It will be seen that a gap is left where the eighth member of the first part of this period should be, an element which would correspond, in this period, with manganese in the period above. This element is at present unknown. The remaining elements belong to three other long periods, in which, however, the number of gaps is very considerable, thus

Those elements that fall in the first eight places of the long periods are termed the even series, while the last seven are distinguished as the odd series; arranging them, therefore, in such a manner as to bring the odd and even series into columns, we get the table on page 117.

In this manner the elements are arranged in nine groups. The first of these groups contains the so-called "inert gases"the five new elements of recent discovery, which take their place rather outside this classification scheme, regarding it from a purely chemical standpoint. And as the system of numbering the groups of elements in this periodic arrangement has become familiarised by long use, this group containing the "inert gases" has been numbered Group O, and the systematic numbering of the other groups begins as usual. The last group contains the transitional elements that come between the even and odd series of the long periods.

In each of the remaining seven groups, the elements belonging

to the even series of their respective long periods, are placed to the left, while those belonging to the odd series are arranged on the right-hand side of each vertical column. In this way the groups are divided into the subdivisions A and B, in which the resemblance between the members is most pronounced. Thus in Group II., although there are certain properties common to all the members, there is a much closer similarity existing between the elements calcium, strontium, and barium than between zinc and calcium, or cadmium and barium.* The elements in the two short periods have been placed in that subdivision or family with the members of which they exhibit the closest resemblance. Thus, in Group I. lithium and sodium are more allied to potassium, rubidium, and caesium, than to copper, silver, and gold; while in Group VII. fluorine and chlorine are placed in the same family with bromine and iodine, with which they exhibit a close similarity.

In the eighth group, containing the transitional elements, the families consist of the horizontal and not the vertical rows; that is to say, the closest resemblance is between the three transitional elements in each series, elements whose atomic weights, instead of exhibiting a regular increase, as in the other families, have almost the same value, such as Fe = 56; Co: 59; Ni = 59.

=

A glance at the table shows that in the last three long periods there is a large number of gaps. It is possible that these gaps may represent elements which yet await discovery. This supposition gains considerable support from the fact, that at the time Mendelejeff first formulated the periodic law, there were three such gaps in the first long period, which have since been filled up by the subsequent discovery of three new elements; these will be referred to later.

The periodic recurrence of some of the chemical properties is indicated in the lowest horizontal column, where the general formulæ of the oxygen compounds and the hydrides are given; R standing for one atom of any element in the group. As explained on page 113, these formulæ are so written as to show the relative amount of oxygen to two atoms of element, in order to establish the true relation between the different groups. For example, the

*This, however, is by no means uniformly the case; thus the element copper (Group I.) in many of its chemical attributes is much more closely allied to mercury (Group II.) than to silver; and silver, again, more strongly resembles thallium (Group III.) than either copper or gold, with which it is associated in this system of classification.

oxides of the elements of Group I. contain two atoms of the element to one of oxygen, as Li,O; but those of the second group only contain one atom of the element, as CaO : hence the general formula is doubled, RO2. It will be seen, therefore, that the proportion of oxygen relative to two atoms of the element regularly increases from the first group to the eighth. The oxides of the members of Group I. are strongly basic in character, and in general this basic nature gradually diminishes as we traverse the series, giving place to acidic characteristics, which are strongly marked in the seventh group.

The periodic reappearance of the physical properties of the elements is seen in such points as their electrical characters, their malleability, ductility, melting-points, &c., all of which are in harmony with the periodic law; but in none is it more strikingly seen than in their atomic volumes in the solid state. The atomic volumes of the elements are the relative volumes occupied by quantities proportional to their atomic weights, or by grammeatoms; and they are obtained by dividing the atomic weights of the elements by their specific gravities. In the case of gases, as has been already explained on page 40, the specific gravity is the density referred to hydrogen as the unit: the atomic volume, therefore, of such a gas as oxygen is―

The specific gravities of solids (and also liquids) are referred to water as the unit, and as I cubic centimetre of water weighs I gramme, the specific gravity of a solid or liquid expresses the weight in grammes of I cubic centimetre of the substance. Dividing the atomic weight, expressed in grammes, by the weight in grammes of I cubic centimetre (ie. the specific gravity), the atomic volume will be represented in cubic centimetres. It must be remembered that the atomic volumes do not express the relative volumes that are actually occupied by the atoms, they represent in reality the relative volume of the atoms plus the unknown volumes of the spaces that separate them.

The following table gives the specific gravities and the calculated atomic volumes of the first and the middle elements of the two short and two long periods, not counting the group of "inert" elements :

From the figures in the last column it will be seen, that beginning with lithium, 11.9, the atomic volume falls as the middle element of the period, namely, carbon, is reached; after which it again rises and reaches a maximum with the first member of the second period, namely, sodium. In this period the same gradual fall in atomic volume is again noticed until the middle element (silicon) is reached, when the value of this function of the elements once more rises, and a second maximum is attained with the first member (potassium) of the third period. The two next are long periods, and the atomic volumes steadily decrease until the middle three (transitional) elements, after which they gradually increase again to a maximum in rubidium, the starting-point of the fourth period. In the fourth period the same thing once more occurs, the minimum atomic volumes being those of the middle or transition elements, after which a maximum is again reached in caesium.

This periodicity of the atomic volumes may be graphically represented by a curve, where the ordinates represent atomic volumes and the abscissæ atomic weights. This curve, which was first constructed by Lothar Meyer, is known as Lothar Meyer's curve (page 120), and a comparison of it with Mendelejeff's table is most instructive.

The divisions indicated by the Roman numerals correspond to the different periods: Groups I. and II. being the two short periods, III. and IV. the two complete long periods, while V., VI., and VII. correspond to the fragmentary portions of the last three periods.

The transitional elements of periods III., IV., and VI. are all to be found at the minima of the large hollows; separating the even series (situated on the descending portion of the curve) from the odd series which lie on the ascending slope The elements belong