Without going into further details, we may add to what has been said above that the conception of specific volumes and atomic distances has formed the subject of a large number of researches, but as yet it is only possible to lay down a few generalisations given by Dumas, Kopp, and others, which are mentioned and amplified by me in my work cited in Note 20, and in my memoirs on this subject. 1. Analogous compounds and their isomorphs have frequently approximately the same molecular volumes. 2. Other compounds, analogous in their properties, exhibit molecular volumes which increase with the molecular weight. 3. When a contraction takes place in combination in a gaseous state, then contraction is in the majority of instances also to be observed in the solid or liquid state--that is, the sum of the volumes of the reacting substances is greater than the volume of the resultant substance or substances. 4. In decomposition the reverse takes place to that which occurs in combination. 5. In substitution (when the volumes in a state of vapour do not vary) a very small change of volume generally takes place--that is, the sum of the volumes of the reacting substances is almost equal to the sum of the resultant substances. 6. Hence it is impossible to judge the volume of the component substances from the volume of a compound, although it is possible to do so from the product of substitution. 7. The replacement of H_{2} by sodium, Na_{2}, and by barium, Ba, as well as the replacement of SO_{4} by Cl_{2}, scarcely changes the volume, but the volume increases with the replacement of Na by K, and decreases with the replacement of H_{2}, by Li_{2} Cu, and Mg. 8. There is no need for comparing volumes in a solid and liquid state at the so-called corresponding temperatures--that is at temperatures at which vapour tension is equal in each case. The comparison of volumes at the ordinary temperature is sufficient for finding a regularity in the relations of volumes (this deduction was developed with particular detail by me in 1856). 9. Many investigators (Perseau, Schröder, Löwig, Playfair and Joule, Baudrimont, Einhardt) have sought in vain for a multiple proportion in the specific volumes of solids and liquids. 10. The truth of the above is seen very clearly in comparing the volumes of polymeric substances. The volumes of their molecules are equal in a state of vapour, but are very different in a solid and liquid state, as is seen from the close resemblance of the specific gravities of polymeric substances. But as a rule the more complex polymerides are denser than the simpler.