﻿276 Lord Rayleigh on tlie 



to the other by a linear retardation X *. Then if X denote the 

 wave-length, the aggregate may be represented 

 cos nt + cos (nt — 2ttX/X) = 2 cos (irXjX). cos (nt— ttX/X). (1) 

 The intensity is given by 



I = 4cos 2 (7rX/\) = 2{l+cos(27rX/\)}. . . (2) 



I£ we regard X as gradually increasing from zero, I is 

 periodic, the maxima (4) occurring when X is a multiple of 

 X and the minima (0) when X is an odd multiple of -JX. If 

 bands are visible corresponding to various values of X, the- 

 darkest places are absolutely devoid of light, and this remains 

 true however great X may be, that is however high the 

 order of interference. 



The above conclusion requires that the light (duplicated by- 

 reflexion or otherwise) should have an absolutely definite 

 frequency, i. e., should be absolutely homogeneous. $uch light 

 is not at our disposal; and a defect of homogeneity will 

 usually entail a limit to interference, as X increases. We 

 are now to consider the particular defect arising in accord- 

 ance with Doppler's principle from the motion of the radiating 

 particles in the line of sight. Maxwell showed that for 

 gases in temperature equilibrium the number of molecules 

 whose velocities resolved in three rectangular directions lie 

 within the range d%dr}d% must be proportional to 



If f be the direction of the line of sight, the component 

 velocities 77, £are without influence in the present problem. 

 All that we require to know is that the number of molecules 

 for which the component f lies between f and % + dg is 

 proportional to 



e'Wdg (3) 



The relation of /3 to the mean (resultant) velocity v is 



* = 7(^) (4> 



It was in terms of v that my (1889) results were expressed, 

 but it was pointed out that v needs to be distinguished from 

 the velocity of mean square with which the pressure is more 

 directly connected. If this be called v f , 



'V&)' < 5) 



sothat ^=y/(&) < 6 > 



* Jn the paper of 1889 the retardation was denoted by 2a. 



