KEFRACTOMETRIC APPLICATIONS 



bles). More recently Kurtz and Ward (120) 

 modified the formula, replacing the figure 1 

 by an empirical constant h of such value 

 that: (?i — b)/d = 0.5. The -slope-intercept 

 form is more convenient: n = 6 + (d/2). 

 It is found that b is often constant in homol- 

 ogous series, thus having a practical useful- 

 ness for the qualitative identification of or- 

 ganic chemicals and of their mixtures. Care 

 must be taken inasmuch as molar refractiv- 

 ities are only partly additive, under re- 

 stricted conditions. 



A comparison of data for a large number 

 of compounds of known chemical composi- 

 tion has led to the step of attributing addi- 

 tive values of a so-called atomic specific re- 

 fraction, Avg , to the atoms. Such values are 

 affected by the nature of the specific groups 

 in which the atoms are involved. This work, 

 initiated by Bruhl (1880), was further de- 

 veloped by Eisenlohr (1913) and by Swietos- 

 lawski (1920) (121). The sum of the Ar.'s 

 plus that of the particular linkages should 

 aggregate the Mvg* value of the molecule, 

 but there is often complete disagreement in 

 the case of electrolytes, with strongly polar 

 molecules, and with most moderately con- 

 centrated solutions. The confusion is greatly 

 increased by the diversity of values at- 

 tributed to some of the elements, e.g., about 

 30 different values are known for nitrogen. 



Another practical formula is Lagemann's 

 relation (122) between Mvg* and Sounders 

 viscosity constant Irj in homologous series: 



Irj = a-Mr,* + 6 = M(lgio n + 2.9)/d {58) 



(where rj is the viscosity in millipoises). Ta- 

 bles of the constant a are available. As a first 

 approximation, a is usually very close to 12. 

 The Lorentz-Lorenz formula is strikingly 

 similar to the relation giving the molar 

 polarization derived from Clausius-Mosotti 

 equation, as a function of the dielectric con- 

 stant e: 



equal the scjuare of the specific refraction at 

 infinite wavelength (zero-frequency), assum- 

 ing that then the molar polarizability factor, 

 which enters into the calculations, is con- 

 stant. Despite this limiting assumption, the 

 relation offers a convenient means of quali- 

 tatively distinguishing between polar and 

 nonpolar molecules. The practical interest 

 of such measurements is found in the obser- 

 vations and the theories relating the refrac- 

 tive index to the dielectric constant in the 

 radiofrequency domain, to the London vibra- 

 tional energy of dipoles at the zero-energy 

 point, and to a number of other phenomena 

 related to the polarization and/or polariza- 

 bility of molecules under the influence of 

 electromagnetic fields. A more complete dis- 

 cussion was given by Debye (123). 



It is clear from the foregoing that refrac- 

 tion measurements cannot be divorced from 

 a consideration of the wavelengths used. Yet, 

 the relationships between refraction and 

 wavelength are often confusing. When meas- 

 urements are made in a region where ab- 

 sorption is low, the Cauchy formula may be 

 used : 



n = A + B/\'' + C/X" • • • {60) 



(where A and B are constants). A plot of n 

 vs l/X^ is then very close to a straight line. 

 The Nutting relation (124) is often more con- 

 venient : 



l/(n - 1) = C + (D/X^) 



{61) 



Both formulas are valid only within rela- 

 tively narrow spectral limits, but the values 

 of the constants are often characteristic of 

 the substances under investigation. Other 

 empirical formulas, such as that of Wright 

 (125): 



n — no = a{nF — nc) — b 

 the Hartman equation: 



n = no + C/C/io)" 



P = M(6 - l)/(e -H 2) {59) or that of Waldmann: 



One demonstrates that, theoretically e should {no - nc) = k{nF - nc) 



{62) 



(63) 



(64) 



517 



