266 Dr. G. J. Stoney on the Resolution of Light 



sense in which resolutions by Fourier's theorem, or into 

 Spherical Harmonics, are unique ; and it has the immense 

 advantage over every other method of resolution that each o£ 

 the flat wavelet components advances unaltered across the 

 medium. When we aim at the most complete theoretical 

 resolution from the purely mathematical point of view, we 

 are to regard each of the component undulations as an 

 uninterrupted train of waves which are all alike — of the 

 same wave-frequency, intensity, and state of polarization 

 throughout — and each occupying the whole of space for all 

 time. Nevertheless it is quite permissible, and is for most 

 purposes convenient, to consider separately what happens 

 within a limited space and definite duration. Moreover, we 

 shall presently see that it is legitimate, when investigating what 

 happens within a limited space, to divide the whole body of 

 undulations of flat wavelets into little groups and to substitute 

 a single undulation of flat wavelets for each of these groups ; 

 and that, in like manner, when dealing with a definite time, it is 

 legitimate to divide the wave-frequencies into little groups 

 and to substitute a single wave-frequency for each group. 

 By these familiar devices we substitute large numbers which 

 can be accepted by the physicist, for the infinite numbers of 

 the mathematician ; and values estimated at a point which 

 falls short of the limit for the limiting values of the mathe- 

 matician. We thus sweep aside the difficulties which would 

 otherwise result from ponderable matter consisting of mole- 

 cules, from electricity consisting of electrons, and from the 

 consequent necessity when dealing with nature of substituting 

 the puncta of the physicist for the points of the mathe- 

 matician. 



5. The proof by the Principle of Reversal has another 

 advantage, not yet referred to, viz. that it can be applied to 

 doubly refracting as well as to isotropic media. The investi- 

 gation at p. 570 of the Report of the British Association for 

 1901, goes with detail only into the resolution of light in 

 isotropic media, as being the case of most practical impor- 

 tance. This having been accomplished, it is easy to modify 

 the investigation so as to embrace both isotropic and doubly- 

 refracting media. To do this it suffices to substitute 

 throughout that proof the term wave- surface in the medium 

 for the term sphere, when treating of light diverging from or 

 converging towards a punctum. Thus, Theorem I. on p. 573 

 of the B. A. Report furnishes, when generalized, the following- 

 more comprehensive one : 



