into Uniform Undulations of Flat Wavelets. 267 



Theorem I., extended. 



All light traversing a uniform medium whether isotropic or 

 doubly refracting is susceptible of being resolved' into undulations 

 of uniform flat wavelets sweeping across that medium with 

 speeds in the different directions represented by the lengths of 

 the perpend icidars in those directions from the centre of the 

 ware-surface upon its tangent-planes. 



6. In like manner the primary aim o£ the present paper is 

 to develop a convenient way o£ applying the flat-wavelet 

 resolution of light to the investigation of the optical problems 

 that arise in isotropic media ; but, like the investigation 

 referred to above, it also can with ease be generalized so as 

 to provide for the optical problems that arise in any uniform 

 medium, whether isotropic or doubly refracting (see § 8). 



The inquiry which we have in view naturally divides 

 itself into two portions, the first of which deals with what 

 we may call the chamber study of optical phenomena, and 

 the other with their laboratory study — that is, with the 

 making of actual experiments and understanding them. The 

 present writer has made extensive use of the new method of 

 analysis in both branches of the study. 



Part I. — How to employ the resolution of light into flat- 

 wavelets in the chamber study of optical phenomena. 



7. If we conceive the light within an isotropic transparent 

 medium to be resolved into its component undulations of flat 

 wavelets, the following will be found a convenient way of 

 dealing with them. 



Imagine a straight line in space, which we may call the 

 optic axis. In most cases the best position for this line is 

 from the observer to the middle of his field of view. Draw 

 a plane perpendicular to the optic axis, preferably near to 

 the object looked at. This we may call the base-plane. With 

 c (the intersection of the optic axis and base-plane) as centre, 

 describe a hemisphere with its convex side towards the 

 observer, and with radii of any assumed length, R. This we 

 may call the reference-hemisphere. 



8. In doubly-refracting media we have to use half the 

 waA^e-surface of the medium instead of the simple hemisphere 

 which suffices for isotropic media. But for the present we 

 intend to confine our attention to the latter. 



Now (see Theorem 1. on p. 573 of the B. A. Report t'ov 

 1901, or in § 5 above) the light with which we are dealing- 

 whatever it is, might be withdrawn, and undulations of flat 



