We have given this table at length, that the reader may estimate the true value of the attempt at classification in question, which, for the first time, embraces all the elements known to chemistry. This attempt, doubtless, still presents many imperfections, greatly due to the uncertain state of our present knowledge, especially with regard to rare elements. Thus tellurium is not in its place, supposing its atomic weight to have been accurately determined. If tellurium were the intermediate element between antimony and iodine it should possess an atomic weight of about 125. A question might also be raised as to whether copper is correctly placed: it is separated from certain elements-mercury, for example, which it appears to resemble. Other simple bodies, such as cobalt and nickel, the atomic weights of which are very similar, if not identical, also give rise to a difficulty. According to the principle of the classification, their properties should similarly coincide, which is not the case. And yet we know that these metals have many points in common. This is also the case with chromium, manganese, and iron, which are placed side by side in the same horizontal series, and between the atomic weights of which there is very little difference. On the other hand, great differences may be observed between the properties of vanadium and bromine, between potassium and calcium, between rubidium and ruthenium, which yet are so closely related by their atomic weights. In the same manner we must confess that the variations or gradations of properties are far from progressing regularly or uniformly in the different groups. In some cases they are too great, as in the

first group, carbon, nitrogen, oxygen, and fluorine; in others too slight, as we have just remarked, for the last terms of the third group. Though it may be generally true that the properties of bodies are subject to periodic modifications with the increase of their atomic weights, the law of these modifications escapes our observation, and seems to be of a complicated nature; for, on the one hand, the atomic weights of successive elements vary within considerable limits, without displaying any regularity in these variations; on the other hand, we must confess that the gradations of properties, or, in other words, the greater or less divergencies between the properties of successive elements, do not appear to depend upon the degree of the differences between the atomic weights. These are real difficulties.

In the preceding table we are principally struck, at first sight, with the gaps which may be noticed between two elements, the atomic weights of which show a greater difference than two or three units, thus marking an interruption in the progression of the atomic weights. Between zinc (64·9) and arsenic (74·9) there were two, one of which has been recently filled up by the discovery of gallium. We must, however, remark that the considerations by which Lecoq de Boisbaudran was led in the 'search' for gallium (for this great discovery is not due to chance) have nothing in common with the conception of Mendelejeff. Again, though gallium has filled up a gap between zinc and arsenic, and though other gaps may be subsequently filled, it is by no means proved that the atomic weights of the

new elements will be those assigned to them by the principle of classification which we have been discussing.

In fact, the atomic weight of gallium is sensibly different to that which was predicted by Mendelejeff. It is also possible that the future may be reserving for us the discovery of a new element, the atomic weight of which will closely resemble or coincide with that of a known element, as the atomic weight of nickel coincides with that of cobalt, and as that of potassium closely resembles that of calcium, and such a discovery would not fill any foreseen gap. For example, if cobalt were unknown, it would not be discovered by Mendelejeff's principle of classification. This imperfection is undoubtedly due to the fact mentioned above, that the rate of increase in the atomic weight of elements belonging to the same period (horizontal series) is altogether irregular.

III.

Among the physical properties dependent upon atomic weight we have not yet mentioned density. Other physical properties seem in the same manner to be subject to periodic variations with the increasing value of the atomic weights. We may mention particularly malleability, fusibility, volatility, and conductibility for heat and electricity. Without entering into the details of this subject, we may give an outline of all the facts, drawing our information from a graphic construction for which we are indebted to Lothar Meyer

who has contributed a detailed and important deve lopment to Mendelejeff 's idea. (See the end of the volume.)

The elements are arranged upon the axis of the abscissæ, at distances from zero proportional to their atomic weights, each element occupying a fixed point upon the axis. At this point an ordinate is drawn, which represents the atomic volume of the given element. The curve which joins the extremities of the ordinates represents, therefore, the variations of the atomic volumes. From the absence or uncertainty of the data relative to certain gaseous or other little studied elements, it has been impossible to give the entire curve. In particular an important gap is visible between didymium and tantalum, and in other places dotted lines are used, where certain unknown atomic volumes are interpolated.1 This being granted, the graphic construction shows at once that the variations of the atomic volumes (and consequently of the densities) are periodic. Starting from lithium, the curve sinks till it reaches a minimum which corresponds with boron; it then rises, attaining a second maximum with sodium. At this point it descends again, then rises to a third maximum with potassium, and so on. Now it is proved that the position occupied by the elements upon this curve is in relation with their physical and chemical properties.

In the first place, as far as the densities are con

1 The atomic volumes of elements may be indirectly determined by deducing them from the molecular volumes of their liquid or solid compounds (see Chapter VII.)

cerned, it is evident, from the very principle upon which the curve is constructed, that the light metals (possessing considerable atomic volumes) should occupy the maxima, and the heavy metals (possessing low atomic volumes) the minima; but the fact which particularly demands our attention is that, with atomic volumes sensibly identical, two metals may possess very different properties, as they are situated upon the ascending or descending portion of the curve.

The ductility, fusibility, and volatility of elements are related to their atomic weights, and are subject to periodic variations with the increase of their atomic weight. The light metals, which occupy the summits, or the immediately succeeding descending portion of the curve, are ductile. The heavy metals, occupying the minima, or the ascending portion near the minima, of the curve, are partially ductile in the fourth, fifth, and sixth groups. Take, for example, the fourth, which comprises the elements placed, from the progression of their atomic weights, between potassium and rubidium. The light metals, potassium and rubidium, which stand at the top of the curve, are ductile. A decrease should be observed in the ductility of the elements placed upon the descending branch, till at the bottom we meet with brittle metals, such as vanadium, chromium, and manganese. From iron, which follows, the ductility increases with the elements which occupy the minima, or the immediately succeeding ascending branch. Ductile copper is the last of this ascending series. With

The three first groups only contain heavy metals.