Molecules of Hydrogen, Oxygen, and Nitrogen. 219 



k making <rb real will be the smallest integer k satisfying 

 the inequality 



k = K6>ik (13) 



This is the condition hinted at. It will be applied 

 numerically in each of the cases to be treated presently. 

 As to the sign of the square root it will be easily decided, 

 remembering that both a and b are essentially positive. 

 Thus, b, g, and therefore k, being known from observation, 

 the product o-b will be found. Inserting this in (8) we shall 

 find the atomic coefficients g , 6 , and therefore also a and 

 the interatomic distance. 



Finally, the condition of stability is (loc. cit., p. 115), 



B . Bo- 4tt 2 



7o> 9 — m ,i.e. — < 



2 » 



2ttW a. " X : 



that is, in terms of b , by formula (5), 



ab <l (14) 



This necessary and sufficient condition of optical stability 

 will be tested in each of the particular cases to which we 

 shall now pass. 



Hydrogen. 

 The observed values of refractivity of hydrogen gas at 

 0° C. and pressure 760 mm. are, for the lines H a , D, H^ 

 and H y respectively, 



^-1 = 1-387 1*392 l-40 6 1-412 . 10" 4 . 



The molecular weight of hydrogen gas (H 2 ) is M=2'Q16, 

 and its density, at the above temperature and pressure, 

 d = 8-9873 . 10" 5 . Whence the corresponding values of the 

 molecular refractivity, 



AT /r-lM .2, _, M 

 N= ^=^7^3 (/ " -1 ^' 

 JS T = 2-074 2-082 2-10 3 2-112. 

 These observed values can be represented with sufficient 

 accuracy by 



•01279 

 N = 2'044 5 H — g — , A, in microns. 



In fact, the latter formula gives, for H a , D, H^, H y , 

 respectively, 2'074, 2*081, 2'099, 2- J 12. Thus, in c.G.s. 

 units, 



6-2-044 5 ; ^ = 1-27 9 .10- 10 , . . . (H 2 ) 



in the visible region of the spectrum at least. Whence the 

 required ratio 



k = b 2 /g = 3-268. 10 lu , 

 i.e.\k = 1-634 . .10 10 . Now e=l'83 . 10 10 . Thus the smallest 



