318 Mr. J. Frenkel o?i the Surface Electric 



by the fact that the radius of an A atom is about ^/100 = 46 

 times smaller than that of Fe or Pt, i. e. is equal to the radius 

 of the first stationary orbit *. This circumstance also 

 accounts for its chemical inactivity. 



To show how far our theory is applicable to compound 

 substances, we shall take the simplest one, liquefied hydrogen, 

 and calculate its surface-tension, assuming for the molecule 

 H 2 the model so successfully applied by Debye f to the 

 calculation of the dispersion of light in hydrogen gas. 



Debye's model consists, as well known, of two hydrogen 

 nuclei at a fixed distance b from each other, and two electrons, 

 situated in two opposite points of a circle whose centre lies 

 at the middle of the line joining the nuclei and whose plane 

 is perpendicular to the said line, the radius of the circle 

 being a, and the angular velocity of the electrons &>. 



The condition of equilibrium for the nuclei is 



(£? = (a4Sp' or ( 1 + 92 ) i=8 ' whence 9=|=V3, (A) 



and for the electrons 



2e 2 .ae 2 



= mo) 2 a, whence by means of (A), 



(ar + b 2 ^ (2a) 



3 9 O /»> 



ma-'co' ov o 



(B) 



To this Debye adds the " quantum condition " that the 

 angular momentum of each electron should be equal to 1 . ~ 



o 1* 



mcocr= ~— 

 2tt 



(C) 



The solution of (B) and (C) gives a = 0'67xl0- 8 and 

 ^ = 0*46 xlO" 8 . 



According to the general principle outlined in the end of 

 § 3, we shall obtain the whole electric field in the quadruple 

 layer on the surface of hydrogen (liquid) by a simple 

 addition of the fields due to the separate constituents of the 

 H 2 molecule, considering it as a superposition of two pairs 

 of doublets the free ends of which are formed by the nuclei 

 and the electrons, the opposite ends being fixed at the centre. 



* The exact calculation gives for argon (A = 40, 8=1'42, k=8), 

 r=0-22xl0-*cm. 



t Ber. Bayer. Akad. p. 1 (1915). 



