[ 577 ] 



LIIT. Flat-Wavelet Resolution,— Part III. 

 By G. Johnstone Stone y, J/..1., Se.-D., F.R.S* 



[Continued from the Philosophical Magazine for February 1903, p. 279.] 



Part III. — How to exhibit in Microscopes and Spectroscopes 

 the resolution of the light into its component Undulations of 

 Flat Wavelets, and How to employ this resolution as our 

 guide in making and in interpreting experiments. 



23. rflHE letters ufw were employed in Part II. of this 

 J_ series and continue to be used throughout the 

 present paper as an abbreviation for Undulation of Flat Wave- 

 lets. By an undulation is meant a train of similar waves ; 

 and the reader is requested to bear in mind that throughout 

 each of the u f w's with which we shall have to deal, the light 

 will be of one wave-length, and the wavelets of which it 

 consists will be alike and each wavelet uniform throughout 

 its whole extent — so that the wave-length, the intensity, and 

 the state of polarization of the light is the same throughout the 

 unlimited extent of each such undulation. The extent of each 

 u f w is theoretically unlimited in time and in lateral direc- 

 tions, and it is possible to carry the analysis so far that the 

 extent of each ufw shall be unlimited in every direction; 

 but nevertheless it is legitimate and often convenient to deal 

 with the part of a u f w which lies during a specified time 

 within a portion of space bounded by a closed surface, and to 

 provide for the outlying parts of the undulation by imagining 

 the medium which happens to lie within the closed space to 

 be indefinitely extended. The state of things described in 

 this paragraph follows from what has been already established 

 in previous papers of this series : see also the Appendix to 

 this paper. 



24:. The first part of the inquiry, which will be found at 

 p. 570 of the Report of the British Association for 1901, 

 contains a proof by the Method of Reversal of the theorem 

 that light, traversing a space S occupied by any uniform 

 transparent medium, can always be completely resolved into 

 ufw's of the kind described above, travelling across that 

 space. 



A less direct proof of this theorem was published by the 

 present writer in 1895 (see ' English Mechanic > for December 

 1895. § 38290;. and he was then and remained until lately 

 under the impression that be was the first to point out that 

 every disturbance within a uniform wave-propagating medium 

 i^ susceptible of being resolved in this way. But he has 

 * Communicated by the Author. 



