combine with _whole molecules_, which fact is best proved by the capacity of substances to form crystalline compounds with water, ammonia, &c. But in some substances this faculty for further combinations is less developed (for instance, in carbon tetrachloride, CCl_{4}), whilst in others it is more so. AlX_{3} combines with many other molecules. Now if a limiting form, which does not combine with new X's, nevertheless combines with other whole molecules, it will naturally in some instances combine with itself, will polymerise. In this manner the mind clearly grasps the idea that the same forces which cause S_{2} to unite itself to Cl_{2}, or C_{2}H_{4} to Cl_{2}, &c., also unite molecules of a similar kind together; thus _polymerisation_ ceases to be an isolated fragmentary phenomenon, and chemical combinations 'by analogy' acquire a particular and important interest. In conformity with these views the following proposition may be made concerning the compounds of aluminium. They are of the type AlX_{3} in the limit, like BX_{3}, but those limiting forms are still able to combine to form AlX_{3},RZ, and the aluminium chloride is a compound of this kind--_i.e._ (AlX_{3})_{2}. In boron, for example, in BCl_{3}, this tendency to form further compounds is less developed. Hence boron chloride appears as BCl_{3}, and not (BCl_{3})_{2}. Polymerisation is not only possible when a substance has not attained the limit (although it is more probable then), but also when the limiting form has been reached, if only the latter has the faculty of combining with other whole molecules. We may therefore conclude that aluminium, like boron, is trivalent in the same sense that lithium and sodium are univalent, magnesium bivalent, and carbon tetravalent. In a word, there is no reason to consider that aluminium is capable of forming compounds AlX_{4}, and in that way to explain the existence of the molecule Al_{2}Cl_{6}. Furthermore, there are many reasons for thinking that AlF_{3}, Al_{2}O_{3}, and other empirical formulæ do not express the molecular weights of these compounds, but that they are much higher: Al_{_n_}F_{3_n_}, Al_{2_n_}O_{3_n_}. In recent years convincing proofs of the truth of the above statements have been obtained, and of the independent existence of AlX_{3} in a state of vapour; for Comb has determined the vapour density of the volatile acetyl of aluminium acetate Al(C_{3}H_{7}O_{2})_{3} (which melts at 193°, boils at 315°, and distils without a trace of decomposition), and has found that it exactly corresponds to the above molecular composition. On the other hand, Louise and Roux (1889) by employing the method of