of CH, has been found to be 22; and similar differences will be found in other cases. The correspondence between the calculated and the observed values is, however, only approximate; thus, e.g., for the first five members of the series of alcohols CnH2n+2O the following values have been obtained :— The deviations from this fundamental rule may in many cases be attributed to differences in the mode of linkage of the atoms. Thus, for instance, two polyvalent atoms occupy less space when united to each other by single affinities than when two or more combining units are used for their mutual combination. Thus the following relations are found to hold : V(—0—C=) < V(0=C=) V(—S—C=) < V(S=C=) V(=N—C=) < V(N=C—) V(=C—C=) < V(=C=C=) &c. This and similar relationships have been frequently used in the investigation of atomic linkage; still, it must be remembered that conclusions drawn from such observations are always more or less uncertain, as there are many deviations from this rule which cannot be explained as due to variations in the mode of union of the atoms. In the meantime investigations of this kind are being steadily carried on. It has, for instance, been shown that when an atom of chlorine or of bromine replaces an atom of hydrogen in organic compounds, the space occupied by the atom of the halogen element is dependent upon the position it occupies, being greater when attached to one atom than when combined with another. In the case of benzene substitution products, the radicals replacing hydrogen in this hydrocarbon have a greater volume when they occupy the para- position than in the meta-, and in the meta- position a greater volume than in the ortho- position. All such results are of great importance as contributing to our knowledge of the properties of matter. + REFRACTION OF LIGHT 123 § 71. Expansion by Heat.-The volume of a liquid varies with the temperature, and as a rule the alterations produced by given changes of temperature are greater in the case of liquids than for solids. Usually the volume increases with rise in temperature, and this expansion becomes greater and greater as the temperature rises. It is only in the neighbourhood of the solidifying point that some liquids, notably water (§ 65), are found to contract in volume as their temperature is raised. Van der Waals has theoretically deduced the law which controls the expansion of liquids by heat, and has demonstrated the truth of the law by a comparison of the deductions made from it with the results of observation. For such comparisons a knowledge of the critical temperature of a liquid is required, which still remains unknown for the majority of those liquids the coefficients of expansion of which have already been determined. The expansion of a liquid is attended by a considerable absorption of heat, which with one and the same substance is, for an equal interval of temperature, greater when in the liquid state than when in the solid condition. The heat capacity or the specific heat of a given substance is greater in the liquid state than in the solid, often twice as great, and is even greater in the liquid than in the gaseous state. By multiplying the specific heat into the molecular weight the so-called molecular heat is obtained, which in the case of homologous organic compounds changes with tolerable regularity. § 72. Refraction of Light by Liquids. The refraction of light by liquids has been very completely investigated. It has been found to be dependent upon the nature and the amount of the elements contained in the liquids, as also upon the manner of their union with one another. This interdependence has been specially studied and demonstrated for the compounds of carbon, the organic compounds, and for many others also. n If ʼn be taken to represent the refractive index of a liquid, and d its density, then it can be shown theoretically that the quotient' 1 Until recently the simpler expression n- -1 was employed to represent the specific refractive index, instead of the expression deduced by H. A. Lorentz and L. Lorenz. The simpler expression, which was arrived at empirically, explains satisfactorily the majority of observed facts, but is not, according to Brühl, so satisfactory in some cases. n2-1 (n2 + 2)d' which is known as the specific refractive power, is practically unaffected by temperature; a conclusion which has been substantiated by actual observation. With the aid of this expression one may, as has been shown by Gladstone and Dale, by Landolt and his pupils, represent the specific refractive power of a liquid as made up of the sum of the refractive powers of its constituents. If the weight P of the liquid contains P1, P2, P31 &c. weights of the constituents, then the following relation will obtain, in which N and D represent the refractive index and density of the liquid, and n1, n2, ng, d1, d2, and d, are the refractive indices and densities respectively of the constituents:— Landolt's investigations have shown that this expression applies equally to mechanical mixtures as well as to chemical compounds. If, therefore, P be the molecular weight, M, made up of a atoms of A1, of y atoms of A,, &c. then, since Or that the molecular refractive power or the molecular refraction of a compound is the sum of the refraction equivalents of its constituents. The refraction equivalent of the elements, which is here represented by the expression MOLECULAR REFRACTION 125 may, in the cases in which these values are known, be calculated from the refractive index n, the density d, and the atomic weight A. It is, however, more convenient to deduce these values from the observed molecular refraction of compounds, which differ in composition by a definite number of atoms of one or other of the elements. Calculations of this kind have been carried out in numerous instances, and are based upon data supplied by a very extensive series of observations. Since light of different colours is refracted differently, the index of refraction, n, must vary with the colour; consequently observations made with light of different colours yield different refraction equivalents for one and the same substance. Inasmuch as up to the present no formula has been discovered which enables one to eliminate satisfactorily this influence of colour, the index of refraction is determined for light of a fixed colour. For instance, that corresponding to Fraunhofer's line C in the sun's spectrum is frequently used for this purpose, and this is identical with the red line in the hydrogen spark spectrum. For this coloured light Landolt found the following to represent the molecular refractions (Mrf) of the compounds in the two following tables, each of which consists of a series of compounds differing from one another by constant difference (CH2) :— A difference in composition of one atom of carbon and two atoms of hydrogen is seen from the above to produce a difference of 4.56 in the molecular refraction. Similarly, the effect on the molecular refraction may be determined for other differences in composition, and from such results the refraction equivalents of individual elements may be calculated. The following represent the refraction equivalents of some of the commoner elements, for the Fraunhofer line C, or the line a in the hydrogen spectrum. Refraction Equivalent By the aid of such numbers the molecular refraction of a compound like ethyl alcohol, for instance, may be calculated, thus: C2H,O= 2 × 2·48 +6 × 1·04+1 x 1.58 = 12.78. 6 x The observed refraction for ethyl alcohol is 12.71. Similarly, the molecular refractions of other compounds may be calculated. § 73. Influence of Atom-linkage on Refraction.-Such agreement between the observed and calculated results does not obtain in all cases; as, for instance, in the following we have Aldehyde, C2HO, Mrf = 2 × 2·48 +4 × 1·04+1 x 1.58 (observed 11.50). = 10.70 Acetic acid, C,H,O2, Mrf 4 = 2 × 2·48 +4 × 1·04+2 × 1.58 = 12.28 (observed 12.93). 10 Valerianic acid, C,H1O2, Mrf = 5 x 2.48 +10 × 1·04+2 × 1·58 = 25.96 (observed 26.72). In each of these three instances the experimental values are greater than the calculated, and the difference is very nearly the same in each case, thus :— 11.50-10708; 12.93-12.28 0.65; 26.72-25.96 0.76. = The molecular refractions of acids, aldehydes, ketones, |