t'rof. Challis on the Theory of Elliptically -polarised Light. 287 



which I have advanced in the Cambridge Philosophical Transac- 

 tions, vol. viii. part 3, and in the Philosophical Magazine for 

 December 1853. I have there demonstrated the existence of 

 axes of rectilinear transmission, and of simultaneous normal and 

 ti-ansverse vibrations, on hydrodynamical principles, no other 

 hypothesis being made respecting the medium than that the 

 density varies as the pressure. Suppose a wave-ray of this 

 theory to be incident on a reflecting surface, and the transverse 

 vibrations to be resolved in directions perpendicular and parallel 

 to the plane of reflexion. Now although we may not yet be able 

 to determine by mathematical reasoning the precise manner in 

 which the ray comports itself at the moment of reflexion, from 

 experimental facts we have reason to say that the reflexion does 

 not take place strictly at the surface of the medium, but that the 

 path of the axis of the ray penetrates to a certain minute distance 

 below the surface. Nothing is less unlikely, considering the 

 geometrical relations of the directions of the vibrations to the 

 superficies of the medium, than that this distance should be differ- 

 ent for the two sets of vibrations, and that the observed change 

 of phase is owing to this circumstance. 



There is another question relating to this experiment which 

 requires an answer. Why is the change of phase' not apparent 

 unless the incident ray be plane-polarized ? The theory of po- 

 larization, founded on hydrodynamical principles, which I have 

 proposed in the Cambridge Philosophical Transactions, vol. viii. 

 part 3, gives the following explanation : — If a ray of common 

 light be divided into two plane-polarized rays which pursue the 

 same course with diff"erence of phase, the compound ray is still 

 equivalent to a ray of common light ; but if a plane-polarized 

 ray be similarly divided, the compound ray is circularly or ellip- 

 tically polarized. The commonly received theory of polarization, 

 which rests upon the hypothetical medium before referred to, is 

 incapable of giving a like explanation, because it is incapable of 

 making a distinction between common light and elliptically- 

 polarized light. 



Being desirous that the objections I advance against the oscil- 

 latory theory should rest on admissions or assertions made by its 

 own supporters, in order to justify the objection just urged, I 

 shall refer to a passage in Mr. Airy's ' Titutise on the Undula- 

 tory Theory of Light.^ Near the end of the treatise the follow- 

 ing statement occurs : — " Common light consists of successive 

 series of elliptical vibrations (including in this term plane and 

 circular vibrations), all the vibrations of each series being similar 

 to each other, but the vibrations of one series having no relation 

 to those of another. The number of vibrations in each series 

 must amount to at least several hundreds ; but the sgries must 



