We must now explain one or two terms which are extremely important for understanding what is to follow. The first of these is _Valency_. We know that chemical combinations take place in fixed proportions by weight; this is known as the “Constancy of Composition.” There is always an equivalence noted. This doctrine of equivalence is merely the numerical expression of the definiteness of chemical change. Calculations are made from the point-of-view of combining with a unit-weight of hydrogen (the Unit element). In chemical compounds, then, the doctrine of equivalence says that these atomic weights represent quantities of different elementary substances which are of the same chemical value as measured by their capacity for displacing the same weight of hydrogen. A new property of the atom is thus brought out, _viz._, its value as measured by the number of atoms with which it can combine. This property is appropriately described as the “Valency” of the atom. If the atomic weight contains the equivalent once, _i. e._, if the equivalent and atomic weight are identical, that atom can combine only with one atom of hydrogen, or of chlorine, bromine, etc. The formulæ of the compounds, HCl, HBr, etc., expresses this fact. If the equivalent is contained twice in the atomic weight, then that atom can obviously combine with two atoms of hydrogen, chlorine, etc.; if it is contained three times in the atomic weight, the combining capacity or valency of the atom is three; and so forth. THE PERIODIC LAW The work which had been done upon the atomic weights rendered possible one of the most brilliant generalizations of modern times, in this field. This was the _Periodic Law_. In the year 1864, Newlands published a Table containing the various elements arranged in the order of their atomic weights. In a side column the differences between these weights were given, each being deducted from the one next higher in the scale. The next year, Newlands announced his “law of octaves,” which he deduced from his arrangement of the elements. He said in part that: “If the elements are arranged in the order of their equivalents, with a few slight transpositions ... it will be observed that elements, belonging to the same group usually appear on the same horizontal line.... It will also be seen that the number of analogous elements generally differ either by seven or by some multiple of seven; in other words, members of the same group stand to each other in the same relation as the extremities of one or more octaves in music.” This pioneer work of Newlands rendered possible the Periodic Law, as finally formulated and worked out in detail by Mendeleeff. Briefly, the Law states that “the properties of an element are a periodic function of its atomic weight.”