118 Dr. L. Silberstein on Molecular 



If our dispersive particle is an electron in the proper 

 sense o£ the word, then a is about 1*8 . 10~ 13 cm., and 



i2 c =5-23.10- 5 .\ 2/3 . 



Thus, for instance, if \ = 1000 A.U., then 



R c = 2*43 A.U. 



Thus far the diatomic molecule composed of two equal 

 atoms. 



More generally we have, for two different atoms, by (18), 



and replacing again 7 by ( — — J , 



V 2 ~ 2 VV + X 2 V 2 V V V XsV *- 4 c 4 R 6 ' 



and a similar expression for \", with + before the radical ; 

 but this second " new " wave-length need not detain us 

 since it falls into the remote ultraviolet, if \ l5 X 2 do so. 

 Here again, the critical distance, marking the limit of 

 stability, is determined by equalling to zero the right 

 member. Thus, 



}? = 2(v + v)"2v(v"v) + x7x?vs) ? (34) 



and the critical distance is given by 



\rX 



R^j^VBA, (35) 



differing from (32) only inasmuch as \ and B are replaced 

 by the geometrical means of the free wave-lengths of the 

 atoms and of their coefficients B 2 and B 2 . The discussion 

 of (34), (35), and the illustration of these formulae by 

 numerical examples, may be left to the reader. No matter 

 how remotely ultraviolet the atomic free oscillations \ x , X 2 , 

 the new free oscillations (V) may well fall into the visible 

 or even the infra-red region, provided that R is but little 

 above the critical distance. Against the opinion, current in 

 more recent times, the infra-red free periods, such as are 

 observed in rock-salt, may well be ascribed to the dispersive 

 electrons under interatomic influence, instead of being at- 

 tributed to the molecule as a whole or to aggregates of 

 molecules. 



