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radicals CH, and NH3. The values of (M2) for benzene and its monohalogen substitution compounds are :
which give for Cl-H the value 10, for Br-H 1·6, and for I-H 2·4; and these, with the values found for the halogens, give for H in benzene the values 1-2, 9, and 8, the mean of which is 10; still a large value and nearly equal to the 11 belonging to each CH in benzene, which, it should be noticed, is larger than the 9 for CH2. Strictly speaking, all that the last numbers really show is that the difference between the halogens and hydrogen in benzene is about the same as the difference between the halogens and the terminal hydrogen in paraffins. The following values form the beginning of a series which, if extended, would illustrate the transition from one type to the other:
They give Cl-H=1·1, 2(Cl-H)=2·7, and 3(Cl — H)=3·6, which are in fair enough agreement. In the following cases we have only CH, groups and halogens.
With 9 for CH, in (M2), these give for Cl the values 2.45 and 2-4, and for Br 2.65 and 2:55, which are a little larger than those adopted from the series, namely 2.2 and 2.5.
The data of table xxv. of the "Laws of Molecular Force" furnish values of (M27) for the elements H2, O2, and N2, and for CH4, which are gathered into
of values for Cl2,
To these may be added an uncertain set namely MB=34 and (M2)=2·4, their ratio being 14; excepting this, we see that the element gases and CH have nearly a constant value 18 for the ratio Mß/(M2), a value which is nearly double the 10 for atoms in the combined state. It should be noticed that the ratio 19 for CH2 in the carbon series ranges itself along with the values for the
elements and CH. It is very remarkable that as regards molecular force, CH, not only detaches itself so completely from the paraffins and compounds in general, but also attaches itself so consistently to the elements. It is interesting to find CH, which is the first of the olefines, detach itself from its class; in the "Laws of Molecular Force " it was proved to have a characteristic equation intermediate in form to those for elements and compounds. It has already been pointed out that the olefine C,H2, has the same value of (M27) as the paraffin CnH2n+2; but this does not apply to C,H1, because instead of the 4·0 for CH, it has the value 2.5 for (M2), and for Mẞ it has 43, which is much larger than the 34 of two ordinary CH, groups; the ratio MB/(M2) is 17, which goes with the values found for CH, and CH4.
The case of the elements will be returned to when the methods of getting further data have been developed in the following parts of this paper.
To close for the present the discussion of the carbon serial compounds, the main result had better be restated, as it has perhaps been obscured by foreign details; it is embodied briefly in Table IV., and is this, that the attracting-power of a molecule is the sum of powers belonging to its atoms, the power of an atom varying with its chemical function, but remaining constant when that function is constant. As a subsidiary result, it has been shown that the attractingpowers of the atoms of Cl, Br, I, O, S, N, and C (C unattached to H) are approximately proportional to their volumes in the
2. (a) and (b). Methods of finding M2l for Compounds of the Metals, with Results.
(a) While we are on the present line of investigation, it will be convenient to consider such values (relative) of the parameter of molecular force, that is of (M2), as are obtainable for solids, both element and compound. These can be got in two ways: first, from the surface-tension of the solids at their melting-points, which are still measurements made on liquids, but at the transition-point into solidity; and second, from the principles of "A Kinetic Theory of Solids " (Phil. Mag. vol. xxxii.). According to the "Laws of Molecular Force" (Phil. Mag. March 1893, p. 258), in terms of the 106 dynes as unit of force is given by
l=2 × 5930av3 M3,
where a is the surface-tension in grammes weight per metre
at of the absolute critical temperature, which is near the ordinary boiling-point, v is the volume of unit mass at the same temperature, and M the ordinary molecular mass (weight); so that with the megamegadyne (1012 dynes) as the unit of force, we have
In the case of melted solids a has been measured at the melting-point only; and as the absolute melting-point of solids is not a constant fraction of their absolute boilingpoints, we shall have to be content with comparatively rough approximations to the values of Ml, if in the above equation (1) we use the value of a at the melting-point instead of that at of the critical temperature. In the case of mercury the surface-tension at the melting-point has been found by Quincke to be 58.8 grammes weight per metre; and I have estimated that at the boiling-point, if mercury behaves as an ordinary liquid, the surface-tension would be 42-6. Then, to keep the values of M2l in a rough way more comparable with those hitherto discussed, we will for all the melted solids take a at of the critical temperature as roughly given by 42.6/58.8 times its value at the melting-point; denoting which by am, we have, when we likewise allow for the difference between p at the melting-point and at 3 of the critical temperature by a factor 1.09, the equation
M2/= 2 × 5930 × 10-6 x 723 x 1.09am (M/p) =9346 × 10-6αm(M/p)§.
To preserve continuity in the work this equation will be applied first to compounds only, and later on to the metals. It is to Quincke that we owe the first measurements of the surface-tensions of a number of elements and compounds at their melting-points (Pogg. Ann. cxxxv. & cxxxviii.); and there are some more recent measurements for a number of compounds by Traube (Ber. der Deut. chem. Ges. xxiv. p. 3074). The values of the surface-tension given by Quincke in his second paper are brought into better agreement with those of his first and with Traube's when multiplied by 14, and accordingly these values multiplied by 14 are entered in brackets in the following Table as values of am, and the numbers derived from them are put in brackets also. The density at 15° C. will be used in place of that at the meltingpoint, because too few values at the melting-point are known, and the difference between the two is really immaterial in comparison with other unavoidable roughnesses in these calculations. The formula by which Quincke calculated am from
his experimental data is not exact (see Worthington, Proc. Roy. Soc. xxxii.); but his values have been taken as exact enough for present purposes. The first set of data for all the K and Na compounds are Traube's, the rest are Quincke's.
Table IX.-Compounds of Sodium (continued).
The first point to attend to in these numbers is to ascertain whether the additive principle applies to the values of (M2)3. The differences for K and Na are 1.2 in the chlorides, 9 in the bromides, 12 in the nitrates, 11 in the nitrites, 11 in the chlorates, 1.1 in the cyanides, of which the mean is 1.1. This is encouraging enough if we remember the roughnesses of calculation and experiment. Proceeding to take the differences for the compounds of the dibasic acids, we get for K,-Na, 1.9 in the carbonates, 1.8 in the sulphates, 1.4 in the chromates, 1.9 in the bichromates, and 16 in the metaphosphates, the mean of which is 1.72, which is less than twice the mean 1.1 for K-Na. It will be shown later that in a compound RS, where for instance R represents an n-basic acid and S a monad metal, (M2/)3= (F,+nF ̧)/n3, where F, and F, are the parts due to R and S: according to this principle the value of K,-Na, in the above compounds ought to be only 2 or 141 times the value for K+Na1; while according to the mean values found above, K.-Na, is 1.6 times K-Na. In view of the relation for RS,
(M2l)3/n3 = Fr/n +F ̧,
the best plan is to take values of (M2/)3/n3 which are the sums of F/n and F, or the sum of parts not due to atoms but to