C4 H4 Br2 04, and three dibromo-pyrotartrates (C5 H6 Br2 (4) are formed. We have therefore to explain how it is that these facts, assuming them to be true, are compatible with each other. Kekulé proceeds as follows:

"In accordance with the views relating to the atomicity of the elements which we have previously unfolded on several occasions (see especially § 1369), all the affinities of the atoms comprising the molecule of succinic (or its homologue pyrotartaric) acid are saturated; these acids constitute, in a manner, closed molecules. They contain two atoms of typical oxygen, that is, oxygen bound on to carbon by only one of its two units of affinity. Two hydrogen atoms are united with the carbon only through the intervention of these typical oxygen atoms. These two typical hydrogen atoms are easily displaceable by metals; but there are two other oxygen atoms present which are attached to the carbon by two units of affinity, aud consequently, in the language of the type theory, belong to the radical.

"Now, it is easy to see that, in addition to these two typical hydrogen atoms, succinic has four, and pyrotartaric acid six, more atoms of hydrogen. This hydrogen, which in the language of type theory belongs to the radical, is, according to the theory of the atomicity of the elements, directly combined with the carbon-in fact, in such a manner that two hydrogen atoms are always united with the same carbon atom.

Next, let us assume that two such hydrogen atoms are absent (fehlen) from one or other of these two normal acids; we have, on the one hand, the composition of fumaric and maleic acid, the formulæ of itaconic, citraconic, and mesaconic acid on the other. But since in succinic acid two pairs of such hydrogen atoms are bound to the carbon, two acids may evidently exist with less hydrogen; and similarly, in the case of pyrotartaric acid, we can understand how there may be three isomers with less hydrogen, according to the absence of one or other of the three pairs of hydrogen atoms, which in the normal substance are directly united with the carbon.

"At that place in the molecule whence the two hydrogen atoms are absent, two units of affinity of the carbon are left unsaturated; at that place there is, so to speak, a gap. Hence we can explain the exceptional facility with which these substances unite, by way of addition, with hydrogen or bromine. The free units of affinity of the carbon make an effort to saturate themselves, and so to fill up the gap.

"If hydrogen be introduced into these unoccupied spaces, all carbon atoms within the molecule are united to the same element-hydrogen; there appears no ground for the existence. of differently modified normal substances as so obtained. In

fact, only one succinic and one pyrotartaric acid are at present known.

"If, on the other hand, bromine be put in those same unoccupied spaces, the carbon within the molecule is partly united with hydrogen, partly with bromine; and it is readily perceived that different modifications of such bromo-acids must necessarily exist, according as the bromine finds itself in one or the other of those spaces."

This mode of explanation is now virtually common to all atomic theorists. It is assumed that substances consist of molecules, these again of atoms; that determinate space or position (Stelle) is conceivable without atoms, and exists indeed in their absence; and that into this space there stretch at all times mysterious units of affinity, which, when the atoms are no longer present, strive after combination. But if all chemical substances consist of atoms, and position is possible without them, how can such position be known or determined? According to Hegel, pure being is pure nothing; and we may assign pure position to the same category. But determinate space or position, with the only thing that can determine it taken away, is contradiction itself. Still more unsatisfactory are the units of affinity (Verwandtchaftseinheiten). They cannot be chemical substance, or they would be identical with the atom; they cannot be dynamical units, similar to foot-pounds, for no such integral relations as they would then present have been found in the measurements of chemical action. Yet unquestionably dynamical language is used of them; they are said "to make an effort," "to bind on," "to rivet together," &c. It is much to be deplored that no atomic theorist has yet thrown light on the obscure question of units of affinity, or even stated in clear terms what he means by them. In the absence of any such statement, I shall class them, as pure number, in the roomy category of Hegel.

If any one were to observe under a microscope a small insect with cephalic, thoracic, and abdominal appendages, and were afterwards to assert that these were six in number, there being two of each name—that he had removed two of them, which the insect made a proportionate effort to reunite to its body, and that as the remaining four were removed an increased struggle was manifest-such statements, I say, would be conceivably true. But when language like this is used to explain to me the "structure" of a succinate, I decline to accept either its substance or its form, until the facts alleged of the succinate are put upon the same footing as those asserted of the insect. Until then," units of affinity" may be considered as false an expression as " units of hunger" would be now.

Kekulé himself, by admitting a class of isomers "im engeren

Sinne," has tacitly shown the weakness of the atomic interpretation of isomerism.

Those who consider isomerism explained by such methods as have just been discussed, must understand by an explanation something different from the scientific meaning of that term. A phenomenon is explained when it is shown to be a part or instance of one or more known and more general phenomena. Isomerism is not, therefore, explained by assertions about indivisibles, which have neither been themselves discovered nor shown to have any analogy in the facts or course of nature-nor by explicit statements about a "structure" which has never been seen-nor by the use of a phrase to which no clear definition has been, or can be, attached.

Before isomerism had acquired the importance it now possesses, the great argument in favour of the atomic theory was that the law of multiple and that of definite proportions undeniably represent facts which can be explained only by the existence of atoms. Here the inadequate and idle notion of an "explanation" recurs. I have already (p. 115) exposed the fallacy of supposing that the equational method of arriving at formulæ is any thing more than the arithmetical process of taking the least common multiple-and pointed out the imaginary nature of Dalton's rules (p. 114); and formulæ that have been obtained by these means, in order to affirm the law of multiple or definite proportions, are condemned accordingly. But the exact point of this argument, so far as it has not been alluded to already, lies in the following considerations. Supposing an aqueous solution of hydric chloride be mixed with successive small quantities of sodic hydrate. Several actions occur; but consider for a moment only that one whereby the hydrogen of the hydric chloride is exchanged for sodium. It is quite evident that, on each addition of the sodic hydrate, a new compound ought to be produced containing, say, the whole of the sodium, in the form H, Na, Cl; and as the quantity of the sodium may be varied infinitely at pleasure, an infinite variety of hydrosodic chlorides must, if matter be infinitely divisible, be the result of the process. But not only does such a variety not arise, there is a perfect absence of any hydrosodic compound; for the sole product of the reaction in every case is sodic chloride, Na Cl. Hence it is inferred that matter cannot be infinitely divisible— that there has been a saltus-in short, that atoms exist.

Now this is a question of a constant ratio considered as existing between sodium and chlorine when brought together under conditions which need not be constant. As the mixture is made, the sodium and chlorine are unquestionably divided by being dissolved in a larger quantity of liquid than before. If

10 grammes of sodium were originally present, they now consist of two lots of, say, 5 grammes each. This makes it quite conceivable that, without the addition of any more of the solvent, the division may continue of its own accord, say, into ten lots of 1 gramme each, a thousand lots of a decigramme each, and so on, without limit. The same is true of the chlorine. On endeavouring to prepare a compound from the solution, only one is obtained with an invariable ratio between the sodium and the chlorine. The reason of this phenomenon is presumed to be unknown and to be now sought. I can only say that the fact, from the above point of view, is as conceivable on the supposition of continuous as it is upon that of limited division. Two phenomena continuously proceeding without obvious end (mathematical "infinites") are well known to be capable of a finite ratio. Through one point an infinite number of curves may be drawn. The neutralization of aqueous hydric chloride is something like the process of differentiation, and its result, a constant finite ratio, like a differential coefficient. Or take as an illustration the properties of the machine known as the "geometric chuck." By a suitable combination of circular movements, this beautiful instrument is capable of describing an endless variety of curves, one of which is roughly represented in the margin: such a figure is drawn by a motion which is visibly continuous, even at the three points, throughout the entire period of delineation; when it has been described, the machine proceeds to draw an exactly similar triangle, which it accurately superimposes on the first, and so on, to any number of triangles. The number of points in the figure is regulated by previous adjustment of the constants of the machine; but the mass of the instrument, its rate of motion, and the number of times it is resolved (beyond the constructionminimum) have nothing to do with the resulting figure. The definite proportions of chemistry, in like manner, precede or accompany each of our experiments; they are independent of mass, rate of action, repetition of action; and doubtless they are produced, like these points, by compound uninterrupted motion. They certainly suggest nothing that is by nature atomic. These mathematical conceptions, however, involve no breach of continuity, which is rather their essential condition; and the chemical phenomenon is at least as conceivable as they are without introducing the supposition of a limit.

I may adduce the process of diffusion as one that, in accordance with the large number of experiments already made, is probably capable of continuance without any clear reason for a limit. Yet if matter consisted of indivisibles, some sign, at any rate, of

a limit ought to have been by this time detected. The continuity of the gaseous and liquid states furnishes a strong experimental presumption against any kind of constitution of matter, corpuscular or otherwise. The atomic conception of definite proportions is therefore not only not absolutely necessary, but doubly improbable.

The law of definite proportions, indeed, is itself tinged with continuity. It represents one side only of the series of bodies, which includes mechanical mixtures on the one hand, definite compounds on the other, and indefinite substances (like albumen) as its middle term. Even should much more refined methods of determining a symbolic value be discovered than we now possess, the law of homology is an instant prophet of their weakness; starting with almost perfect definition, it ever points to some possible transcendent complexity.

Such is the nature of the arguments involved in ratiocination upon a materialistic basis. Matter, it is asserted, must be either infinitely or finitely divisible, as if either conception had ever been realized by the interlocutor. What if matter do not exist at all? And if it exist, where is the proof that it and division have any mutual connexion whatever? It is these prior questions that chemists, as a rule, never raise, or dismiss as fruitlessforgetting that in philosophy, the storehouse of the most general propositions of all the sciences, they have their only court of appeal. Under the impression of these convictions, I now proceed to give an abstract of Digby's* most able argument on the nature of quantity, a subject which evidently involves the atomic theory among its component questions.

In the first place, Digby investigates the meaning tacitly or otherwise assigned to the idea of quantity by the learned as well as the uninstructed. "If you ask what quantity there is of such a parcell of cloth, how much wood in such a piece of timber, how much gold in such an ingot, how much wine in such a vessel, how much time was taken up in such an action? he that is to give you an account of them measureth them by ells, by feet, by inches, by pounds, by ounces, by gallons, by pints, by dayes, by houres, and the like; and then telleth you how many of those parts are in the whole that you enquire of.... Wherefore, when we consider that Quantity is nothing else, but the extension of a thing; and that this extension is expressed by a determinate number of lesser extensions of the same nature; (which lesser ones, are sooner and more easily apprehended then greater; because we are first acquainted and conversant with such; and our understanding graspeth, weigheth and discerneth such more steadily; and maketh an exacter judgment of then ;) *On the Natvre of Bodies (1645), p. 11 et seq.