and XV. In the baloid compounds of the Li family the mean difference in (M2) for the chlorides and fluorides (Cl-F) is 11, for Br-F 1.8, and for I-F 2·5; which are a little smaller than the 1.2, 1.8, and 2.7 which we got before, although the values of (M2)* in Table XIII. are larger than those in Table IX. Similarly we have the average values Na-Li=1·1, K-Li=22, Rb-Li=36, and Cs-Li=49, which nearly as 1, 2, 3, and 4. The corresponding differences in the molecular domains with Clarke's values given in Table XIII., are Na-Li=54, K-LI=16·6, Rb-Li=324. The same molecular domains taken in conjunction with Thorpe's values for the halogens in organic compounds lead, as has been already shown, to the domains 9 for F, 19 for Cl, 26 for Br, and 36 for I, which lead to a mean value 2.0 for Li; so that the molecular domains of the metals of the Li family in the compound state are 20 for Li, 74 for Na, 18.6 for K, 344 for Rb, and probably 56 for Cs. To obtain the values contributed to (M2/) by these atoms, it must be remembered that from the results in Table IX. we found that the value for fluorine might be taken as 9, so for the numbers in Table XIII. it should be taken as about 9, giving for the halogens the values 9 for F, 2.0 for Cl, 2.7 for Br, and 3'4 for I, nearly the same as the former values 9, 2.1, 2.7, and 3.6; which will be retained and lead to the values 24 for Li, 3.5 for Na, 4.6 for K, 6·0 for Rb, and 7-3 for Cs, which go very nearly as 2, 3, 4, 5, and 6. To complete the data for the Be family we require the densities of the haloid compounds of Be, but as these appear to be wanting we must approximate to the molecular volumes of the Be compounds by means of the fact that the molecular volume of BeÒ is 5 less than that of MgO; subtracting then 5 from the molecular volumes of MgCl2, MgBr2, and MgI2, we can supply the following On passing from the haloid compounds of the monad metals in Table XIII. to the compounds of the dyads, triads, and tetrads in Tables XIV. and XV., the first point to arrest attention is that the values for I-Cl2, 13-Cl3, 14-Cl, are not 2 and 3 and 4 times the value of I-Cl already found in connexion with the monad metals: we have the following mean values: The discrepancies in these values might be ascribed to an error in the assumption that kMc/6.4 is equal to the same constant 1 for all these types of compounds; and it might be supposed that the constant ought in each case to be chosen so that I-Cl,, I3-Cl3, and I-Cl, are 2 and 3 and 4 times. I-CI. But this supposition breaks down when it is remembered that in the types RC1, and RC, values of (M2)* as found by the independent boiling-point method are only 8 per cent. larger than those by the other method. It is true that the boiling-point method is only approximate, but that the approximation is fairly close can be seen by comparing the following pairs of values, the first of each pair being the approximate value from Table XV. and the second the value from Table VII., namely: = These comparisons show that the phenomenon that the values in (M2) for I-Cl, 1,-Cl2, I3-Cl3, and I-Cl, do not stand as 1, 2, 3, 4 is a real one, and not the result of accumulated imperfections in the methods of calculation. The values given above for these differences stand more nearly in the relation 1, 2, 3, 4*; and supposing it to be the true one, they can be brought into almost complete harmony if we return to the old relation bTM constant, and denoting by E an equivalent replace it by ¿TE=constant, which would reduce the values of (M27) for the four types in Tables XIII., XIV., and XV. by factors 1, 1/2, 1/3, 1/4'1⁄2: then the numbers 14, 1.8, 2.7, and 3.1 for I-Cl, I2—Cl2, I3—Cl3, and I-Cl ought to be as 1, 1/2, 1/3, and 1/42. Dividing the numbers by these powers, we get for I-Cl the series of values 1.4, 1.2, 1·4, and 14, which are as nearly constant as possible under the circumstances. This constitutes the main part of the proof that in compounds of the type RS,, where R is an n-valent atom and S a monad, (M) is of the form (F,+nF.)/n, whence (M2)$ /n3 = F,/n+ F. Thus our best plan will be to divide the numbers in Table XIII. by 27, and those in XIV. by 3 and 4, and tabulate the results as F,/2+ F., F,/3+ F., and F,/4+F,, according to the type of compound. There are some irregularities among these numbers, the most pronounced being where the value for SrI, falls below that for Cal2; but ignoring these as due to no fundamental error, we get, taking the data for the chlorides as the best, with 21 as the value for Cl, the following values for F,/2 or F/2, and approximate values of B derived from the best values of M/p in Table XIV. The values just given for the types RC1, and RC, are the means of those given by both the melting-point and boilingpoint methods, the latter being reduced first by dividing by 1.08 the mean ratio of results by the two methods, and then converted to equivalent values by dividing by 3 and 4*. Again, amongst the types RC1, and RC, taking the values of F/3+ F. and F/4+F. for the chlorides as the most reliable, but allowing for the others where necessary, and using 2.1 as the value of F, for Cl as S, we get the approximate values : TABLE XVIII. P. As. Sb. Bi. B. Al. F/3... 8 *85 1.05 1.5 .6 1.2 C. Si. Ti. Sn. F/4... 5 '6 •95 .95 In the compounds of the zinc family irregularities appear in (M2): thus for I-Cl, we get with Zn 2.7, with Cd 1-6, and with Hg(ic) 1.3, instead of the 1-8 proper to dyads: so also are the compounds of Cn(ous) and Ag exceptional, for Cul-Cu,Cl, is 3.4 and AgI-AgCl is 1.9; but the reasons for these irregularities can hardly be gone into in the present paper, though in a general way they suggest themselves. So far the method of the Kinetic Theory of Solids has been applied to only the haloid compounds of the metals, and it will be interesting to see how it works with compounds involving more complicated acid monovalent radicals such as NO3, ČIO3. The equation (13), which for the haloid compounds was shown to simplify down to (9), must for these compounds be used in its original form (13) with k=1/2: for the nitrates of the form RNO3, Mc has a mean value 24, so that (13) becomes which will be used as near enough for the chlorates, bromates, and iodates, though in them Me is a little larger. The following are the data for this type of compound :— With the values 24 for Li in (M2), 3.5 for Na, and 4.6 for K obtained from the haloid compounds, we derive from the last table the following mean values for the parts con 3 tributed by the radicals NO, CIO, BrOs, and IO, to (M2)*, along with the values reproduced from Table XI., where they were obtained by the surface-tension method : The agreement in the two sets of values is good only for NO3, but it should be noted that the value for BrO, from Table XI. is too small in comparison with that for CIO. With 3.6 as the value for NO, we can obtain from Table XIX. values for Ag and Tl, namely Ag=3'4, which is 1 less than Na, while the irregular results for the haloid compounds of Ag would make it about 5 less; for Tl the value is 4.2. To the data for the carbonates, sulphates, and metaphosphates of the monad metals similar considerations have to be applied as to those for the nitrates. Equation (13) has to be used with a value 28 for Me in the carbonates of type R2CO3, 33 in the sulphates R2SO4, and 50 in the metaphosphates. As there are 3 radicals in these types k will be 1/3, and as in the case of RC, we divided our original values of (M2) by 2 to get true values of (M2)/2 or EF, so also in these types we must do the same: thus for the carbonates R2CO, M2l the same with 33 in place of 28, and for the metaphosphates the same with 50 in place of 28. These equations give the following values: |