luhen Light is radiated from Moving Molecules. 303 



If 0j V^ ? be the rectangular components of v, the number of 

 molecules whose component velocities lie at any time between 

 f and ^ + d^, rj and r] + drj, ^ and ^ + d^, will be proportional 

 to 



e-P(^'+^'+i'M^ dv di;. 



If ^ be the direction of the line of sight, the component velo- 

 cities 7], ^ are without influence in the present problem. All 

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

 which the component ^ lies between^ and ^ + d^is propor- 

 tional to 



e-P^'d^. (18) 



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



^=vk) <'''> 



If the natural frequency of the waves emitted by the mole- 

 cules be N, the actual frequency of the waves from a molecule 

 travelling with component velocity f is by Doppler's principle 



.^ = N(l+|) (20) 



Hence by (8) the expression to be investigated, and corre- 

 sponding to (9), is 



4j''%in^^(l+|)6-P^\e . . . (21) 



In (21) we have 



(lH-|)=l-003i^(l4) 





A 



47rA 47rA^ . 47rA 

 = 1 — cos — 7 — cos ' ■^"^ 



A AV ' A 



The last of the three terms, being of uneven order in ^, 



dependent upon other causes than the width of the line and the distribu- 

 tion of brightness over it. In this view I cannot agree. " The narrow- 

 ness of the bright line of light seen in the spectroscope, and the possibility 

 of a large number of (interference) bands, depend upon precisely the same 

 conditions ; the one is in truth as much an interference phenomenon as 

 the other " (Enc. Brit., Wave Theory, vol. xxiv. p. 425). It is obvious that 

 nothing could give rise in the spectroscope to a mathematical line of 

 light, but an intinite train of waves of harmonic type and of absolute 

 regularity. 



* This must be distinguished from the velocity of mean square, with 

 which the pressure is most directly connected. 



