Now A. Lorenz and H. Lorenz', within the last few years, independently deduced the expression from the general principles of the undulatory theory of light (and more especially from Maxwell's electromagnetic theory), as giving a statement of the relation between the velocity of transmission of light, and the density of the liquid medium through which it is propagated. Landolt has applied the two formulæ to calculate the refraction-equivalents of mixtures, on the supposition that these equivalents are equal to the sums of the equivalents of the constituents, and has found that the results are the same whichever formula is adopted; and moreover that the observed agree with the calculated results, except when very strongly refractive liquids, such as carbon disulphide, are employed. Hence Landolt argues that conclusions regarding the connection between the molecular composition and the refraction-equivalents of compounds, deduced by aid of the first (purely empirical) formula, are confirmed by the use of the second formula, which is deduced from the general principles of the undulatory theory of light. But neither formula is independent of dispersion. It is however possible by the use of Cauchy's formula to arrive at an expression for the refraction-equivalent which is practically independent of dispersion3. This expression may be formulated as Άμ (A1) M 1 Wied. Ann. 9. 641; and 11. 70. 2 Ber. 15. 1031. 3 For details consult a text-book on Optics (e. g. see Glazebrook's Physical Optics, pp. 244-46). But it appears, from an investigation by Langley, that this formula gives erroneous results 'when extended far beyond the limits within which the observations on which it is founded are made.' See Phil. Mag. for March 1884; or in full, Ann. Phys. Chim. (6) 2. 145. Hence, the apparently anomalous refraction-equivalents of some carbon compounds (see post., par. 142) may be due to the very great dispersion which is noticed in these cases. See Gladstone, C. S. Journal. Trans. for 1884. 241. = where A refractive index of the theoretical ray of infinite μ wave-length. We have then the four expressions for finding the refraction-equivalent of a liquid compound; The values obtained by equations (3) and (4) are about one-third less than those obtained by the use of equations (1) and (2). These formulæ yield expressions for finding the refractionequivalent of each constituent of a mixture, or that of each atom in the molecule of a liquid compound, if it is assumed that the equivalent of the mixture, or of the molecule, is the sum of the equivalents of the constituents of the mixture, or of the atoms which constitute the molecule. The 'atomic refraction' of an element, deduced by each equation (1) to (4), may be represented by the symbols (1) ra, (2) r1, (3) ra, (4) r respectively. 139. Is the value of r, or ra, constant for each element in all its liquid compounds? This question has been considered by Gladstone and Dale (loc. cit.), and by Landolt (loc. cit.)*, but more especially by Brühls. Assuming that the refraction-equivalent of each elementary atom has a constant value in all compounds of that element, and that the equivalent of a molecule is the sum of the equivalents of the constituent atoms, we have the expression for finding the refraction-equivalent of a compound, CnH2mOp, (R)=n.r,C+2m. r,H+p.r10: 1 Light with wave-length of the red hydrogen line Ha is usually employed for determining μ. 2 See Landolt, Ber. 15. 1033. 3 See also, Gladstone, C. S. Journal. Trans. for 1884. 241. 4 See also Pogg. 117. 353. and Annalen, Supplbd. 4. 1. 5 Ber. 12. 2135: 13. 1119 and 1520: 14. 2533, 2736 and 2797; also (in more detail) in Annalen 200. 139: 203. 1, 255, and 363: 211. 120 (Abstracts in C. S. Journal for 1880. 293 and 781: 1881. 15: 1882. 445). and similarly for compounds of other elements. From the application of such expressions, Landolt, and others, deduced the following values; r for H=1'29; for O=2'71; for C=486; for S=13'53; for Cl=9'53. Or, if equation (4) [p. 309] is employed, then TA for H=102; for O=1'56; for C=2'43; for S=7'65; for Cl=5·89. The values of (R), thus calculated, for many liquid carbon compounds, were found to agree with the observed values. Thus, the refraction-equivalents of pairs of carbon compounds differing in composition only by H, should differ by 2. 129=258; the following are some of the differences observed, (R1)C2HO − (R)C2H2O=2'14: (R)С2H ̧O−(R)C2H ̧O=2'45 : But the following numbers shew that this generalisation does not always hold good; The refraction-equivalent of the carbon, hydrogen, oxygen, or chlorine atom, or of all these atoms, is evidently not constant. Now, if the structural formulæ of propyl compounds are compared with those of allyl compounds, it is seen that in the former all the carbon atoms are represented as tetravalent (singly-linked), but in the latter two carbon atoms are represented as trivalent (doubly-linked); e.g. Hence, the disagreement between the calculated and the observed values of (R) in the case of allyl compounds may be correlated with the presence of trivalent (doubly-linked) carbon atoms in the molecules of these compounds. Moreover, the actual values of (R) for propyl compounds agree for with those calculated by the equation on p. 309, taking C=486, for H = 1.29 and for O= 2'71; but the values found for allyl compounds are about 2 units greater than the calculated values. Thus, Brühl has compared the values of (R) for a great many pairs of carbon compounds, one series containing only tetravalent, the other also trivalent carbon atoms, and has found that the observed agree with the calculated values in the first series, but in the second the observed values are about 2 units greater than the calculated values, for each pair of trivalent carbon atoms in the molecule1. This conclusion may be summarised by saying, that two values are to be assigned to the refraction-equivalent of the carbon atom, according as it acts as a tetravalent (singlylinked), or trivalent (doubly-linked) atom. The values are these, r1C1=4·86 : rAC"=243 r1CI=5.86 : TA CI=3'22 Further, Brühl has compared series of compounds containing tetravalent carbon, and divalent oxygen atoms, with series containing tetravalent carbon, and monovalent (doublylinked) oxygen atoms, and he has found that the value of (R) for any compound of the second series is about 06 greater (for each monovalent oxygen atom) than that for the compound of the first series having the same empirical formula2. We may then assign these values to the atoms of oxygen : r1O"=2'71 Hence it would appear that the TAO"=1'56 influence exerted on the refraction-equivalent of a liquid carbon compound by the 1 See numbers in Ber. 12. 2142. 2 See numbers in Ber. 13. 1121. atoms of carbon in the molecule, depends on whether each carbon atom acts on, and is acted on by, four or three other atoms. 140. But does this influence vary in accordance with the nature of the atoms, between which and the carbon atoms there is direct mutual action? Brühl' finds that each of the following groups of isomeric compounds of carbon, hydrogen, and oxygen has practically the same refraction-equivalent. |