XXVIII. A Theory of the Polarhai'ion of Light on the Hypothesis of Unchdationft. 

 By the Rev. J. Challis, M.A., Plumian Professor of Astronomy and Eaperi- 

 mental Philosophy in the University of Cambridge. 



[Read May 2r., 1846.] 



The Theory of Polarization contained in this Paper is founded on the Theory of Luminous 

 Rays, given in my last communication, of which the present may be regarded as a continuation. 

 I shall, therefore, use the same symbols as in the former Paper, and suppose their signification to he 

 known, and for the sake of convenience, the reference numbers attached to the equations will be in 

 continuation of those of the other Paper. 



Conceive a ray of common light to be submitted to some action which is not symmetrical with 

 respect to its axis, and which divides it into rays subsequently pursuing different paths. In general 

 the arrangement of the condensation in neither of these rays will be symmetrical about its axis: but 

 each may be supposed to consist of a symmetrical part having the properties of common light, and 

 a part which has a different arrangenient. The unsynimetrical part is considered to be polarized. 

 A difference in the arrangement of the condensation in different directions transverse to the axis, 

 corresponds in this Theory to Polarization. By experiment it appears that a polarized ray has 

 a certain definite character, which is quite independent of the particular action producing the bifur- 

 cation of the original ray, being the same under modes of separation of very different kinds. The 

 explanation of the pha?nomena of polarization is therefore to be sought for in the modifications of 

 which the vibrations of a ray of common light are susceptible according to Hydrodynamical principles. 

 In the pha;nomena of common light there is nothing to decide whether the sensation of light is due 

 to the direct or the transverse vibrations. The phienomena of polarized light shew that it is to be 

 attributed to the tr/insnerse vibrations, and our attention must therefore be directed to the modifica- 

 tions which these may undergo. The direct vibrations very probably are productive of heat. 



In the Theory of Luminous Rays it was shewn that a ray in which the condensation at any point 

 is «, may be supposed to be compounded of two rays in the same phase of vibration whose con- 

 densations are <t, and a-j, if .s = u, -(- a-., independently of any relation between a, and a,. We are 

 therefore at liberty to assume another condition which these quantities shall satisfy. The assump- 

 tion I shall make is, that the bifurcation of a ray takes place so that the transverse velocity at each 

 point is converted into two velocities at right angles to each other, and that these are respectively 

 the velocities at the corresponding points of the two polarized rays. This law is most probably 

 deducible from purely Hydrodynamical principles; but in the present state of Hydrodynamics it 

 must be regarded as an hypothesis. By the reasoning and notation of the former Paper, the com- 

 ponent velocities in one ray are '1> — '- , and '!> - '; and in the other, <!' ■ — , and 't -r ' ? a>"J '''^ 



dx dy dx dy 



+ ^^'.^= = (Ui). 



dy dy 



3 B!2 



