598 On Flat- Wavelet Resolution. 



is now no longer encumbered with interference from outside 

 the medium and the resulting turmoil within sphere p. 



52. The rest of what we have to do has now been made 

 easy. Inside M 2 draw a concentric sphere, R. When travelling- 

 westward after the First Reversal the waves of the undulation 

 come in succession to coincide with the right-hand half of 

 sphere R ; and when travelling eastward after the Second 

 Reversal they successively coincide with the left-hand half of 

 sphere R. On both these occasions the undulation is travelling 

 inwards towards the centre of the diagram. On either of these 

 occasions we may imagine a spherical shell one wave-length 

 in thickness which is bounded by sphere R, to be divided up 

 into elements SS, and each of these made the centre of 

 spherical wavelets directed inwards. This is in fact Huy gens' 

 construction with the improvement suggested on p. 539 of 

 the B.A. Report for 1902. If the resolution takes place on 

 the western half of sphere R (after both reversals) then be- 

 tween t — lOr and £ = 11t, it causes slightly convex wavelets 

 to sweep across the glass lens which lies within sphere r. If 

 the resolution takes place on the eastern half of sphere R 

 (after the First Reversal), we must allow the wavelets to 

 advance westward until t = Sr, submit them then to Reversal, 

 after which they travel eastwards and between t = 10r and 

 £ = 11t will cross the lens which lies within sphere r, in the 

 form of slightly concave wavelets. Finally, we may increase 

 t ad libitum, and assign any size we please to sphere R; and 

 the limit when both are increased indefinitely produces the 

 resolution into flat wavelets. Furthermore, the construction 

 makes obvious the respects in which the resolutions are related 

 to one another. To every concave or convex wavelet there 

 corresponds a flat wavelet consisting of precisely the same 

 kind of light. 



Although we have only spoken of the resolution of the 

 light emitted by P l5 this is sufficient ; for an exactly similar 

 resolution is available for the light emitted by any of the 

 other P's, and therefore for all of them. Thus the whole of 

 the light which crosses the glass lens may be resolved either 

 into flat or into convex or into concave wavelets sweeping 

 across that portion of space. 



53. Again, when dealing with microscopes and spectro- 

 scopes we have had no occasion to deal with other than 

 uniform isotropic media ; but the resolution into flat wavelets 

 equally applies to any luminous disturbance traversing a 

 uniform crystalline medium. The only change that has to be 

 made is to substitute everywhere throughout the proof the 

 wave-surface in the crystal for the spheres of which we have 

 hitherto made use. 



