Döbereiner believed that the basis of a systematic classification of the elements might be found in these relations, but it was long before this idea was successfully developed. The attempts which were made in this direction by Pettenkofer (1851), Dumas (1859), and others could scarcely be successful, as at this time the atomic weights had not been deduced from the analytical results in a uniformly systematic manner. When this had once been accomplished, it was found possible to arrange all the elements in groups of three, four, or five members, in which the same differences of, approximately, sixteen, forty-six, and eighty-eight units occur.

When the old values for the atomic weights are used, some groups exhibit differences double those observed for other groups. As the difference is approximately identical in different groups, it follows that if the atomic weight of the first member of group X is larger than that of the first member of another group Y, then the second and third members of group X will have higher atomic weights than the corresponding members of group Y. It seemed possible that the systematic classification of the elements which Döbereiner strove to accomplish might be realised by arranging these groups in the order of their atomic weights. This idea could not be carried into effect, as many atomic weights had been incorrectly determined. An attempt to classify the elements according to the order of their atomic weights was also unsuccessful. The classification of the

elements in groups of three, four, five, or six members, and the arrangement of these groups in the order of the atomic weights of their members could only be satisfactorily achieved when the atomic weights of vanadium, tantalum, indium, the cerium metals and several other elements had been re-determined and corrected.

§ 35. Arrangement of the Elements in the Order of their Atomic Weights.-Most of the groups in the second table are related to one of the groups in the first table by analogies in the properties of their members, and especially by the isomorphism of their compounds. Vanadium, V, is associated with phosphorus, P, and arsenic, As, by isomorphism; in the same way chromium, Cr, and molybdenum, Mo, are related to sulphur, S, and selenium, Se; by the isomorphism of the permanganates with the perchlorates, manganese, Mn, is associated with chlorine, Cl. The first table does not contain

any elements analogous to iron, nickel, cobalt, and the six platinum metals; but copper, Cu, and silver, Ag, are related to sodium, Na; and zinc, Zn, to magnesium, Mg, and calcium, Ca; indium, In, to aluminium, Al; and tin, Sn, is isomorphous with silicon, Si, and titanium, Ti. We are therefore not only justified in joining these two tables together, but in uniting them to form the following table. The perpendicular columns contain not only closely allied elements, but also others which only bear an analogy to them in certain respects, but differ from them widely in other points.

elements are

If the right

In the horizontal rows of this table the arranged in the order of their atomic weights. side of each row is connected with the left side of the following row a single continuous series of all the elements will be produced. In this arrangement the nature and properties of the members will be represented as periodic functions of the atomic weights, changing systematically as the atomic weight increases from member to member, and returning to the beginning after a certain number of members. The periodicity may be more clearly indicated by means of the table at the end of this book. The table should be pasted on a wooden or pasteboard cylinder of suitable dimensions, so that the right and left sides meet.

'Helium and argon are omitted from this table. See Appendix.

The first two periods or series each embrace seven elements.

II Na Mg Al Si Р S Cl

The corresponding members closely resemble each other— e.g. lithium and sodium, beryllium and magnesium.

This resemblance continues in the third and fourth periods, so far as the first members are concerned; the following members do not exhibit corresponding properties, and it is not until we reach the seventeenth member after potassium that another alkali metal, rubidium, recurs. The next alkali metal, caesium, is again the seventeenth element after rubidium. Both metals are preceded by elements which are closely related to the last members of the first and second periods. On closer consideration these large periods are found to split up into two smaller periods, in which some of the properties of the elements recur at a shorter interval. This is seen in the following table:

The elements in the same column all have certain properties in common, but only the alternate elements bear a close resemblance to one another. After cerium, Ce, there is a gap of about forty units. This will probably be filled by the rare earth metals, which have not yet been sufficiently well investigated. Then comes ytterbium (the atomic weight of this metal has not been accurately determined) and tantalum; they are followed by elements resembling the former members, in the same order as in the preceding periods, but leaving some gaps and spaces:

The gaps in this and the preceding tables will probably be filled by elements which have not yet been discovered. Several of the gaps which existed when the periodic system of the elements was first promulgated have been filled up by the discovery of scandium, gallium, and germanium, and by the correction of the atomic weights of indium, yttrium, cerium, and lanthanum.

It appears from the table on page 56 that a dozen elements are yet to be discovered. The majority of these gaps will probably be filled by rare earth metals with atomic weights lying between 140 and 180.

This natural and systematic arrangement of the elements, first attempted by Döbereiner and brought to perfection by the labours of Newlands, Mendeléeff and Lothar Meyer, is analogous to the classification in organic chemistry of compounds in homologous and heterologous series.

§ 36. Periodicity of the Physical Properties of the Elements.— If we examine the long series of elements from member to member, we find a change in the properties, sometimes gradual and sometimes sudden, which recurs in the following periods in a similar way, so that almost every property of an element occurs again in one or more of the later members, so that the properties of each individual element are determined by its position in the series. This is not only true of the chemical and physical properties of the elements, but also of the compounds.

This recurrence of the physical properties is very striking in the case of density, which regularly increases and decreases in each period. The connection between density and atomic weight is best exhibited by taking the atomic volume instead of the density-i.e. the volume occupied by the atomic weight instead of the weight of the unit volume. The simplest expression for the atomic volume is obtained by dividing the atomic weight by the density.

These quotients represent the volume of the atoms in the solid state compared with the volume occupied by the unit weight of liquid water as unity. As the absolute weight of an atom of hydrogen is not known, the unit of atomic weights is not known, and this unit of volume must remain