On Molecular' Refr 'activity and Atomic Interaction. 93 



experimentally known, as well as the numbers c u c 2 , etc. 

 for each of them, then we have k linear equations of the 

 form (2) and, these being mutually independent, the required 

 k atomic refractivities are found by solving the system of 

 equations. There is, of course, not the least objection to 

 such a procedure. The question then is whether the values 

 of iVi, ]$%, . . . A 7 ^, thus obtained, are consistent with the 

 observed refractivities of other compounds of the same 

 elements. And, as has already been mentioned, the additive 

 law stands this test in a remarkably large number of cases. 

 The chemists, it is true, complain but too often of " excep- 

 tions to the rule/'' and these, especially since J. W. Briihl's 

 time, make up a rather formidable list. To the physicist's 

 mind, however, the surprising fact is that the additive law 

 does hold at all in certain cases. For to him it means 

 absence of atomic interaction *, a state of things which one 

 would hardly expect. 



At any rate, the chief object of the present paper is to lay 

 stress precisely on what are usually called the " exceptions" 

 and to attempt to derive from these some knowledge about 

 the electrical interaction of the atoms of a molecule. 



Before entering upon our subject, it will be well to quote 

 a few numbers exhibiting the degree of approximation with 

 which the additive law holds, and the values of certain extra- 

 terms to be added when the law does not hold. Since the 

 atomic refractivities, as sanctioned by the chemical authori- 

 ties, do not seem to be easily accessible, it may be advisable 

 to reproduce here, for the sake of reference, the numbers 

 given in Landolt-Bornstein's Tafeln (1^12), p. 103 l J, the 

 sources quoted by them in this connexion being : Eisenlohr, 

 Z. phys. Ch. (1910), 75, 585, and Roth and Eisenlohr, 

 Refraldometr. Hilfsbuch, Leipzig, 1911. The figures given 

 in this Table under the heads H a , H^, H y , D are the atomic 

 refractivities Ni for the hydrogen lines a, ft, y of the Balmer 

 series and for the "D-line" of sodium; the last two columns 

 contain the corresponding dispersions of Ni, shortly called 

 the atomic dispersions. The Table contains also the mole- 

 cular refractivity of the important group CH 2 , and some 

 extra-terms, such as due to a double bond in the case of 

 carbon. In using this Table, and comparing the calculated 



* The reader wDl remember that, in Lorentz's electromagnetic 

 theory of dispersion, the additive law is a consequence of the express 

 assumption that the (dispersive) electric particle contained in one atom 

 is not disturbed by what is going on in the remaining atoms of the same 

 or of other molecules. H. A.- Lorentz, Arch, neerl. xxy. (1892), p. 363; 

 more recently treated in Lorentz's ' Theory of Electrons,' Leipzig (1909), 

 Chap. IV. 



