[ M ] 



VII. Molecular Refractivity and Atomic Interaction. By 

 L. Silberstein, Ph.D., Lecturer at the University of 

 Rome, Scientific Adviser to Adam Hilger, Ltd.* 



1. The Additive Law and its Limitations. 



nHHE modern chemist makes an extensive use of Lorentz's 

 JL additive law of optical refractivities, especially in the 

 vast domain o£ organic compounds. 



Let fi be the refractive index, M the molecular weight, 

 and d the density of a chemical compound, whose molecule 

 consists of c\ atoms A ly c 2 atoms A 2 , and so on. Let us 

 write 



I& + 2' d W 



for what will be called the molecular refractivity t of the 

 compound in question. Then the additive law states that it 

 is possible to ascribe to each of the constituent atoms Ai a 

 certain number JV» (a function of frequency only) called its 

 -atomic refractivity, such that 



N=c 1 N 1 + c 2 N 2 + c i Nz+ ..., . ... (2) 



no matter what the state of aggregation or the remaining 

 physical conditions of the compound. And it is certainly a 

 very remarkable fact that this additive formula holds, at 

 least within a few units of the second decimal place, in 

 many cases. 



If all the ingredients A; were available as monoatomic sub- 

 stances, accessible to the refractometer, then each Ni could 

 be measured directly. Mi and di being the corresponding- 

 values of atomic weight and of density, we should have 



l*>i— 1 Mj 

 !H 2 + 2 ' di' 



AV- 



But such is by no means the case. On the contrary, none 

 of the atomic refractivities A 7 ;, contained in the chemist's 

 table, has been obtained directly. The chemist's actual 

 method of procuring atomic refractivities amounts to the 

 following mathematical procedure : — If fc molecular refrac- 

 tivities J of /c different compounds of k elements are 



* Communicated by the Author. 



t Some authors call it "the molecular refraction," others "the 

 refraction equivalent " and " molecular refractive power." The above 

 name has seemed more convenient. 



