Temperature Radiation of Gases. 213 



Thus far we have dealt with the electrodynamics of the 

 atomic system, i. e. the possible stable -orbits of the vibrating 

 electron calculated according to quantum-mechanics. We 

 have now to deal with the statistics of the case, for the 

 higher stable orbits are produced in sufficient proportion 

 only with increasing stimulus, which we obtain only at 

 higher temperatures. The intensity of a line will depend 

 upon the product of the numbers which show the relative 

 proportions of orbits in the initial and final stages at any 

 instant, and also upon the chance of changing from one 

 orbit to another. Thus the intensity of (1, s) — (2, p) will 

 be proportional to U'e, where \ is the number of orbits 

 in state (1, s), V is the number in state (2,p), and € is the 

 chance that the orbit will change from the state (2, p) 

 to (M). 



When the stimulus is sufficiently great, some of the 

 electrons will pass off to infinity, and we shall have partial 

 ionization. This problem can be treated thermodynamically, 

 for here we have to consider a sort of chemical equilibrium 

 between three distinct phases — the neutral atom, the ionized 

 atom, and the electron. But radiation cannot be so treated, 

 for this is a case of internal change of orbits only, not 

 involving any phase-changes. 



The problem before us can therefore be thus stated : — 

 " How to find out the statistical distribution of atoms into 

 different possible stable orbits when the mass of the gas is 

 subjected to a given thermal stimulus? " According to the 

 theory of ionization sketched in paper A, if Ca- vapour is 

 enclosed in a vessel, such that the pressure is always main- 

 tained at 10 ~ 3 atm., we have seen that with increasing 

 temperature the proportion ionized varies as follows : — 



Temperature... 2000° 3000° 4000° 5000° 6000° 7000°") 



Percentage of I 



Ionization ... oXlO~ 4 2X10" 1 6 47 91 100 J 



The non-ionized atoms cannot all be with the primitive 

 orbit (1, s), but a good proportion will be found with the 

 other possible stable orbits, for the electron, while detaching 

 itself from the neutral atom, has a chance of taking its 

 habitat in some of these stable orbits , and hence some 

 must be found in these states. The phenomena of line- 

 radiation therefore comes before the ionization becomes 

 complete. 



Phil. Mag. S. 6. Vol. 41. No. 242. Feb. 1921. T 



