ART. XLI.-The Numerical Relation between the Atomic Weights, with some Thoughts on the Classification of the Chemical Elements; by JosIAH P. COOKE, Jr., A.M., Erving Professor of Chemistry in Harvard University.*

NUMERICAL relations between the atomic weights of the chemical elements have been very frequently noticed by chemists. One of the fullest expositions of these relations was that given by M. Dumas of Paris, before the British Association for the Advancement of Science, at the meeting of 1851. This distinguished chemist at that time pointed out the fact, that many of the elements might be grouped in triads, in which the atomic weight of one was the arithmetical mean of those of the other two. Thus the atomic weight of bromine is the mean between those of chlorine and iodine; that of selenium is the mean between those of sulphur and tellurium, and that of sodium, the mean between those of lithium and potassium. M. Dumas also spoke of the remarkable analogies between the properties of the members of these triads, comparing them with similar analogies observed in organic chemistry, and drew, as is well known, from these facts arguments to support the hypothesis of the compound nature of many of the now received elements. Similar views to those of Dumas have been advanced by other chemists.

The doctrine of triads is, however, as I hope to be able to show in the present memoir, a partial view of this subject, since these triads are only parts of series similar in all respects to the series of homologues of organic chemistry, in which the differences between the atomic weights of the members is a multiple of some whole number. All the elements may be classified into six series, in each of which this number is different, and may be said to characterize its series. In the first it is nine, in the second eight, in the third six, in the fourth five, in the fifth four, and in the last three. The discovery of this simple numerical relation, which includes all others that have ever been noticed, was the result of a classification of the chemical elements made for the purpose of exhibiting their analogies in the lecture-room. A short notice of this classification will, therefore, make a natural introduction to the subject.

Every teacher of chemistry must have felt the want of some system of classification like those which so greatly facilitate the acquisition of the natural-history sciences. In most elementary text-books on chemistry, the elements are grouped together with little regard to their analogies. Oxygen, hydrogen, and nitrogen are usually placed first, and therefore together, although there are hardly to be found three elements more dissimilar; again, phos

* Communicated to the American Academy, Boston, Feb. 28, 1854.

phorus and sulphur, which are not chemically allied, are frequently placed consectively, while arsenic, antimony, and bismuth in spite of their close analogies with phosphorus, are described in a different part of the book. This confusion, which arises in part from retaining the artificial classification of the elements into metals and metalloids, is a source of great difficulty to the learner, since it obliges him to retain in his memory a large number of apparently disconnected facts. In order to meet this difficulty, a classification of the elements into six groups, differing but slightly from that given in the table accompanying this memoir, was made. The object of the classification was simply to facilitate the acquisition of chemistry, by bringing together such elements as were allied in their chemical relations considered collectively. As the classification has been in use for some time in the courses of lectures on chemistry given in Harvard University, I have had an opportunity for observing its value in teaching, and cannot but feel that the object for which it was made has been in a great measure attained. The series which is headed the Six Series will illustrate the advantage gained from the classification in a course of lectures, the elements which compose it being among those especially dwelt upon in lectures to medical students, and, generally, very widely separated in a text-book on the science. As chemistry is usually taught, the properties of the members of this series, nitrogen, phosphorus, arsenic, and antimony, as well as the composition and properties of their compounds, make up a large body of isolated facts, which, though without any assistance for his memory, the student is expected to retain. Certainly it cannot be wondered at, that he finds this a difficult task. The difficulty can, however, be in a great measure removed, if, after he has been taught that nitrogen forms two important acids with oxygen, NO3 and NOs, that it unites with sulphur and chlorine to form NS3 and NC13, and also with three equivalents of hydrogen to form NH 3, he is also told, that, if in these symbols of the nitrogen compounds he replaces N by P, As, or Sb, he will obtain. symbols of similar compounds of phosphorus, arsenic, and antimony; for he thus learns, once for all, the mode of combination of all four elements, so that when he comes to study the properties, in turn, of phosphorus, arsenic, and antimony, he has not to learn with each an entirely new set of facts, but finds the same repeated with only a few variations. Moreover, these very variations he will learn to predict, if he is shown that the elements are arranged in the series according to the strength of their electro-negative properties, or, in other words, that their affinities for oxygen, chlorine, sulphur, etc. increase, while those for hydrogen decrease, as we descend. He will then readily see why it is that, though nitrogen forms NO and NOs, it forms only NCIs and NS3, and that this reason is correct he will be pleased to find

confirmed when he learns that phosphorus, which is more electropositive than nitrogen, and has, therefore, a stronger affinity both for chlorine and sulphur, forms not only PC13 and PS3, but also PCL5 and PS5. Again, he will not be surprised, after seeing the affinity of the elements for hydrogen growing constantly weaker as he descends in the series, to learn that a compound of bismuth and hydrogen is not certainly known. Should he inquire why, though NH3 has basic properties, PH3, AsH 3, and SbH 3 have not, he can be shown that the loss of basic properties in passing from NH 3 to PH 3 corresponds to a decrease in the strength of the affinity between the elements, and that if in PH 3, SbH 3, or AsH 3, atoms of methyle, ethyle, or other organic radicals analogous to hydrogen, are substituted for the hydrogen atoms, and more stable compounds thus obtained, strong bases are the result. The other series would afford similar illustrations, and, from my own experience, I am confident that no teacher who has once used a classification of the elements like that here proposed, would ever think of attempting to teach chemistry without its aid.

Classifications of the elements, more or less complete, have been given by many authors; but the fact that no one has been generally received, is sufficient to prove that they are all liable to objections, and would, indeed, also seem to show that a strictly scientific classification is hardly possible in the present state of the science. The difficulty with most of the classifications is, undoubtedly, that they are too one-sided, based upon one set of properties to the exclusion of others, and often on seeming, rather than real resemblances. This is the difficulty with the old classification into metals and metalloids, which separated phosphorus and arsenic, sulphur and selenium, because arsenic and selenium have a metallic lustre, while phosphorus and sulphur have not, though there could hardly be found another point of difference. For a zoologist to separate the ostrich from the class of birds because it cannot fly, would not be more absurd, than it is for a chemist to separate two essentially allied elements, because one has a metallic lustre and the other has not. Yet it is surprising to see how persistently this classification is retained in every elementary work on the science; and if it is sometimes so far modified as to transfer elements analogous to selenium and arsenic to the class of metalloids, this is only acknowledging the worthlessness of the principle, without being willing to abandon it. If there were any fundamental property common to all the elements, the law of whose variation was known, this might serve as the basis of a correct classification. Chemistry, however, does not as yet present us with such a property, and we must, therefore, here, as in other sciences, base our classification on general analogies. The most fundamental of all chemical properties is, unSECOND SERIES, Vol. XVII, No. 51.-May, 1854.

50

doubtedly, crystalline form; but a classification of the elements based solely on the principles of isomorphism is defective in the same way as it is in mineralogy. It brings together, undoubtedly, allied elements, but it also groups with them those which resemble each other only in their crystalline form. The inode of combining seems to be also a fundamental property; but, like crystalline form, it would bring together in some instances elements differing very widely in their chemical properties. A classification of the elements which shall exhibit their natural affinities, must obviously pay regard to both of these properties. It must at the same time seek to group together isoinorphous elements, and those which form analogous compounds. Moreover, in such a classification, other less fundamental properties must not be disregarded. There are many properties both physical and chemical, which, although they cannot be exactly measured, and are oftentimes difficult to define, (such properties as those by which a chemist recognizes a familiar substance, or a mineralogist a familiar mineral,) and which ou account of their indefinite character cannot be used as a basis of classification, may, nevertheless, render important aid in tracing out analogies. Judging from such properties as these, chemists are generally agreed in grouping together carbon, boron, and silicon, although they cannot be proved to be isomorphous, and are not generally thought to form similar compounds.

It is, however, much easier to point out what a classification should be, than to make one which shall fulfil the required conditions. Indeed, as has been already said, past experience would seem to show that a perfect scientific classification of the elements is hardly possible in the present state of chemistry. At best, the task is attended with great difficulties, and it cannot be expected that these should be surmounted at once. The classification which is offered in this memoir will, undoubtedly, be found to contain many defects. If, however, it is but one step in advance of those which have preceded it, it will be of value to the science. It was originally made, as has already been said, simply for the purpose of teaching, and never would have been published had it not led to the discovery of the numerical relation between the atomic weights.

On turning to the table which accompanies this memoir, it will be seen that the elements have been grouped into six series. These correspond entirely to the series of homologues of organic chemistry. In the group of volatile acids, homolognes of formic acid, for example, we have a series of compounds yielding similar derivatives, and producing similar reactions, and many of whose properties, such as boiling and melting points, specific gravity, etc., vary as we descend in the series according to a determinate law. From formic acid, a highly limpid, volatile, and corrosive fluid,

the acids become less and less volatile, less and less finid, less and less corrosive; first oily, then fat-like, and finally hard, brittle solids, like wax. As is well known, the composition of these acids varies in the same way, and the variation follows a regular law, so that by means of a general symbol we can express the composition of the class. This symbol for the volatile acids may be written (CH)O3, HO+n(C 2 H 2 ).

This description of the well-known series of the volatile acids, applies, word for word, nominibus mutatis, to each of the six series of chemical elements. The elements of any one series form similar compounds and produce similar reactions; moreover, they resemble each other in another respect in which the members of the organic series do not. Their crystalline forms are the same, or, in other words, they are isomorphous. Although this may be true of the volatile acids, yet it cannot be proved in the present state of our knowledge. Still further, many of their properties vary in a regular manner as we descend in the series. In one case, at least, the law of the variation is known, and can be expressed algebraically, though in most instances it cannot be determined. Finally, as one general symbol will express the composition of a whole organic series, so a simple algebraic formula will express the atomic weight, or, if you may please so to term it, the constitution of a series of elements.

These points may be illustrated with any of the series in the table; with the first, for example, which consists of oxygen, fluorine, cyanogen, chlorine, bromine, and iodine. All these elements form similar compounds, as will be seen by inspecting the symbols of their compounds given at the right hand of the list of names, where the similar or homologous compounds are arranged in upright columns. Moreover, they are all isomorphous, as may be seen by referring to the left-hand side of the list, where the similar compounds in each upright series are isomorphous, the numbers at the heads of the columns indicating the systems of crystallization, as described in the explanation accompanying the table. That the properties of these elements vary as we descend, can be easily shown. Oxygen is a permanent gas, as is also fluorine. Cyanogen is a gas, but may be condensed to a liquid. Chlorine, a gas also, can be condensed more easily than cyanogen. Bromine is a fluid at the ordinary temperature; and, finally, iodine is a solid. Moreover, starting from cyanogen, the solubility of these elements in water decreases as we descend in the series; and, again, the specific gravity of their vapors follows the inverse order of progression, gradually increasing from oxygen down. The atomic weights vary in the same order, and admit of a general expression, which is 8+n9, or, in other words, the differences between the atomic weights of these elements are always a multiple of nine. This general formula may be said to repre