380 point, crystalline form, &c. Thus calcium carbonate (CaCO) crystallises in rhombic, and also in rhombohedral, forms; the rhombic crystals separate from hot solutions, the rhombohedral from cold solutions; when the rhombic crystals are heated they change to the rhombohedral forms. The molecular and atomic theory cannot as yet be applied to give a detailed explanation of the allotropy of solid elements or compounds. The molecular and atomic theory gives then a partial explanation of the phenomena of isomerism; it represents the change from one isomeride to another as a change in the configuration of a system of atoms; and in the hypothesis of valency it supplies a means whereby these changes may be pictured to the mind with some degree of clearness, and may be expressed in a consistent language. Structural formulae are the most developed forms of chemical language; they express much but not all; of them it may emphatically be said "they are wise men's counters but the money of fools." CHAPTER XVIII. THE PERIODIC LAW. We have now to some extent studied the more important 381 relations which exist between changes of composition and of properties of compounds, and we have seen that there are definite points of connexion between the properties of a compound and the properties of the elements which compose it. The meaning of the term composition widened as we proceeded. At first the composition of a compound was a statement of the quantity of each element combined in a definite quantity of the compound; then it was a statement of the number of combining weights of each element combined in one reacting weight of the compound; then it was a statement of the number of atoms of each element combined in a molecule of the compound; then it was not only a statement of the number, but also an attempted representation of the arrangement, of the atoms which formed the molecule of the compound. As the meaning of composition has become wider, so have the terms in which composition is expressed become more symbolic. The properties of elements and compounds studied have been the properties exhibited in those actions and reactions which result in the production of new elements and compounds. Chemistry considers elements and compounds when they form members of systems undergoing change, rather than when they are isolated from other kinds of matter. Attempts have been made to indicate the methods by which chemists will probably be able to find, and state in quantitative terms, the connexions which certainly exist between the compositions and the chemical functions of compounds. 382 383 We have also glanced at the changes of energy which accompany changes of composition, and we have seen that when equilibrium is attained in a chemical system there is a certain distribution of the members of the system, and also of the energy of the system. We have arranged compounds in classes, such as acids, alkalis, salts, acidic oxides, &c. &c. We have found that all the members of each class shew certain similarities of composition. We have traced some of the connexions between the composition of each class and the typical property or properties of the class. It has been found possible to assign to each member of certain classes of compounds a number, called the affinityconstant of the compound, which tells how much of a specified chemical change will be accomplished under definite conditions by that compound; and it has been found possible to establish the fact that there is a definite relation between this value and the composition of the compound, and, in some cases, to state the nature of this relation. We have traced certain elements through the changes which they undergo by combining with other elements to form compounds belonging to different classes; we have seen the properties of the elements modified by the nature, and relative quantities, of the other elements with which they are combined; but we have not altogether lost sight of the original elements in these changes. Each element to some extent impresses its own properties on all the compounds of which it forms a part. Is it possible then to connect the properties of the compounds of an element, using the term properties in its widest sense, with some one definite and measurable property of the element itself? Can it be shewn that the properties of the compounds vary with variations in the chosen property of the element? If this can be done, we shall have the basis of a satisfactory method of chemical classification both of elements and compounds. We have had instances of a regular variation of properties of similar compounds of a group of allied elements accompanying variations in the atomic weights of these elements (s. especially Chap. XI. par. 182). Various chemists, among whom Newlands must be especially mentioned, from time to time have drawn attention to points of connexion between the properties and the atomic weights of the elements. БІСНУУД Геш In 1864 Newlands arranged a number of elements in order of their atomic weights, and shewed that these elements might be divided into groups of seven, each of which groups to some extent repeated the properties of the next group. "The eighth element" said Newlands "starting from a given element is a kind of repetition of the first, like the eighth note of an octave in music." In subsequent papers Newlands insisted on the general applicability of what he called the law of octaves.' It is however chiefly to Mendelejeff that we owe the systematic correlation of the atomic weights with the chemical and physical properties of the elements, and the properties of their compounds. The properties of the elements and their compounds vary 384 periodically with variations in the atomic weights of the elements. This statement is the outcome of the work of Mendelejeff, Lothar Meyer, Newlands, and many other chemists. This statement, or a statement equivalent to this, is known as the periodic law. The rest of this book will be devoted to an attempt to amplify and explain the periodic law. The properties of the chemical elements and their com- 385 pounds is the phenomenon to be examined; the variable is the atomic weight of the elements: the law asserts that with a continuous change of the variable the phenomenon repeats itself at definite intervals. A quantitative value cannot be given to the phenomenon 'properties of the elements and their compounds.' To illustrate the statement of the periodic law, it is necessary to choose a definite measurable property of the elements, or of a series of similar compounds, and to trace the relation between the variation in the values of this property and the variation in the values of the atomic weights of the elements. We shall choose two properties, one physical, the other partly chemical and partly physical. The properties are (1) the melting points, (2) the atomic volumes, of the elements. The atomic volume of an element is defined to be this quotient represents the volume occupied by a mass of the 386 solid element proportional to the atomic weight of the ele ment. The most striking way of exhibiting the connexion between the variable, atomic weight, and each of the variants, melting point and atomic volume, is to represent the values of the former as lengths marked off on a horizontal line, and the values of the latter as lengths on a vertical line; then, from each pair of points so marked to produce lines until they meet, and to draw a curve cutting the points of intersection of these lines. The curves thus obtained are drawn in the plate on page 269. The melting points are calculated from the initial temperature -273°; the numbers so obtained are divided by 7 in order to bring the curve within manageable limits. The values of the atomic volumes are multiplied by 4 to make the scale of the curve comparable with that of the curve of melting points. Lack of data is indicated by a broken line, or by a gap in the curve. Thus if the elements are arranged in order of increasing atomic weights, nitrogen, oxygen, and fluorine come after carbon and before sodium; but the atomic volumes of these elements are unknown, hence the dotted line in the curve of atomic volumes. Similarly a number of elements come between didymium and tantalum; the gap in the curve indicates that the atomic volumes of these elements have not been determined. The melting points of only about two-thirds of the elements have been determined; hence many parts of the curve of melting points are shewn as dotted lines. The curves shew that the melting points, and the atomic volumes, of the elements vary periodically with variations in the atomic weights of the elements. The value of either variant does not exactly repeat itself at definite intervals; but the elements fall into periods, in each of which the values of the melting point and the atomic volume decrease from a maximum to a minimum, and then again increase to a maximum. The nature of this periodical variation is best shewn by the curve of atomic volumes, as the data are here more abundant. The first period comprises the elements from lithium to sodium; the second, the elements from sodium to potassium; the third, the elements from potassium to rubidium; the fourth, the elements from rubidium to caesium; after caesium there is a great want of data. Elements, the values of whose atomic weights place them about midway between the first and last element of a period, have atomic volumes |