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Rh But upon closer investigation it must be confessed that these regularities can be called only rules, and not laws. In the first line one would expect that the steps in the values of the atomic weights should be regular, but it is not so. There are even cases when it is necessary to invert the order of the atomic weights to satisfy the chemical necessities. Thus argon has a larger number than potassium, but must precede it to fit into its proper place. The same is true of tellurium and iodine. It looks as if the real elements were scattered somewhat haphazard on a regular table, or as if some independent factor were active to disturb an existing regularity. It may be that the new facts mentioned above will lead also to an explanation of these irregularities; at present we must recognize them and not try to explain them away. Such considerations have to be kept in mind especially in regard to the very numerous attempts to express the series of combining weights in a mathematical form. In several cases rather surprising agreements were found, but never without exception. It looks as if some very important factor regulating the whole matter is still unknown, and before this has been elucidated no satisfactory treatment of the matter is possible. It seems therefore premature to enter into the details of these speculations.

In recent times not only our belief in the absolute exactness of the law of the conservation of weight has been shaken, but also our belief in the law of the conservation of the elements. The wonderful substance radium, whose

existence has made us to revise quite a number of old and established views, seems to be a fulfilment of the old problem of the alchemists. It is true that by its help lead is not changed into gold, but radium not only changes itself into another element, helium (Ramsay), but seems also to cause other elements to change. Work in this line is of present day origin only and we do not know what new laws will be found to regulate these most unexpected reactions (see ). But we realize once more that no law can be regarded as free from criticism and limitation; in the whole realm of exact sciences there is no such thing as the Absolute.

Another question regarding the values of atomic weights was raised very soon after their first establishment. From the somewhat inexact first determinations William Prout concluded that all atomic weights are multiples of the atomic weight of hydrogen, thus suggesting all other

elements to be probably made up from condensed hydrogen. Berzelius found his determinations not at all in accordance with this assumption, and strongly opposed the arbitrary rounding off of the numbers practised by the partisans of Prout’s hypothesis. His hypothesis remained alive, although almost every chemist who did exact atomic weight determinations, especially Stas, contradicted it severely. Even in our time it seems to have followers, who hope that in some way the existing experimental differences may disappear. But one of the most important and best-known relations, that between hydrogen and oxygen, is certainly different from the simple ratio 1 : 16, for it has been determined by a large number of different investigators and by different methods to be undoubtedly lower, namely, 1 : 15.87. Therefore, if Prout’s hypothesis contain an element of truth, by the act of condensation of some simpler substance into the present chemical elements a change of weight also must have occurred, such that the weight of the element did not remain exactly the weight of the simpler substance which changed into it. We have already remarked that such phenomena are not yet known with certainty, but they cannot be regarded as utterly impossible.

It may here be mentioned that the internationality of science has shown itself active also in the question of atomic weights. These numbers undergo incessantly small variations because of new work done for their determination. To avoid the uncertainty arising from this inevitable state of affairs, an international committee was formed by the co-operation of the leading chemical societies all over the world, and an international table of the most probable values is issued every year. The following table is that for 1910:—

International Atomic Weights, 1910.

In the long and manifold development of the concept of the element one idea has remained prominent from the very beginning down to our times: it is the idea of a primordial matter. Since the naive statement of Thales that all

things came from water, chemists could never reconcile themselves to the fact of the conservation of the elements. By an experimental investigation which extended over five centuries and more, the impossibility of transmuting one element into another—for example, lead into gold—was demonstrated in the most extended way, and nevertheless this law has so little entered the consciousness of the chemists that it is seldom explicitly stated even in carefully written text-books. On the other side the attempts to reduce the manifoldness of the actual chemical elements to one single primordial matter have never ceased, and the latest development of science seems to endorse such a view. It is therefore necessary to consider this question from a most general standpoint.

In physical science, the chemical elements may be compared with such concepts as mass, momentum, quantity of electricity, entropy and such like. While mass and entropy are determined univocally by a unit and a number, quantity of electricity has a unit, a number and a sign, for it can be positive as well as negative. Momentum has a unit, a number and a direction in space. Elements do not have a common unit as the former magnitudes, but every element has its own unit, and there is no transition from one to another. All these magnitudes underlie a law of conservation, but to a very different degree. While mass was