116 



The refrangibility of the several streams is supposed to be the same, 

 and the polarization to be of the most general nature, that is, to be 

 elliptic. The following proposition is established. 



When any number of independent polarized streams, of given 

 refrangibility, are mixed together, the nature of the mixture is com- 

 pletely determined by the values of four constants, A, B, C, D, de- 

 fined in the following manner : — Let J be the intensity of one of the 

 elliptlcally-polarized streams, a the azimuth of its plane of maximum 

 polarization, tan /3 the ratio of the axes of the ellipse described by 

 the sethereal particles ; then 



A=S(J); B = 2(Jsin2/3); C = 2(Jcos 2/3 cos 2a) ; 



D = S(Jcos2(Ssin2a). 



Two groups of polarized streams, of the same refrangibility, which 

 are such as to give the same values to each of the four constants 

 A, B, C, D, are defined to be equivalent; and the author has shown, 

 that if two equivalent groups be transmitted through any optical 

 train, and be afterwards analysed, they will present exactly the same 

 appearance ; so that equivalent groups may be regarded as optically 

 identical. 



It readily follows from the above theorem, that any group of 

 polarized streams is equivalent to a stream of common light com- 

 bined with a stream of elliptically-polarized light from a different 

 source. If J, J' be the intensities of these streams, a' the azimuth 

 of the plane of maximum polarization of the latter, tan /3' the ratio 

 of the axes of the characteristic ellipse, 



J = A- a/(A 2 + B 2 + 0) ; J'- //(As + B^ + C 2 ) ; 



sin2/3'= — j— — — ; tan 2a'= — . 



The author has applied these formulae to a few examples, and has 

 likewise shown, from the general principles established in the paper, 

 that the changes which are continually taking place in the epoch and 

 intensity of the vibrations of polarized light may be of any nature. 

 In the case of common light, the author contends that there is no 

 occasion to suppose the transition from a series of vibrations of one 

 kind to a series of another kind to be abrupt, but that it may be of 

 any nature. 



Professor Miller made a communication on the Artificial Forma- 

 tion of Crystallized Minerals. 



March 1,1852. 



Mr. Hopkins, F.R.S. &c, gave a Lecture on the Influence of In- 

 ternal Heat, Stellar Radiation, and Configuration of Land and Sea 

 in producing Changes of the Earth's Superficial Temperature. 



