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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

The empirical formula (n2 – 1)/(n2 + 0.4)d apparently gives more constant values with change of temperature than the Lorenz-Lorentz form. The superiority of the Lorenz-Lorentz formula over the Gladstone and Dale formula for changes of state is shown by the following observations of Brühl (Zeit. f. phys. Chem., 1891, 71, p. 4). The values are for the D line:—

Substance. Temp. Gladstone and Dale. Lorenz and Lorentz.
Vapour. Liquid. Vapour. Liquid.
 Water 10° 0.3101 0.3338 0.2068 0.2061
 Carbon disulphide  10° 0.4347 0.4977 0.2898 0.2805
 Chloroform 10° 0.2694 0.3000 0.1796 0.1790

Landolt and Gladstone, and at a later date J. W. Brühl, have investigated the relations existing between the refractive power and composition. To Landolt is due the proof that, in general, isomers, i.e. compounds having theAdditive relations. same composition, have equal molecular refractions, and that equal differences in composition are associated with equal differences in refractive power. This is shown in the following table (the values are for Hα):—

Substance. Mol.
Substance. Mol.
Diff. for
 Ethylene chloride C2H4Cl2 20.96  Acetic acid 12.93 } 4.49
 Ethylidene chloride 21.08  Propionic acid 17.42
 Fumaric acid C4H4O4 70.89  Butyric acid 22.01 } 4.59
 Maleic acid 70.29 . . . .. .
 o-Cresol C7H8 32.52  Acetaldehyde 11.50 } 4.43
 m-Cresol 32.56  Propionaldehyde  15.93
 p-Cresol 32.57  Butylaldehyde 20.52 } 4.59

Additive relations undoubtedly exist, but many discrepancies occur which may be assigned, as in the case of molecular volumes, to differences in constitution. Atomic refractions may be obtained either directly, by investigating the various elements, or indirectly, by considering differences in the molecular refractions of related compounds. The first method needs no explanation. The second method proceeds on the same lines as adopted for atomic volumes. By subtracting the value for CH2, which may be derived from two substances belonging to the same homologous series, from the molecular refraction of methane, CH4, the value of hydrogen is obtained; subtracting this from CH2, the value of carbon is determined. Hydroxylic oxygen is obtained by subtracting the molecular refractions of acetic acid and acetaldehyde. Similarly, by this method of differences, the atomic refraction of any element may be determined. It is found, however, that the same element has not always the same atomic refraction, the difference being due to the nature of the elements which saturate its valencies. Thus oxygen varies according as whether it is linked to hydrogen (hydroxylic oxygen), to two atoms of carbon (ether oxygen), or to one carbon atom (carbonyl oxygen); similarly, carbon varies according as whether it is singly, doubly, or trebly bound to carbon atoms.

A table of the atomic refractions and dispersions of the principal elements is here given:—


Element. Hα D. Hγ Dispersion
Hγ - Hα.
 Hydrogen 1.103 1.051 1.139 0.036
 Oxygen, hydroxyl 1.506 1.521 1.525 0.019
 Oxygen, ether 1.655 1.683 1.667 0.012
 Oxygen, carbonyl 2.328 2.287 2.414 0.086
 Chlorine 6.014 5.998 6.190 0.176
 Bromine 8.863 8.927 9.211 0.348
 Iodine 13.808 14.12 14.582 0.774
 Carbon (singly bound) 2.365 2.501 2.404 0.039
 Double linkage of carbon 1.836 1.707 1.859 0.23 
 Triple linkage of carbon 2.22   2.41 0.19 
 Nitrogen, singly bound and only to carbon  2.76   2.95 0.19 

Dispersion and Composition.—In the preceding section we have seen that substances possess a definite molecular (or atomic) refraction for light of particular wave-length; the difference between the refractions for any two rays is known as the molecular (or atomic) dispersion. Since molecular refractions are independent of temperature and of the state of aggregation, it follows that molecular dispersions must be also independent of these conditions; and hence quantitative measurements should give an indication as to the chemical composition of substances. This subject has been principally investigated by Brühl; he found that molecular dispersions of liquids and gases were independent of temperature, and fairly independent of the state of aggregation, but that no simple connexion exists between atomic refractions and dispersions (see preceding table). He also showed how changes in constitution effected dispersions to a far greater extent than they did refractions; thus, while the atomic dispersion of carbon is 0.039, the dispersions due to a double and treble linkage is 0.23 and 0.19 respectively.

Colour and Constitution.—In this article a summary of the theories which have been promoted in order to connect the colour of organic compounds with their constitution will be given, and the reader is referred to the article Colour for the physical explanation of this property, and to Vision for the physiological and psychological bearings. A clear distinction must be drawn between colour and the property of dyeing; all coloured substances are not dyes, and it is shown in the article Dyeing that the property of entering into chemical or physical combination with fibres involves properties other than those essential to colour. At the same time, however, all dyestuffs are coloured substances.

A survey of coloured substances led O. N. Witt in 1876 to formulate his “chromophore-auxochrome” theory. On this theory colour is regarded as due to the presence of a “chromophore,” and dyeing power to an “auxochrome”; the latter by itself cannot produce colour or dyeing power, but it is only active in the presence of a chromophore, when it intensifies the colour and confers the property of dyeing. The principal chromophores are the azo, –N=N–, azoxy, =N2O, nitro, –NO2, nitroso, –NO, and carbonyl, =CO, groups. The azo-group is particularly active, both the aliphatic and aromatic compounds being coloured. The simplest aliphatic compounds, such as diazo-methane, diazo-ethane, and azo-formic acid, are yellow; the diamide of the latter acid is orange-red. Of the aromatic compounds azo-benzene is bright orange-red, and α-azo-naphthalene forms red needles or small steel-blue prisms. The azo-group, however, has little or no colouring effect when present in a