prof. Challis on the Theory of Elliptically-polarized Light. 285 



in the general form z + y'^ — \. It is, in fact, on this account that 

 an equation not only gives by its solution the answer to a ques- 

 tion which is possible, but also has a symbol to indicate that a 

 question is impossible. It is true that, because of the generality 

 of algebraic operations in respect to their being independent of 

 relative magnitude, several algebraic functions may satisfy at 

 the same time the final equation which denotes the relation of 

 the unknown quantity to the given quantities. But these are 

 all included in the same general form. Hence for the x of an 

 equation we may always substitute z + yV — \, y vanishing for 

 a possible root. These considerations would justify us in saying 

 at the very beginning of the theory of equations, that the un- 

 known quantity is z-Yy^ — 1, and that .r is substituted for this 

 expression for the sake of brevity. Unless this be understood 

 to be the signification of x, the theory does not possess the re- 

 quisite degree of generality. If this principle be admitted, the 

 method of finding the impossible roots of an equation which I 

 have indicated, is a necessary consequence. Mr. Airy Avill not 

 move me from my position unless he points out an error or false 

 principle in this a priori argument, or adduces a numerical in- 

 stance that contradicts it. 



Cambridge Observatory, 

 March 7, 1859. 



XLVI. On the Theory of Elliptically-polarized Light. 

 By Professor Challis*. 



I VENTURED, in a former communication (Philosophical Ma- 

 gazine for January 1859), to advance the idea that a mathe- 

 matical theory of physical forces may be based upon the dyna- 

 mical action of a fluid medium pervading space, and so consti- 

 tuted that its pressure varies proportionally to its density. The 

 theory of light which is generally advocated in the present day, 

 assumes that space is occupied by a medium more resembling a 

 solid than a fluid, and attributes the phsenomena of light to the 

 oscillations of its individual atoms. As the two media cannot 

 be identical, or coexist, it is requisite, for the maintenance of my 

 views, to inquire how far the phsenomena of light are explained 

 by the oscillatory theory ; and in this inquiry I shall be com- 

 pelled to canvass freely the views of its supporters. I have 

 already shown, in the Philosophical Magazine for February, that 

 that theory has hitherto failed to determine the direction of the 

 transverse vibrations of a polarized ray, while the hydrodyna- 

 mical theory decides on this point unequivocally. And even if 



* Communicated by the Author. 



