The value of ΣF, for Tl,CO, is probably too small because the melting-point given for this compound seems to be too low. Confining our attention to the Na and K data, which are the best, we get for F/2 for CO, the value 2.8 as against 33 by the surface-tension method, and for SO, F/2 is 43 as against 40 in the surface-tension method. This value 4:3 gives for F in Ag a value 3-6, while 3-4 was the value derived from the nitrate, in T F is 4.9 from the sulphate as against 4.2 from the nitrate; the values for the metaphosphates again show that Na and Ag have nearly equal values for F, and that for P20 F/2 is 74, while 67 was the value found by the former method.

We advance to a higher degree of molecular complexity when we take up the nitrates of the dyad metals of type R(NO3)2; here Me is 416, and as there are three radicals in the molecule k is 1/3, and thus

41.6

M2 5.8 × 10-4 (M/p)TM3. . . . (17)

3 x 6.4

It happens that this equation, when applied as in the next Table to the nitrates of Ca, Sr, and Ba, gives values for (M2) which are nearly the sum of F for Ca and twice F for NO,, and so on, so that the effect of valency does not appear here; but before remarking further about this let us take the data :

With F for NO, as 3.6, for Ca as 64, Sr 74, and Ba 8.4 (see Table XVII.), we get for the nitrates 13.6, 146, and 15.6, when valency is ignored, and these values are in substantial agreement with those just given in the Table. The question arises whether this is merely the fortuitous effect of some peculiarity of these nitrates not taken account. of in equation (17), or whether it is due to the fact that the valency of the atom which determines the type exercises less influence as the radicals to which it is united become more complex; or, in other words, do the compounds of the metals when complex enough tend towards obeying the same law for (M2) as holds in the carbon compounds? The question

is merely raised in connexion with the results of the last table, to which by themselves little weight need be attached, but we will return to the matter shortly in connexion with the organometallic compounds. Meanwhile we will take the data for a few compounds of tri- and tetrabasic acids with which to gain some more knowledge of the influence of the basicity of an acid radical on its attracting-power; these compounds are Li,PO, and Ag3PO4, the orthophosphates of Li and Ag, Na,P2O, and Ag,P,O,, the pyrophosphates of Na and Ag, and along with these will be taken Na2B4O7, the Na salt of the dibasic pyroboric acid.

For the orthophosphates Mc=41, for the pyrophosphates 63, and for the pyroborate 63; in the orthophosphates there are four radicals to the molecule, so that k=1/4, so for the pyrophosphates k=1/5, and for the pyroborate k=1/3: thus the equation (13) becomes for the orthophosphates

M2 5.8 × 10-4 x

41
4 × 6.4

(M/p)TM',. . . (18)

and so on. To reduce (M2) to ΣFe, we must divide it by 3 for the orthophosphates, by 41 for the pyrophosphates, and by 2 for the pyroborate; and thus we get

With 2-4 as the value of F for Li, and 3 4 for Ag, we get that for PO4, F/3 is 3-4 and 4:1, or in the mean 3.7; so with 3.5 for Na and 34 for Ag, F/4 for P2O, is 5·0 and 4·6, or 4.8 in the mean; so also F/2 for BO, is 8.5, the value found by the surface-tension method for F/2 in B,O, was 7.2, and for F/4 in P2O, was 4.1 (see Table XI.), which would be obtained on dividing the values just found by 12.

We are now in a position to make the same comparison between the values of F for a large number of acid radicals in inorganic compounds, and the volumes B of these radicals, as was made in connexion with organic compounds. In the following Table the first row contains the value of F as given by the surface-tension method in Table XI., in the second row the values of F given by the Kinetic Theory of Solids, in the third the mean of these two sets of values, in the fourth the

volumes of the radicals deduced from those of their compounds given in previous tables, and in the fifth the ratio of B to F.

The values of the ratio for NO3, NO2, and CN, namely 8.5, 8, and 9, are not far from the mean value 10 found for the same ratio in organic compounds: for these three radicals the values of the ratio in Table VI. were 10, 9, and 8; for CIO, the ratio in the last table is 9, but for BrO, it falls to 7.5, and for 103 to 6. This is due to the values of B for these radicals being smaller than they ought to be if regular, for B for BrO instead of being less than for CIO, ought to be 64 greater, which would make it 41, and bring the ratio up to 9; similarly B for 10, ought to be 16.5 greater than that for CIO3, which would bring it up to 51, and make the ratio 8.

This part of the table shows that for the dibasic acid radicals the ratio 2B/F is constant within the limits of accuracy attainable; and the remarkable fact appears that 2B/F for the dibasic acid radicals has the same value as B/F for the monobasic. There is only one datum for a tribasic acid and one for a tetrabasic, namely,

For the tribasic acid radical the ratio 3B/F is 12, and therefore 2B/F is 8; for the tetrabasic radical 4B/F is 17, and therefore 2B/F is 8.5; and both these values for 2B/F range themselves with the values found for 2B/F in the dibasic radicals. This, then, is a noteworthy result, that for all acid radicals of a basicity higher than 1 the ratio 2B/F is nearly constant, and has half the value of the same ratio for radicals of basicity 1. This recalls the result we found before, that for atoms in organic compounds the ratio B/F has a value nearly half of that for the elements and CH, C2H1, and CH2. Our results for the acid radicals may be summed up in the two formulas-B=9F nearly in the unibasic, 2B=9F nearly in the polybasic.

The last compounds to be considered briefly in the present paper are the organometallic, for which M2l can be calculated by the equation (14),

M2=1190 × 10− Mv1TË,

with the data collected by Carnelley (Phil. Mag. 5th ser. xx. p. 260), namely, the boiling-points and densities at about 15° C. of various methides, ethides, and so on. In the following table these data are not reproduced, but only the values of M/p and (M2) calculated from them. The types of compound are indicated by the headings Zn R, SnR1, and so R being CH, in the first row, and so on.

on,

The values for compounds of O, S, Cl, Br, and I have been introduced into the table only to give an idea of the degree of approximateness of the values in the table, for more accurate values for these compounds have been already discussed. First let us consider the values of M/p which may be taken as MB.

These numbers show that in MB CH, has a value about 165, which is close to the limiting domain for CH, in the organic compounds, though it ought to be larger, seeing that the density p used in the organometallic compounds is not the limiting density, but that of the liquids about 15° C. We will take the value for H to be the same as in the organic compounds, namely 4.5, and then CH, is 21, C2H, is 37.5, CH, is 54, and CH, is 70.5; with which we get the following mean values of the atomic domains of the metals in the organometallic compounds :

Except for P and As, these domains are much larger than in the inorganic compounds: for instance, the domain of PbCl is only 47-8, which is actually less than the domain of Pb in the organic compounds. Of course the one number is calculated for the solid state, and the other for the liquid, but this could explain only a small part of the discrepancy. There is no doubt that the metallic atoms occupy more space in the organic than in the inorganic compounds; in the inorganic compounds Sb may be seen to have a domain about 20, while in the organic compounds the value is 46. This is a very significant fact, that seems not to have been noticed by those who have occupied themselves with the question of molecular domains (volumes).

As regards (M2), we know that in organic compounds CH, has a value 9, which is the value it possesses amongst the chlorides, bromides, and iodides of the last table; but in the metallic compounds the values are smaller. In the Zn compounds 2CH, has the values 18 and 1.5, with Hg 1.7 and 1.2; in the Sn compounds 4CH, is 2-8 and 17, and in the Pb compounds 2:4: in every case the greater the number of CH, groups the smaller the value of CH2; the compounds of S show the diminution clearly, for they give for CH, instead of 1.8 the values 1.6, 1.5, 1.4. These results seem to show that the approximate equation (14), used to calculate the values of (M2) in Table XXV., gives less and less accurate results the more complex the molecule becomes, but at the Phil. Mag. S. 5. Vol. 39. No. 236. Jan. 1895.

D