Constitution of Natural Radiation. 581 



appears to impose a limit to the types of disturbances that 

 are subject to regular dispersion. 



Even in the case of wave-trains excited on the surface of 

 water by a travelling source, where, as Lord Ray lei gh 

 remarks, there is no structural periodicity *, the presence of 

 the wave-trains travelling in any direction does, at any rate, 

 depend on the persistence of free periodic trains of waves. 

 If we imagined the water replaced by a medium in whicli no 

 free wave-trains could travel with velocities within certain 

 limits, then we would expect a gap in the wave pattern formed 

 by the travelling source, corresponding to those limits. The 

 passing remark of Sir George Stokes, which likens the syn- 

 chronous optical vibration of a transparent solid body to the 

 sonorous vibration of the sounding-board of' a pianoforte, 

 thus assigning it to regions of the material medium in bulk 

 rather than to its individual molecules f ? would bring the 

 optical effect somewhat nearer to the water-wave phenomenon. 



But the feature in the case or! the water-waves to which 

 Lord Rayleigh doubtless intends to draw special attention, is 

 the absence of gradual initiation and delay of effects ; as soon 

 as the source begins to move with uniform velocity, the wave- 

 pattern begins to travel out from it, and as soon as motion of 

 the source stops, so does the formation of the wave-pattern. 

 By a legitimate application of the principle of group-velocity, 

 the number of undulations formed is shown to be connected 

 with the distance over which the source has moved ; just as 

 the number of waves formed from a single freely travelling- 

 pulse by a grating is determined by the number of its lines 

 over which the pulse has travelled. 



At first sight, as above stated, it is difficult to detect 

 sufficient similarity to the optical case. But if we consider 

 (with Lord Rayleigh, p. 404) a thin plane pulse incident 

 from free aether obliquely on an infinitely extended plane face 

 of a refracting medium, the intersection of the pulse with the 

 face will be just such a maintained disturbance, travelling 



* Prof. Schuster (Phil. Mag. Jan. 1904) puts the point as follows : — 

 " As we may imagine continuous media of such elastic properties as to 

 give dispersion, the true explanation must be independent of the 

 sympathetic vibrations," on which I had relied in ' iEther and Matter,' 

 p. 248. The force of this is obvious: yet, when friction is ruled out, 

 what can there be, as a matter of fact, except conspiring periodicities 

 in time (free periods) or space, to modify simple elastic waves, which 

 travel without change, into the dispersive type ? 



t In the case of a vapour, the molecules, being isolated, must however 

 operate independently. 



