Flat- Wavelet Resolution. 597 



diagram, with a radius p of one or two wave-lengths, the 

 turmoil will not extend beyond it : all beyond will be a regular 

 undulation of luminous waves. The tiny sphere we may call 

 sphere p. 



51. We must contrive means of securing one more condi- 

 tion, namely, that the medium shall be freed from outside 

 interference. To effect this, we shall employ the Principle of 

 Reversal, ami imagine the following series of events. Let 

 P, beoin to emit its light at the instant t = 0. Of that light 

 we need only attend to that which enters the lens. This is an 

 undulation of hemispherical waves advancing towards the 

 east, that is towards the right-hand side of our diagram. 

 Let this emission of light continue from the epoch £ = until 

 the instant t = r. and let the right-hand half of sphere M l 

 represent the front of the undulation at that instant. At that 

 instant the luminous undulation extends from sphere p (which 

 is too minute to be represented in the diagram) on to sphere 

 Mj : and during the whole of the period from t = to t = r 

 there have been within the tiny sphere p both Pj, the source 

 of the energy thrown into the medium, and turmoil surround- 

 ing Pj. These we get rid of by supposing the whole of the 

 contents of sphere p to he annihilated at the instant t — r, and 

 quiescent medium substituted for them. This in no way in- 

 terferes with the further progress of the luminous undulation, 

 which when the instant t — or arrives will find itself within 

 the eastern half of the spherical shell between spheres M 2 

 and M 3 . At the instant t = or let Reversal take place. All 

 the motions in the medium are reversed; and the outflowing 

 waves suddenly become inflowing waves. They will retrace 

 their steps, converge upon the central punctum* of the 

 diagram, as upon a focus, and after passing it will diverge 

 towards the west, that is towards the left-hand side of the 

 diagram. At the instant £ = 8t, the undulation finds itself 

 within the left-hand half of the spherical shell between M 2 

 and M 8 , At this instant let a Second Reversal take place. 

 The wave- which since the First Reversal have been moving 

 westward, resume an eastward course, converge upon the 

 focus at the centre and after passing it diverge towards the 

 east. In this way they reproduce between t = 10t and t = 11t 

 isely the same transmission of light to the east of sphere p, 

 as had prevailed before the reversals in the period from t = to 

 t = r; and with the advantage that tlii- transmission of light 



* The mathematical point has no place in physics. Its place is taken, 

 asitcan he taken, by the physical punctual, i <■. by the smallest speck 

 of which we have to take notice in the prohleni upon which we are 

 enga^.d. It- size depends 14)011 the conditions of the problem, and differs 

 from one problem to another. The luminous punctual may be taken to 

 be a sphere with a diameter of from one-half to one wave-length. 



