THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[FOURTH SERIES.] 



MA Y 1865. 



XLVI. Supplementary Considerations relating to the Undulatory 

 Theory of Light. By Professor Challis, F.R.S., F.R.A.S.* 



ON a review of the arguments by which I have now for a 

 long time maintained that the phenomena of light are 

 referable to the vibrations and pressures, as mathematically de- 

 termined, of a continuous elastic fluid the pressure of which 

 varies proportionally to its density, I have found that there are 

 certain points of the reasoning which require rectification or 

 confirmation. To discuss these points is the object of the pre- 

 sent communication. 



(1) By pure reasoning, founded on admitted principles, I have 

 ascertained that the vibratory motion of the supposed elastic 

 fluid is composite independently of particular modes of disturb- 

 ance, and that each component consists of vibrations partly 

 parallel and partly transverse to an axis. The former of these 

 results is at once applicable in accounting for the composition of 

 light as indicated by prismatic analysis, and the other in the 

 explanation of facts of polarization. As the reasoning also showed, 

 independently of arbitrary disturbances, that for small vibrations 

 udx + vdy + wdz is an exact differential, the motion relative, as 

 above stated, to an axis is analytically expressed by the equation 



(d . fcf>) — udx -f vdy + wdz, 



f being a function of x and y only, (f> a function of z and t only, 

 and the axis of the motion coinciding with the axis of z. In 



fact this equation gives 



a 



, df ,df „d<f> 



u =*i' ***£ w = f £> 



* Communicated by the Author. 

 Phil. Mag, S. 4. Vol. 29. No. 197. May 1865, 



