572 REPORT— 1901. 



repetition of what the corresponding actual wave emitted by P in the first 

 minut« was, and what it would have continued to be if neither reversal had taken 

 place. 



Hitherto we have only dealt with the undulation as an undulation of spherical 

 waves. Let us now go again over the same ground, and avail ourselves of its 

 being legitimate to resolve the light into wavelets by Huygens's theorem. 



In addition to little sphere p, let us draw round / two other spheres with 

 radii r and R, r being some moderate length such as a metre, and R a much 

 greater length, such as two or three metro-tens.' We shall find it convenient to 

 imagine other spheres to be also described round /, viz., the series with radii 

 M, 2M, 3M, &c., where M is the length of the journey which light describes 

 each minute, which in the open sether is a distance of 1'8 metro-tens. Let us 

 now make it our special aim to consider in what way the process we are going to 

 apply will resolne the 2)art of the ioidulation of spherical waves %vhich lies within 

 sphere r. 



As before, let P for the first minute emit light of wave length A. This light 

 consists of the spherical waves which travel outwards through the space beyond 

 sphere p. At the close of the first minute the foremost wave has reached 

 sphere M. Throughout almost the whole of this minute a portion of the 

 undulation has been within sphere r, which (if r is a metre) is large enough to 

 include from 13 to 25 hundred thousand (according to the colour) of the expanding 

 light waves. 



At the end of the minute P and the rest of the contents of sphere p are to 

 be annihilated, and quiescent jether is to be substituted for them within that 

 little sphere. 



Two minutes latter, i.e., when < = 3 minutes, the immense undulation of 

 spherical waves has got beyond the great sphere R, and has advanced into the 

 spherical shell between spheres 2M and 3M, leaving quiescent jether behind it. 



At this instant — i.e., when f = 3 minutes — the first reversal is to take place, 

 whereupon the waves that have been hitherto outward bound become inflowing. 



Let them pursue their new course after this first reversal until the time 

 t = S minutes. By that time the undulation has converged upon the focus, has 

 passed it, and has again become divergent light, each part of the undulation 

 having crossed to the opposite side of f. When the epoch ^ = 8 minutes 

 arrives the undulation of spherical waves is travelling outwards, and has reached 

 the space between spheres 2M and 3M, and sphere R lies in the quiescent space 

 within the undulation. 



At this instant — i.e., when t = 9, minutes — let the second reversal take place. 

 The undulation for the second time travels inwards, and on their inward journey 

 the spherical waves come successively to coincide with sphere R, Accordingly 

 if we divide the surface of sphere R into its elements rfo-j, da.-,, &c., then by 

 Huygens's theorem we may subt:titute undulations of hemispherical wavelets 

 radiating inwards from the innumerable centres dcr^, da-.^, &c., to take the place of 

 the further progress of the inward-bound undulation of spherical waves. As 

 these innumerable undulations of wavelets advance, they sweep over the space 

 occupied by sphere r, which is two metres across, and ivithin the limits of that 

 space the wavelets differ but very little from wavelets that are accurately flat and 

 accurately uniform. In this way the converging spherical waves within sphere r 

 succeeded by the same waves diverging after they pass the centre of the sphere, 

 produce identically the same motion within sphere r as would develop itself if 

 the innumerable undulations of nearly plane wavelets described above were 

 made to sweep across it simultaneously. It can further be proved that the 

 equation of energy is fulfilled in this resolution, and that in every respect the 

 resolution is a true physical resolution. 



The next step is an easy one. It is legitimate by an application of the method 

 of limits to make the wavelets where they cross sphere r accurately plane wavelets 



' A metro-ten is the tenth of the metros or decimal multiples of the raet^^, 

 In other words, it is 10'" metres, 



