Kekulé was of opinion that the valency, or affinity-value, of an element was a definite and invariable quantity—a fundamental property of the atom as immutable as its atomic weight. Many facts appear to show that such is not the case. Thus phosphorus and nitrogen are sometimes trivalent and at other times pentavalent; tin, in certain of its compounds, is divalent; in others, tetravalent. Sulphur may be a dyad, a tetrad, or a hexad. It will be seen that the valency of these particular elements varies by two units: this was at one time held to be a natural law, and the various elements were divided by Frankland into the two main groups of (1) _perissads_, or elements of odd atomic value, and (2) _artiads_, or elements of even atomic value. Experience has demonstrated that a rigid classification on this basis is not possible. Many instances are known of elements not only varying in valency by two units, but even by one unit. Thus nitrogen, which is usually a perissad, is apparently an artiad in nitric oxide and in gaseous nitrogen peroxide. Roscoe has shown that uranium and tungsten, originally regarded as artiads, form pentachlorides. To what the difference in the affinity-value of an element is due, and why different elements should manifest different values, is at present unknown. Valency, like other properties, appears to be a periodic function of atomic weight; from the behaviour of such analogous compounds as phosphorus pentafluoride, phosphorus pentachloride, phosphorus pentabromide, it seems, too, to be related to the weights of the atoms in combination. Further, it would appear that the mutual affinities of substances vary with temperature—_i.e._, with the energy imparted to their molecules; numerous instances appear to indicate that the atom-fixing power of an element decreases when it is strongly heated—that is, when the internal energy imparted to its combinations exceeds a certain limiting value. Van ’t Hoff has attempted a mechanical explanation of valency depending on the shape of the atoms, as affected by variation in their vibratory motions resulting from differences of temperature. Helmholtz suggested that the different charges of electricity associated with the atoms may determine their affinity-values—that, for example, a monad carries a single charge, a dyad two, a triad three charges. Many considerations go to show that the affinity-value of an element is not capable of definite numerical expression in the sense which the doctrine of valency as generally understood implies, and that the variations are not of the _per saltum_ character assumed by saying that the affinity-value is sometimes 1, sometimes 2, at other times 3, and so on. When we have apparently satisfied the accepted atomic value of an element by allocating to it what we regard as the necessary complement of atoms of other bodies, it is frequently evident that the capacity for combination of the whole molecule is not satisfied.