and i and i' tiie angles of 

 incidence and refraction, 



cot a' =:= cot a cos {i — tO. 



" On the Laws of the Polarization of Light by Refraction," PAjV. Trans. 1830. 



f Journ. Royal Inst., vol. iii. 



X Suppl. Encyc. Brit., Art. Chromatics. 



