526 Dr. L. Silberstein on Molecular 



Subcase : Equal Atoms. — If the molecule consists of two 

 equal atoms, that is if the gas is of the type of H 2 , we have 

 N 1 = N 2 — N Q , say, and y l =zj 2 = y^ B 1 = B 2 = B. The mole- 

 cular refractiviry of such a gas is, by (5), 



1 _ 1 oM 

 lN — iN o (1 _ 5NoX1+ ^ o/ • ■ • ; W 



where s = ul2irB*, as above. Applications of this formula * 

 to ordinary hydrogen, oxygen, and nitrogen gas will be 

 given presently. 



The free frequencies (6a), (6£) are given, in the present 

 case, by 



/ If -Do . ., — XjS //t\ 



Ja,Ja =70-H~; Vt,Vt = 7o + i^ ... (9) 



The absorption spectrum will thus consist of four lines or 

 bands, all different from the atomic one (70). Two of these 

 bands, 7/', y a ", will be ultra-y , and two, 7/, 7/, will he 

 infra-y . In ascending order of wave-lengths we shall have 



X a , \t , (X ), \ 1 X a , 



X being abolished by interaction. The greatest of these 

 wave-lengths being \J, corresponding to yj = z, yo~ Bs\a, the 

 critical distance M c , determining the limit of optical stability 

 (cf. I.) will be given by 



a ay () 



(10) 



and the condition of stability will be s<s c . 



Returning to (8), let us remember that J¥ = B/ot{y — y), 

 B = e 2 l»i. If A, is the wave-length and u=l/X 2 , then 

 y = 4t7r 2 c 2 u. Writing, therefore, 



4:TT 2 mu Uq ° u 7 g Q 

 as in Phil. Mag. Feb. 1917, we shall have 



No=-^~ = J +^«, (12) 



Uq — U ' 



since u falls into the extreme ultra-violet and since in the 

 concrete examples to be treated below u will be limited to 

 the visible region of the spectrum. By (11), and writing 



* Which replaces the erroneous formula (2) of the Note published in 

 Phil. Mag. for February, 1917, p. 215. The numerical results given in 

 that Note will be recalculated, a little further on, by means of the present 

 formula (8). 



