Refractivity and Atomic Interaction. 1.11 



remarks concerning the chemist's table of atomic refrac- 

 tivities and dispersivities. If not otherwise stated, we 

 shall assume, throughout this Section, an optically isotropic 

 substance. 



Molec. Refractivity and Interatomic Distance. — Let us 

 consider two diatomic substances, S\ and # 2 , whose mole- 

 cules consist of the same atoms, but placed from one 

 another in different distances, R x for the first, and 

 R 2 = R^ + AR for the second substance, where AR may 

 have any finite value. Let AiV be the corresponding dif- 

 ference of the molecular refractivities, JV' and N'\ of these 

 substances. We shall consider here the simplest case of 

 two equal atoms, each having the atomic refractivity iT , a 

 known function of 7 : 



To — 7 

 Thus, by (24 b) } using the singular distance R' given 

 by (26 a), 



N 



'- V[ 2+ r=TR7R0 3 J ; N "--3-°L 2 + 



(R'/Rj) 8 .]' 3 L 1-(R'/R 2 ) 3 J' 



. . . (28) 



Let us remember that N Q would be the refractivity of a 

 strictly monoatomic substance, S , of the element in ques- 

 tion. If such a substance, as well as the two different kinds 

 of diatomic substances, S l9 # 2 , of the same element, were 

 available for refractometric examination, then it would be 

 possible to derive from the observed iV , iV', N", by means 

 of the above formulae, some information about the inter- 

 atomic distances B^ and R 2 i n the molecules of the substances 

 Si and S 2 . But no such actual data being available at 

 present, we must content ourselves with a provisional, and 

 to a certain extent ideal, and arbitrarily constructed, 

 numerical example which may, none the less, afford an 

 instructive illustration of the general formulas. 



Let our atoms be the carbon atoms and let us suppose, 

 for the sake of argument, that there is a substance in whose 

 molecules the group C — C (with "single bond") occurs, 

 possibly among other atoms of any kind, such, however, 

 that their total influence on that group is negligible *. For 



* This clause is indispensable, for there is, of course, no such substance 

 as C 2 . We could take hydrogen which does exist as H 2 , i. e. as 

 H— H, in ordinary hydrogen gas, but this would give us no opportunity 

 of considering the huge extra-term |= of Land.-Born.'s table. And then 

 we know nothing about the optical properties of monoatomic hydrogen. 



