578 Br. G. Johnstone Stoney on 



lately had his attention directed to one of Sir George Stokes's 

 early papers in which the resolution is distinctly enunciated. 

 Stokes's words are "...., for we may represent an arbi- 

 trary disturbance in the medium, as the aggregate of series 

 of plane waves propagated in all directions " (see Stokes's 

 Collected Papers, vol. i. p. 192). Sir George Stokes here 

 refers to the theorem incidentally and without proving it, or 

 giving a reference to where a proof may be found ; from 

 which the natural inference seems to be that it could be 

 cited as a well-known theorem so long ago as 1845, when 

 Stokes's paper was published. The present writer desires to 

 call especial attention to this, lest it should be supposed that 

 he claims the discovery of the theorem. What he has done 

 has been only to rediscover the theorem when it seemed to 

 be forgotten, and to show the conspicuous use that can be 

 made of it in investigating optical problems. 



25. In the chamber study of optical problems it is found 

 to be most convenient to employ this resolution into abso- 

 lutely flat wavelets ; but in making experiments the com- 

 ponents usually consist of wavelets which are either somewhat 

 convex or somewhat concave. This is permissible, inasmuch 

 as the superiority of the resolution of light into undulations 

 of absolutely flat wavelets over other kinds of resolution, 

 depends on the circumstance that each such component 

 undergoes no change as it advances through space ; and, 

 accordingly, a resolution into components consisting of nearly 

 flat wavelets is allowable in all cases where the approximation 

 to being flat is sufficient to carry the nearly flat components 

 across the space to which the experiment extends without 

 more change than may legitimately be left out of considera- 

 tion. Moreover, cases sometimes arise in practical work, 

 where a resolution into conspicuously curved components is 

 found useful. To be prepared for such eventualities it is 

 proposed to show, in an Appendix to the present paper, that 

 a resolution into concave or convex wavelets is legitimate, 

 and to study how the three resolutions into concave, flat, and 

 convex wavelets stand related to one another. 



26. There does not seem to be any such thing in nature as 

 light of a single wave-frequency. The nearest approach to 

 it that has been found is such light as is met with in the 

 rays of a spectrum that consists of narrow lines : these 

 rays include wave-frequencies ranging from <f> to <£ + £(/>, 

 where S<£ is finite though small. Notwithstanding this, when 

 we have occasion to deal with monochromatic light, we shall 

 provisionally treat it as though it were light of the single 

 frequency <p, reserving the necessary correction till we 



