These involve pentavalent nitrogen. These formulae, however, only apply to aliphatic amines; the results obtained in the aromatic series are in accordance with the usual formulae.
Optical Relations.
Refraction and Composition.—Reference should be made to the article [Refraction] for the general discussion of the phenomenon known as the refraction of light. It is there shown that every substance, transparent to light, has a definite refractive index, which is the ratio of the velocity of light in vacuo to its velocity in the medium to which the refractive index refers. The refractive index of any substance varies with (1) the wave-length of the light; (2) with temperature; and (3) with the state of aggregation. The first cause of variation may be at present ignored; its significance will become apparent when we consider dispersion (vide infra).The second and third causes, however, are of greater importance, since they are associated with the molecular condition of the substance; hence, it is obvious that it is only from some function of the refractive index which is independent of temperature variations and changes of state (i.e. it must remain constant for the same substance at any temperature and in any form) that quantitative relations between refractivity and chemical composition can be derived.
The pioneer work in this field, now frequently denominated “spectro-chemistry,” was done by Sir Isaac Newton, who, from theoretical considerations based on his corpuscular theory of light, determined the function (n²-1), where n is the refractive index, to be the expression for the refractive power; dividing this expression by the density (d), he obtained (n²-1)/d, which he named the “absolute refractive power.” To P.S. Laplace is due the theoretical proof that this function is independent of temperature and pressure, and apparent experimental confirmation was provided by Biot and Arago’s, and by Dulong’s observations on gases and vapours. The theoretical basis upon which this formula was devised (the corpuscular theory) was shattered early in the 19th century, and in its place there arose the modern wave theory which theoretically invalidates Newton’s formula. The question of the dependence of refractive index on temperature was investigated in 1858 by J.H. Gladstone and the Rev. T.P. Dale; the more simple formula (n-1)/d, which remained constant for gases and vapours, but exhibited slight discrepancies when liquids were examined over a wide range of temperature, being adopted. The subject was next taken up by Hans Landolt, who, from an immense number of observations, supported in a general way the formula of Gladstone and Dale. He introduced the idea of comparing the refractivity of equimolecular quantities of different substances by multiplying the function (n-1)/d by the molecular weight (M) of the substance, and investigated the relations of chemical grouping to refractivity. Although establishing certain general relations between atomic and molecular refractions, the results were somewhat vitiated by the inadequacy of the empirical function which he employed, since it was by no means a constant which depended only on the actual composition of the substance and was independent of its physical condition. A more accurate expression (n²-1)/(n²+2)d was suggested in 1880 independently and almost simultaneously by L.V. Lorenz of Copenhagen and H.A. Lorentz of Leiden, from considerations based on the Clausius-Mossotti theory of dielectrics.
Assuming that the molecules are spherical, R.J.E. Clausius and O.F. Mossotti found a relation between the dielectric constant and the space actually occupied by the molecules, viz. K = (1 + 2a)/(1 - a), or a = (K - 1)/(K + 2), where K is the dielectric constant and a the fraction of the total volume actually occupied by matter. According to the electromagnetic theory of light K = N², where N is the refractive index for rays of infinite wave-length. Making this substitution, and dividing by d, the density of the substance, we obtain a/d = (N² - 1)/(N² + 2 )d. Since a/d is the real specific volume of the molecule, it is therefore a constant; hence (N² - 1)/(N² + 2)d is also a constant and is independent of all changes of temperature, pressure, and of the state of aggregation. To determine N recourse must be made to Cauchy’s formula of dispersion (q.v.), n = A + B/λ2 + C/λ4 + ... from which, by extrapolation, λ becoming infinite, we obtain N = A. In the case of substances possessing anomalous dispersion, the direct measurement of the refractive index for Hertzian waves of very long wave-length may be employed.
It is found experimentally that the Lorenz and Lorentz function holds fairly well, and better than the Gladstone and Dale formula. This is shown by the following observations of Rühlmann on water, the light used being the D line of the spectrum:—
| t. | (n - 1)/d. | (n² - 1)/(n² + 2)d. |
| 0 | 0.3338 | 0.2061 |
| 10 | 0.3338 | 0.2061 |
| 20 | 0.3336 | 0.2061 |
| 90 | 0.3321 | 0.2059 |
| 100 | 0.3323 | 0.2061 |
Eykmann’s observations also support the approximate constancy of the Lorenz-Lorentz formula over wide temperature differences, but in some cases the deviation exceeds the errors of observation. The values are for the Hα line:—
| Substance. | Temp. | (n² - 1)/(n² + 2)d. |
| Isosafrol, C10H10O2 | 17.6° | 0.2925 |
| 141.2° | 0.2962 | |
| Diphenyl ethylene, C14H12 | 22° | 0.3339 |
| 143.4° | 0.3382 | |
| Quinoline, C9H7N | 16.2° | 0.3187 |
| 141° | 0.3225 |