it is reasonable to imagine that in the last equation 1-E11, 1-E2/e, and so on, can be replaced by a single mean value proportional to be, where b is the linear coefficient of expansion of the solid compound. Denote each by abe, where a is a constant which may or may not be the same as the 7 for metals, and replace nim,v,2+nq m q v 2 2 + ..., which is twice the total kinetic energy of the molecule, by its value 2J Mc0, where c is the specific heat of the compound, then the last equation becomes 2J Mc 1 = 623 Σεφ(r), in which bis at present unknown for most compounds. But as in the metals bTM044, so we may assume for compounds that 6TM is constant; and merging this unknown. constant and 1/a into a single constant k, for compounds of the same type we get finally M21=5.8 × 10-4k Mc differing from the equation (9) for elements only in the constant k to be ascertained for each type of compound. It so happens that for binary compounds of monad elements such as NaCl or KI, the value 1/2 for k gives good results; and as Mc for the chlorides of this type is 12.7, and for the bromides 13 8, and the iodides 134, the mean of which can be taken as practically double the 64 for the atomic specific heat of the elements, then the equation (13) for such compounds reduces to the same as that for the elements (9). We will first take the data for the haloid compounds of the metals of the Li family; the melting-points are those given in Carnelley's paper on the Periodic Law (Phil. Mag. ser. 5, xviii., also Journ. Chem. Soc. xxix., xxxiii., xxxv., xxxvii.); the molecular domains (volumes) are those given by F. W. Clarke (Phil. Mag. ser. 5, iii.), and differ slightly from those previously given in this paper in Table IX. Below the values of (M2) calculated by the equation (9) are given values from Table IX. found from surface-tensions. The general agreement between the two sets of values of (M2) is surprisingly good, the values found by (9) being on the average about 7 per cent. larger than those found from surface-tensions. The data for the haloid compounds of the other metal of this family, namely Cs, are incomplete, at least I have failed to find data for the densities of C's compounds; but the following considerations give us the molecular domains of Cs compounds in a satisfactory manner; the mean difference in the molecular domains of the corresponding Na and Li compounds is 5'4, for K and Na it is 11-2, and for Rb and K 15.8, numbers which are closely 1 x 54, 2 x 5.4, and 3 x 54. Consequently for Cs and Rb compounds we should expect a difference 4 x 54 or 21.6, which when added to the domains for the Rb compounds gives the domains tabulated hereunder with the melting-points taken from Carnelley's diagram: The simplest way to deal with compounds of the type RC12, RCI,, and RC, is to replace kMc/6'4 in equation (13) by 1, as we have done with the type RCI, and then ascertain what values must be assigned to kMc/64 to make the results consistent with one another; then, having the value of Mc for each type, we can assign the value of k for each. As the event proves that kMc/64 is 1, or nearly 1, for the simple types RCI, RC12, RC13, and RC, we can proceed to tabulate values of (M2) from (9), namely, M2=5.8 × 10-(M/p) TM3, (9) which thus becomes the fundamental equation for the elements and the above types of compounds. For these types k therefore varies inversely as Mc, but Mc is mic1+mqCq + ..., that is the sum of the atomic specific heats, which for most atoms are each nearly equal to 6'4, so that for these types Mc/6-4 is equal to the number of atoms in the molecule, and accordingly k is inversely proportional to the number of atoms in the molecule. When we come to types such as RNO3, involving a compound radical NO,, some of whose component atoms have an atomic specific heat less than 6'4, k is inversely as the number of radicals in the molecule, so that for RNO, it remains 1/2 as for RC1, but Mc is no longer 2 × 64. The case of R(NO3)2 is not so simple, but these matters will be gone into later on; at present we proceed with the application of (9) to the types RC12, RCI, and RC. The data and results for a number of haloid compounds of these types are given in the next table, the melting-points being as before taken from Carnelley's table and diagram, and the densities used in calculating the molecular domains being derived from various sources (chiefly F. W. Clarke's collection of data in Smithsonian Miscellaneous Collections, xii. and xiv.); the bracketed values of the molecular domains are the approximate results of interpolation. *Compare with these the values in Table IX. from surface-tensions, namely, 98 for CaCl, 10-6 for SrCl2, 124 for BaCl2, 63 for AgCl, and 6.7 for AgBr, which are all about 1-2 times the values in this table, but the values of the surface-tensions are uncertain. For the haloid compounds of other metals data are available for the boiling-point as well as for the melting-point, so that, besides the equation (9) relating to the melting-point, we can use the approximate equation ("Laws of Molecular Force," p. 247) M2=1190 × 10-Mʊ1T¿ (14) relating to the boiling-point To, and so obtain two sets of values for (M2), which are given in the next table along with their ratio (v, is strictly the volume of a gramme at To, but the value of 1/p at 0° C. can be taken as a good enough approximation). From the row of ratios it appears that the boiling-point method gives results which on the average are 1.08 times larger than those given by the melting-point, an accord which is again surprising, seeing that in an arbitrary manner we assumed for compounds the relation TUM-constant, established experimentally only for the metals: if instead of '044 we took 040 for the constant, the agreement between the two methods would become complete for most of the compounds. This agreement proves what was asserted in connexion with equation (13), that k for these types is inversely proportional to the number of atoms in the molecule. Before accumulating any more data it will be well to extract the general results from those just given in Tables XIII., XIV., |