104 Dr. L. Silberstein on Molecular 



therefore, by (10) and (13 s), writing e 1 2 /m l = B li e 2 2 lm 2 = B 2 , 



». = 35^=9«-^+&^=»i + « a , (14.) 

 &* + 2 Yi — 7 72 — 7 



that is to say, the transversal refractivity is purely additive. 

 This is simply the result o£ the axiality of interaction, based 

 on our assumption, made at the beginning, that the second 

 and the higher powers of {r^JR), OV-^j' are negligible. 

 Passing on to the axial direction we have in (13 a) two 

 linear equations for e x x x , e 2 x 2 . Let D be the determinant of 

 these equations, i. e. 



D=( 7 - 7l )( 7 - 72 )-iIA. . . . (15) 



Then, introducing e } x x , e 2 x 2 from (13 a) into 

 (K a -l)E a =9?(^ 1 + ^' 2 ), 

 the axial component of (10), we have 



*V= I [B I (7,-7) + B,(7i-7) + ^], 



or, in terms of the atomic attributes o> 1? co 2 , 



ft)! + C0 2 + ^COiWjSlW , ' 



»«= i-^ lW w • • • • (Wa) 



Thus, the axial refractivity , unlike the transversal one, 

 shows an essential departure from additivity, and this is 

 of such a nature that the difference co a —(coi + g> 2 ) cannot 

 obviously be thrown either upon the first or upon the 

 second, nor partly upon the first and partly upon the 

 second of the constituent atoms. Any such splitting of 

 terms containing the product w^ and the mutual distance 

 of the atoms would be entirely artificial. Thus far the 

 qualitative aspect of the matter. And as concerns its quanti- 

 tative side, notice that, in a true molecule, the departure 

 from the additive law cannot be negligible and will, in 

 most cases, be very considerable. In fact, 9? is the number 

 of (diatomic) molecules per unit volume, and therefore 

 9^R 3 the number of molecules per cube whose edge is the 

 mutual distance of the atomic centres. Now if the system 

 of each pair of atoms deserves at all the name of a molecule, 

 R is certainly not greater than, the average mutual distance 

 of molecules. Thus the (pure) number 31R 3 is certainly not 

 greater than unity, and in most cases even a fraction only. 



