Column 17 gives the specific gravity of the elements in a solid and a liquid state. An asterisk (*) is placed by those which can either only be assumed from analogy (for example, the sp. gr. of fluorine and hydrogen, which have not been obtained in a liquid state), or which vary very rapidly with a variation of temperature and pressure (like oxygen and nitrogen), or physical state (for instance, carbon in passing from the state of charcoal to graphite and diamond). But as the sp. gr. in general varies with the temperature, mechanical condition, &c., the figures given, although chosen from the most trustworthy sources, can only be regarded as approximate, and not as absolutely true. They clearly show a certain periodicity; for instance, the sp. gr. diminishes from Al on both sides (Al, Mg, Na, with decreasing atomic weight; and Al, Si, P, S, Cl, with increasing atomic weight, it also diminishes on both sides from Cu, Ru, and Os.) The same remarks refer to the figures in the 18th column, which gives the so-called atomic volumes of the simple bodies, or the quotient of their atomic weight and specific gravity. For Na, K, Rb, and Cs the atomic volume is greatest among the neighbouring elements. For Ni, Pd, and Os it is least, and this indicates the periodicity of this property of the simple bodies. The last (19th) column gives the melting points of the simple bodies. Here also a periodicity is seen, i.e. a maximum and minimum value between which there are intermediate values, as we see, for instance, in the series Cl, K, Ca, Sc, and Ti, or in the series Cr, Mn, Fe, Co, Ni, Cu, Zn, Ga, and Ge. * * * * * CHAPTER XV THE GROUPING OF THE ELEMENTS AND THE PERIODIC LAW It is seen from the examples given in the preceding chapters that the sum of the data concerning the chemical transformations proper to the elements (for instance, with respect to the formation of acids, salts, and other compounds having definite properties) is insufficient for accurately determining the relationship of the elements, inasmuch as this may be many-sided. Thus, lithium and barium are in some respects analogous to sodium and potassium, and in others to magnesium and calcium. It is evident, therefore, that for a complete judgment it is necessary to have, not only qualitative, but also quantitative, exact and measurable, data. When a property can be measured it ceases to be vague, and becomes quantitative instead of merely qualitative.