Criticism of Theories of Microscopic Vision. 157 



may perhaps find an alternative proof of my fundamental 

 theorem, which (\vc< not employ replicas, more intelligible. 

 This proof is given in the Phil. Mag. for April 1897, at p. 273. 

 It is a proof *by the Principle of Reversal, and lias the advan- 

 tage of furnishing some additional information. 



It is by no means an easy task to give a description which 

 will he quite intelligible to the non-mathematical reader, of 

 an analysis of light which involves the conception of trains of 

 wavelets infinite in number, each of infinitesimal intensity, 

 and each occupying the whole of space*. But I will endeavour 

 to do so. And as a first step I shall use throughout this letter 

 the term wavelet wherever what is meant is a wave of infini- 

 tesimal intensity. By thus employing a distinctive name for 

 this special kind of wave I hope to guard my non-mathematical 

 readers from some of the misapprehensions into which I regret 

 to see that Mr. Wright has fallen. 



When an undulation, however complex, is propagated 

 through a uniform isotropic medium (meaning by undulation, 

 ivave-motion which is propapated through the medium by the 

 exclusive agency of the forces inherent in the medium) it is 

 an established theorem well known to physicists that this 

 undulation can be resolved into — in other words, may be re- 

 placed by; or, in other words, is the same physical event as — 

 the simultaneous propagation of systems of concentric spherical 

 waves from the several points of the medium, each spherical 

 ivave decreasing in its intensity as it advances by the law 

 of inverse square, and the systems of concentric waves round 

 the several puncta of the medium being of such a kind that 

 the medium, if of unlimited extent, would be competent 

 to propagate any one of them separately to any distance. 

 What the proofs of mv first theorem (see Phil. Mag. for 

 October 1896, p. 335, and April 1897, p. 273) have added to 

 this is that, if the medium be regarded as extended indefinitely, 

 any one of these systems of concentric spherical waves can in 

 its turn be further resolved into, and legitimately replaced by, 

 the propagation forwards of innumerable trains of uniform plane 

 ivavelets, each wavelet being of unlimited extent sideways, and 

 the trains of plane wavelets being all of such a kind that the 

 medium is competent to propagate forward any one of them 



* The reader, if not a mathematician, may need to be warned that in 

 a uniform medium a wave to be plane must be of unlimited extent. It 

 can be proved that it is physically impossible for it to exist of limited 

 extent. Nevertheless the mathematical physicist can of course picture 

 to himself a limited portion of this unlimited plane wave ; and he rinds it 

 possible to ascertain by the laws of interference, where and when it is 

 legitimate in his physical inquiries to use this limited portion, disregarding 

 the rest. 



