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 development 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.

gallium the ductility again decreases; arsenic is brittle.

Thus we see that in the fourth group of elements, while the density increases and diminishes regularly with the increase of the atomic weight, from potassium to rubidium, the ductility diminishes and increases twice. Thus the variations of ductility extend to two groups instead of one, as is the case with density. It also appears that elements which have evidently the same atomic volume, such as chromium and copper, vanadium and zinc, differ to a striking extent in ductility. Vanadium and chromium, situated upon the descending branch of the curve, are brittle; copper and zinc are ductile, though in a different degree. And since we have drawn attention to the elements ranged in group IV between potassium and rubidium, we may remark that there was a considerable gap between zinc (Zn 64.9) and arsenic (As=74.9). It was here that Mendelejeff placed his ‘ekaluminium,' which is the gallium of Lecoq de Broisbaudran.

From the place of this element, between zinc and arsenic, though nearer to zinc, Mendelejeff was able to predict that its density would be about 5.9. Now Lecoq de Boisbaudran has found it to be 5.96. From the place occupied by gallium in the third vertical series on p. 159 the eminent Russian chemist was able to discover a connection with aluminium, which is found to be correct; thus gallium oxide resembles aluminium. oxide.

We should be exceeding the limits which we have imposed upon ourselves in this treatise, if we gave fresh