﻿282 Lord Rayleigh on the 



Calculations of this kind serve as illustrations ; but it is 

 not to be supposed that they can represent the facts at all 

 completely. There must surely be encounters of a milder 

 kind where the free vibrations are influenced but yet not in 

 such a degree that the vibrations after the encounter have 

 no relation to the previous ones. And in the case of flames 

 there is another question to be faced : Is there no distinction 

 in kind between encounters first of two sodium atoms and 

 secondly of one sodium atom and an atom say of nitrogen ? 

 The behaviour of soda flames shows that there is. Otherwise 

 it seems impossible to explain the great effect of relatively 

 very small additions of soda in presence of large quantities of 

 other gases. The phenomena suggest that the failure of the 

 least coloured flames to give so high an interference as is 

 calculated from Dopplers principle may be due to encounters 

 with other gases, but that the rapid falling off when the 

 supply of soda is increased is due to something special. This 

 might be of a quasi-chemical character, e. g. temporary asso- 

 ciations of atoms ; or again to vibrators in close proximity 

 putting one another out of tune. Jn illustration of such 

 effects a calculation has been given in the previous paper *. 

 It is in accordance with this view that, as Gouy found, the 

 emission of light tends to increase as the square root of 

 the amount of soda present. 



We come now to cause (iv.). Although it is certain that 

 this cause must operate, we are not able at the present time 

 to point to any experimental verification of its influence. 

 As a theoretical illustration "we may -consider the analysis 

 by Fourier's theorem of a vibration in which the amplitude 

 follows an exponential law, rising from zero to a maximum 

 and afterwards falling again to zero. It is easily proved 

 that 



i r°° 



e~ a -*- cos rx — - — — 1 du cos u.vS e- (u - r) - :ia '- + e-( u + r y-<* a -i 



. . . (20) 



in which the second member expresses an aggregate of 

 trains of waves, each individual train being absolutely 

 homogeneous. If a be small in comparison with r, as will 

 happen when the amplitude on the left varies but slowly, 

 g -(u+r)2/4o2 ma y k e neglected, and r^"^ 482 is sensible only 

 when u is very nearly equal to r " t- 



An analogous problem, in which the vibration is repre- 



* Phil. Mag. supra, p. 209. 



t Phil. Mag-, vol. xxxiv. p. 407 (1892) ; Scientific Papers, vol. iv. 

 p. 10. 



