I. ATTEMPTS TO CONCEIVE ELEMENTARY COMPOSITION…

I. ATTEMPTS TO CONCEIVE ELEMENTARY COMPOSITION

1. WE have now to bring into view, if possible, the Ideas and General Principles which are involved in Chemistry,--the science of the composition of bodies. For in this as in other parts of human knowledge, we shall find that there are certain Ideas, deeply seated in the mind, though shaped and unfolded by external observation, which are necessary conditions of the existence of such a science. These Ideas it is, which impel man to such a knowledge of the Composition of bodies, which give meaning to facts exhibiting this composition, and universality to special truths discovered by experience. These are the Ideas of Element and of Substance.

Unlike the Idea of Polarity, of which we treated in the last Book, these Ideas have been current in men's minds from very early times, and formed the subject of some of the first speculations of philosophers. It happened however, as might have been expected, that in the first attempts they were not clearly distinguished from other notions, and were apprehended and applied in an obscure and confused manner. We cannot better exhibit the peculiar character and meaning of these Ideas than by tracing the form which they have assumed {4} and the efficacy which they have exerted in these successive essays. This, therefore, I shall endeavour to do, beginning with the Idea of Element.

2. That bodies are composed or made up of certain parts, elements, or principles, is a conception which has existed in men's minds from the beginning of the first attempts at speculative knowledge. The doctrine of the Four Elements, Earth, Air, Fire and Water, of which all things in the universe were supposed to be constituted, is one of the earliest forms in which this conception was systematized; and this doctrine is stated by various authors to have existed as early as the times of the ancient Egyptians[1\6]. The words usually employed by Greek writers to express these elements are ἀρχὴ a principle or beginning, and στοιχεῖον, which probably meant a letter (of a word) before it meant an element of a compound. For the resolution of a word into its letters is undoubtedly a remarkable instance of a successful analysis performed at an early stage of man's history; and might very naturally supply a metaphor to denote the analysis of substances into their intimate parts, when men began to contemplate such an analysis as a subject of speculation. The Latin word elementum itself, though by its form it appears to be a derivative abstract term, comes from some root now obsolete; probably[2\6] from a word signifying to grow or spring up.

[Note 1\6: Gilbert's Phys. 1. i. c. iii.]

[Note 2\6: Vossius in voce. "Conjecto esse ab antiqua voco eleo pro oleo, id est cresco: a qua signiflcatione proles, suboles, adolescens: ut ab juratum, juramentum; ab adjutum, adjumentum: sic ab eletum, elementum: quia inde omnia crescunt ac nascuntur."]

The mode in which elements form the compound bodies and determine their properties was at first, as might be expected, vaguely and variously conceived. It will, I trust, hereafter be made clear to the reader that the relation of the elements to the compound involves a peculiar and appropriate Fundamental Idea, not susceptible of being correctly represented by any comparison or combination of other ideas, and guiding us to clear and definite results only when it is illustrated {5} and nourished by an abundant supply of experimental facts. But at first the peculiar and special notion which is required in a just conception of the constitution of bodies was neither discerned nor suspected; and up to a very late period in the history of chemistry, men went on attempting to apprehend the constitution of bodies more clearly by substituting for this obscure and recondite idea of Elementary Composition, some other idea more obvious, more luminous, and more familiar, such as the ideas of Resemblance, Position, and mechanical Force. We shall briefly speak of some of these attempts, and of the errours which were thus introduced into speculations on the relations of elements and compounds.

3. Compounds assumed to resemble their Elements.--The first notion was that compounds derive their qualities from their elements by resemblance:--they are hot in virtue of a hot element, heavy in virtue of a heavy element, and so on. In this way the doctrine of the four elements was framed; for every body is either hot or cold, moist or dry; and by combining these qualities in all possible ways, men devised four elementary substances, as has been stated in the History[3\6].

[Note 3\6: Hist. Ind. Sc. b. i. c. ii. sec. 2.]

This assumption of the derivation of the qualities of bodies from similar qualities in the elements was, as we shall see, altogether baseless and unphilosophical, yet it prevailed long and universally. It was the foundation of medicine for a long period, both in Europe and Asia; disorders being divided into hot, cold, and the like; and remedies being arranged according to similar distinctions. Many readers will recollect, perhaps, the story[4\6] of the indignation which the Persian physicians felt towards the European, when he undertook to cure the ill effects of cucumber upon the patient, by means of mercurial medicine: for cucumber, which is cold, could not be counteracted, they maintained, by mercury, which in their classification is cold also. Similar views of the operation of medicines might {6} easily be traced in our own country. A moment's reflection may convince us that when drugs of any kind are subjected to the chemistry of the human stomach and thus made to operate on the human frame, it is utterly impossible to form the most remote conjecture what the result will be, from any such vague notions of their qualities as the common use of our senses can give. And in like manner the common operations of chemistry give rise, in almost every instance, to products which bear no resemblance to the materials employed. The results of the furnace, the alembic, the mixture, frequently have no visible likeness to the ingredients operated upon. Iron becomes steel by the addition of a little charcoal; but what visible trace of the charcoal is presented by the metal thus modified? The most beautiful colours are given to glass and earthenware by minute portions of the ores of black or dingy metals, as iron and manganese. The worker in metal, the painter, the dyer, the vintner, the brewer, all the artisans in short who deal with practical chemistry, are able to teach the speculative chemist that it is an utter mistake to expect that the qualities of the elements shall be still discoverable, in an unaltered form, in the compound. This first rude notion of an element, that it determines the properties of bodies by resemblance, must be utterly rejected and abandoned before we can make any advance towards a true apprehension of the constitution of bodies.

[Note 4\6: See Hadji Baba.]

4. This step accordingly was made, when the hypothesis of the four elements was given up, and the doctrine of the three Principles, Salt, Sulphur, and Mercury, was substituted in its place. For in making this change, as I have remarked in the History[5\6], the real advance was the acknowledgment of the changes, produced by the chemist's operations, as results to be accounted for by the union and separation of substantial elements, however great the changes, and however unlike the product might be to the materials. And this step once made, chemists went on constantly {7} advancing towards a truer view of the nature of an element, and consequently, towards a more satisfactory theory of chemical operations.

[Note 5\6: Hist. Ind. Sc. b. iv. c. 1.]

5. Yet we may, I think, note one instance, even in the works of eminent modern chemists, in which this maxim, that we have no right to expect any resemblance between the elements and the compound, is lost sight of. I speak of certain classifications of mineral substances. Berzelius, in his System of Mineral Arrangement, places sulphur next to the sulphurets. But surely this is an errour, involving the ancient assumption of the resemblance of elements and compounds; as if we were to expect the sulphurets to bear a resemblance to sulphur. All classifications are intended to bring together things resembling each other: the sulphurets of metals have certain general resemblances to each other which make them a tolerably distinct, well determined, class of bodies. But sulphur has no resemblances with these, and no analogies with them, either in physical or even in chemical properties. It is a simple body; and both its resemblances and its analogies direct us to place it along with other simple bodies, (selenium, and phosphorus,) which, united with metals, produce compounds not very different from the sulphurets. Sulphur cannot be, nor approach to being, a sulphuret; we must not confound what it is with what it makes. Sulphur has its proper influence in determining the properties of the compound into which it enters; but it does not do this according to resemblance of qualities, or according to any principle which properly leads to propinquity in classification.

6. Compounds assumed to be determined by the Figure of Elements.--I pass over the fanciful modes of representing chemical changes which were employed by the Alchemists; for these strange inventions did little in leading men towards a juster view of the relations of elements to compounds. I proceed for an instant to the attempt to substitute another obvious conception for the still obscure notion of elementary composition. It was imagined that all the properties of bodies and their mutual operations might be {8} accounted for by supposing them constituted of particles of various forms, round or angular, pointed or hooked, straight or spiral. This is a very ancient hypothesis, and a favourite one with many casual speculators in all ages. Thus Lucretius undertakes to explain why wine passes rapidly through a sieve and oil slowly, by telling us that the latter substance has its particles either larger than those of the other, or more hooked and interwoven together. And he accounts for the difference of sweet and bitter by supposing the particles in the former case to be round and smooth, in the latter sharp and jagged[6\6]. Similar assumptions prevailed in modern times on the revival of the mechanical philosophy, and constitute a large part of the physical schemes of Descartes and Gassendi. They were also adopted to a considerable extent by the chemists. Acids were without hesitation assumed to consist of sharp pointed particles; which, 'I hope,' Lemery says[7\6], 'no one will dispute, seeing every one's experience does demonstrate it: he needs but taste an acid to be satisfied of it, for it pricks the tongue like anything keen and finely cut.' Such an assumption is not only altogether gratuitous and useless, but appears to be founded in some degree upon a confusion in the metaphorical and literal use of such words as keen and sharp. The assumption once made, it was easy to accommodate it, in a manner equally arbitrary, to other facts. 'A demonstrative and convincing proof that an acid does consist of pointed parts is, that not only all acid salts do crystallize into edges, but all dissolutions of different things, caused by acid liquors, do assume this figure in their crystallization. These crystals consist of points differing both in length and bigness one from another, and this diversity must be attributed to the keener or blunter edges of the different sorts of acids: and so likewise this difference of the points in subtilty is the cause that one acid can penetrate and dissolve with one sort of mixt, that another can't rarify at all: Thus vinegar dissolves lead, {9} which aqua fortis can't: aqua fortis dissolves quicksilver, which vinegar will not touch; aqua regalis dissolves gold, whenas aqua fortis cannot meddle with it; on the contrary, aqua fortis dissolves silver, but can do nothing with gold, and so of the rest.'

[Note 6\6: De Rerum Natura, ii. 390 sqq.]

[Note 7\6: Chemistry, p. 25.]

The leading fact of the vehement combination and complete union of acid and alkali readily suggested a fit form for the particles of the latter class of substances. 'This effect,' Lemery adds, 'may make us reasonably conjecture that an alkali is a terrestrious and solid matter whose forms are figured after such a manner that the acid points entering in do strike and divide whatever opposes their motion.' And in a like spirit are the speculations in Dr. Mead's Mechanical Account of Poisons (1745). Thus he explains the poisonous effect of corrosive sublimate of mercury by saying[8\6] that the particles of the salt are a kind of lamellæ or blades to which the mercury gives an additional weight. If resublimed with three-fourths the quantity of mercury, it loses its corrosiveness, (becoming calomel,) which arises from this, that in sublimation 'the crystalline blades are divided every time more and more by the force of the fire:' and 'the broken pieces of the crystals uniting into little masses of differing figures from their former make, those cutting points are now so much smaller that they cannot make wounds deep enough to be equally mischievous and deadly: and therefore do only vellicate and twitch the sensible membranes of the stomach.'

[Note 8\6: P. 199.]

7. Among all this very fanciful and gratuitous assumption we may notice one true principle clearly introduced, namely, that the suppositions which we make respecting the forms of the elementary particles of bodies and their mode of combination must be such as to explain the facts of crystallization, as well as of mere chemical change. This principle we shall hereafter have occasion to insist upon further.

I now proceed to consider a more refined form of assumption respecting the constitution of bodies, yet {10} still one in which a vain attempt is made to substitute for the peculiar idea of chemical composition a more familiar mechanical conception.

8. Compounds assumed to be determined by the Mechanical Attraction of the Elements.--When, in consequence of the investigations and discoveries of Newton and his predecessors, the conception of mechanical force had become clear and familiar, so far as the action of external forces upon a body was concerned, it was very natural that the mathematicians who had pursued this train of speculation should attempt to apply the same conception to that mutual action of the internal parts of a body by which they are held together. Newton himself had pointed the way to this attempt. In the Preface to the Principia, after speaking of what he has done in calculating the effects of forces upon the planets, satellites, &e., he adds, 'Would it were permitted us to deduce the other phenomena of nature from mechanical principles by the same kind of reasoning. For many things move me to suspect that all these phenomena depend upon certain forces, by which the particles of bodies, through causes not yet known, are either urged towards each other, and cohere according to regular figures, or are repelled and recede from each other; which forces being unknown, philosophers have hitherto made their attempts upon nature in vain.' The same thought is at a later period followed out further in one of the Queries at the end of the Opticks[9\6]. 'Have not the small particles of bodies certain Powers, Virtues, or Forces, by which they act at a distance, not only upon the rays of light for reflecting, refracting and inflecting them, but also upon one another for producing a great part of the phenomena of nature?' And a little further on he proceeds to apply this expressly to chemical changes. 'When Salt of Tartar runs per deliquium [or as we now express it, deliquesces] is not this done by an attraction between the particles of the Salt of Tartar and the particles of the water which float in the air in {11} the form of vapours? And why does not common salt, or saltpetre, or vitriol, run per deliquium, but for want of such an attraction? or why does not Salt of Tartar draw more water out of the air than in a certain proportion to its quantity, but for want of an attractive force after it is saturated with water?' He goes on to put a great number of similar cases, all tending to the same point, that chemical combinations cannot be conceived in any other way than as an attraction of particles.

[Note 9\6: Query 31.]

9. Succeeding speculators in his school attempted to follow out this view. Dr. Frend, of Christ Church, in 1710, published his Prælectiones Chymicæ, in quibus omne fere Operationes Chymicæ ad vera Principia ex ipsius Naturæ Legibus rediguntur. Oxonii habitæ. This book is dedicated to Newton, and in the dedication, the promise of advantage to chemistry from the influence of the Newtonian discoveries is spoken of somewhat largely,--much more largely, indeed, than has yet been justified by the sequel. After declaring in strong terms that the only prospect of improving science consists in following the footsteps of Newton, the author adds, 'That force of attraction, of which you first so successfully traced the influence in the heavenly bodies, operates in the most minute corpuscles, as you long ago hinted in your Principia, and have lately plainly shown in your Opticks; and this force we are only just beginning to perceive and to study. Under these circumstances I have been desirous of trying what is the result of this view in chemistry.' The work opens formally enough, with a statement of general mechanical principles, of which the most peculiar are these:--'That there exists an attractive force by which particles when at very small distances from each other, are drawn together;--that this force is different, according to the different figure and density of the particles;--that the force may be greater on one side of a particle than on the other;--that the force by which particles cohere together arises from attraction, and is variously modified according to the quantity of contacts.' But these principles are not {12} applied in any definite manner to the explanation of specific phenomena. He attempts, indeed, the question of special solvents[10\6]. Why does aqua fortis dissolve silver and not gold, while aqua regia dissolves gold and not silver? which, he says, is the most difficult question in chemistry, and which is certainly a fundamental question in the formation of chemical theory. He solves it by certain assumptions respecting the forces of attraction of the particles, and also the diameter of the particles of the acids and the pores of the metals, all which suppositions are gratuitous.

[Note 10\6: P. 54.]

10. We may observe further, that by speaking, as I have stated that he does, of the figure of particles, he mixes together the assumption of the last section with the one which we are considering in this. This combination is very unphilosophical, or, to say the least, very insufficient, since it makes a new hypothesis necessary. If a body be composed of cubical particles, held together by their mutual attraction, by what force are the parts of each cube held together? In order to understand their structure, we are obliged again to assume a cohesive force of the second order, binding together the particles of each particle. And therefore Newton himself says[11\6], very justly, 'The parts of all homogeneal hard bodies which fully touch each other, stick together very strongly: and for explaining how this is, some have invented hooked atoms, which is begging the question.' For (he means to imply,) how do the parts of the hook stick together?

[Note 11\6: Opticks, p. 364.]

The same remark is applicable to all hypotheses in which particles of a complex structure are assumed as the constituents of bodies: for while we suppose bodies and their known properties to result from the mutual actions of these particles, we are compelled to suppose the parts of each particle to be held together by forces still more difficult to conceive, since they are disclosed only by the properties of these particles, which as yet are unknown. Yet Newton himself has not abstained from such hypotheses: thus he says[12\6], 'A particle of {13} a salt may be compared to a chaos, being dense, hard, dry, and earthy in the center, and moist and watery in the circumference.'

[Note 12\6: Opticks, p. 362.]

Since Newton's time the use of the term attraction, as expressing the cause of the union of the chemical elements of bodies, has been familiarly continued; and has, no doubt, been accompanied in the minds of many persons with an obscure notion that chemical attraction is, in some way, a kind of mechanical attraction of the particles of bodies. Yet the doctrine that chemical 'attraction' and mechanical attraction are forces of the same kind has never, so far as I am aware, been worked out into a system of chemical theory; nor even applied with any distinctness as an explanation of any particular chemical phenomena. Any such attempt, indeed, could only tend to bring more clearly into view the entire inadequacy of such a mode of explanation. For the leading phenomena of chemistry are all of such a nature that no mechanical combination can serve to express them, without an immense accumulation of additional hypotheses. If we take as our problem the changes of colour, transparency, texture, taste, odour, produced by small changes in the ingredients, how can we expect to give a mechanical account of these, till we can give a mechanical account of colour, transparency, texture, taste, odour, themselves? And if our mechanical hypothesis of the elementary constitution of bodies does not explain such phenomena as those changes, what can it explain, or what can be the value of it? I do not here insist upon a remark which will afterwards come before us, that even crystalline form, a phenomenon of a far more obviously mechanical nature than those just alluded to, has never yet been in any degree explained by such assumptions as this, that bodies consist of elementary particles exerting forces of the same nature as the central forces which we contemplate in Mechanics.

When therefore Newton asks, 'When some stones, as spar of lead, dissolved in proper menstruums, become salts, do not these things show that salts are dry earth and watery acid united by attraction?' we may {14} answer, that this mode of expression appears to be intended to identify chemical combination with mechanical attraction;--that there would be no objection to any such identification, if we could, in that way, explain, or even classify well, a collection of chemical facts; but that this has never yet been done by the help of such expressions. Till some advance of this kind can be pointed out, we must necessarily consider the power which produces chemical combination as a peculiar principle, a special relation of the elements, not rightly expressed in mechanical terms. And we now proceed to consider this relation under the name by which it is most familiarly known.

{{15}} CHAPTER II.

ESTABLISHMENT AND DEVELOPMENT OF THE IDEA OF CHEMICAL AFFINITY.

1. THE earlier chemists did not commonly involve themselves in the confusion into which the mechanical philosophers ran, of comparing chemical to mechanical forces. Their attention was engaged, and their ideas were moulded, by their own pursuits. They saw that the connexion of elements and compounds with which they had to deal, was a peculiar relation which must be studied directly; and which must be understood, if understood at all, in itself, and not by comparison with a different class of relations. At different periods of the progress of chemistry, the conception of this relation, still vague and obscure, was expressed in various manners; and at last this conception was clothed in tolerably consistent phraseology, and the principles which it involved were, by the united force of thought and experiment, brought into view.

2. The power by which the elements of bodies combine chemically, being, as we have seen, a peculiar agency, different from mere mechanical connexion or attraction, it is desirable to have it designated by a distinct and peculiar name; and the term Affinity has been employed for that purpose by most modern chemists. The word 'affinity' in common language means, sometimes resemblance, and sometimes relationship and ties of family. It is from the latter sense that the metaphor is borrowed when we speak of 'chemical affinity.' By the employment of this term we do not indicate a resemblance, but a disposition to unite. Using the word in a common unscientific manner, we might say that chlorine, bromine, and iodine, have a great {16} natural affinity with each other, for there are considerable resemblances and analogies among them; but these bodies have very little chemical Affinity for each other. The use of the word in the former sense, of resemblance, can be traced in earlier chemists; but the word does not appear to have acquired its peculiar chemical meaning till after Boerhaave's time. Boerhaave, however, is the writer in whom we first find a due apprehension of the peculiarity and importance of the Idea which it now expresses. When we make a chemical solution[13\6], he says, not only are the particles of the dissolved body separated from each other, but they are closely united to the particles of the solvent. When aqua regia dissolves gold, do you not see, he says to his hearers, that there must be between each particle of the solvent and of the metal, a mutual virtue by which each loves, unites with, and holds the other (amat, unit, retinet)? The opinion previously prevalent had been that the solvent merely separates the parts of the body dissolved: and most philosophers had conceived this separation as performed by mechanical operations of the particles, resembling, for instance, the operation of wedges breaking up a block of timber. But Boerhaave forcibly and earnestly points out the insufficiency of the conception. This, he says, does not account for what we see. We have not only a separation, but a new combination. There is a force by which the particles of the solvent associate to themselves the parts dissolved, not a force by which they repel and dissever them. We are here to imagine not mechanical action, not violent impulse, not antipathy, but love, at least if love be the desire of uniting. (Non igitur hic etiam actiones mechanicæ, non propulsiones violentæ, non inimicitiæ cogitandæ, sed amicitiæ, si amor dicendus copulæ cupido.) The novelty of this view is evidenced by the mode in which he apologizes for introducing it. 'Fateor, paradoxa hæc assertio.' To Boerhaave, therefore, (especially considering his great influence as a teacher of chemistry,) we may {17} assign the merit of first diffusing a proper view of Chemical Affinity as a peculiar force, the origin of almost all chemical changes and operations.

[Note 13\6: Elementa Chemiæ, Lugd. Bat. 1732, p. 677.]

3. To Boerhaave is usually assigned also the credit of introducing the word 'Affinity' among chemists; but I do not find that the word is often used by him in this sense; perhaps not at all[14\6]. But however this may be, the term is, on many accounts, well worthy to be preserved, as I shall endeavour to show. Other terms were used in the same sense during the early part of the eighteenth century. Thus when Geoffroy, in 1718, laid before the Academy of Paris his Tables of Affinities, which perhaps did more than any other event to fix the Idea of Affinity, he termed them 'Tables of the Relations of Bodies;' 'Tables des Rapports:' speaking however, also, of their 'disposition to unite,' and using other phrases of the same import.

[Note 14\6: See Dumas, Leçons de Phil. Chim. p. 364. Rees' Cyclopædia, Art. Chemistry. In the passage of Boerhaave to which I refer above, affinitas is rather opposed to, than identified with, chemical combination. When, he says, the parts of the body to be dissolved are dissevered by the solvent, why do they remain united to the particles of the solvent, and why do not rather both the particles of the solvent and of the dissolved body collect into homogeneous bodies by their affinity? 'denuo se affinitate suæ naturæ colligant in corpora homogenea?' And the answer is, because they possess another force which counteracts this affinity of homogeneous particles, and makes compounds of different elements. Affinity, in chemistry, now means the tendency of different kinds of matter to unite: but it appears, as I have said, to have acquired this sense since Boerhaave's time.]

The term attraction, having been recommended by Newton as a fit word to designate the force which produces chemical combination, continued in great favour in England, where the Newtonian philosophy was looked upon as applicable to every branch of science. In France, on the contrary, where Descartes still reigned triumphant, 'attraction,' the watch-word of the enemy, was a sound never uttered but with dislike and suspicion. In 1718 (in the notice of Geoffroy's Table,) the Secretary of the Academy, after pointing out some of the peculiar circumstances of chemical {18} combinations, says, 'Sympathies and attractions would suit well here, if there were such things,' 'Les sympathies, les attractions conviendroient bien ici, si elles étaient quelque chose.' And at a later period, in 1731, having to write the éloge of Geoffroy after his death, he says, 'He gave, in 1718, a singular system, and a Table of Affinities, or Relations of the different substances in chemistry. These affinities gave an easiness to some persons, who feared that they were attractions in disguise, and all the more dangerous in consequence of the seductive forms which clever people have contrived to give them. It was found in the sequel that this scruple might be got over.'

This is the earliest published instance, so far as I am aware, in which the word 'Affinity' is distinctly used for the cause of chemical composition; and taking into account the circumstances, the word appears to have been adopted in France in order to avoid the word attraction, which had the taint of Newtonianism. Accordingly we find the word affinité employed in the works of French chemists from this time. Thus, in the Transactions of the French Academy for 1746, in a paper of Macquer's upon Arsenic, he says[15\6], 'On peut facilement rendre raison de ces phenomènes par le moyen des affinités que les différens substances qui entrent dans ces combinaisons, ont les uns avec les autres:' and he proceeds to explain the facts by reference to Geoffroy's Table. And in Macquer's Elements of Chemistry, which appeared a few years later, the 'Affinity of Composition' is treated of as a leading part of the subject, much in the same way as has been practised in such books up to the present time. From this period, the word appears to have become familiar to all European chemists in the sense of which we are now speaking. Thus, in the year 1758, the Academy of Sciences at Rouen offered a prize for the best dissertation on Affinity. The prize was shared between M. Limbourg of Theux, near Liege, and M. Le Sage {19} of Geneva[16\6]. About the same time other persons (Manherr[17\6], Nicolai[18\6], and others) wrote on the same subject, employing the same name.

[Note 15\6: A. P. 1746, p. 201.]

[Note 16\6: Thomson's Chemistry, iii. 10. Limbourg's Dissertation was published at Liege, in 1761; and Le Sage's at Geneva.]

[Note 17\6: Dissertatio de Affinitate Corporum. Vindob. 1762.]

[Note 18\6: Progr. I. II. de Affinitate Corporum Chimica. Jen. 1775, 1776.]

Nevertheless, in 1775, the Swedish chemist Bergman, pursuing still further this subject of Chemical Affinities, and the expression of them by means of Tables, returned again to the old Newtonian term; and designated the disposition of a body to combine with one rather than another of two others as Elective Attraction. And as his work on Elective Attractions had great circulation and great influence, this phrase has obtained a footing by the side of Affinity, and both one and the other are now in common use among chemists.

4. I have said above that the term Affinity is worthy of being retained as a technical term. If we use the word attraction in this case, we identify or compare chemical with mechanical attraction; from which identification and comparison, as I have already remarked, no one has yet been able to extract the means of expressing any single scientific truth. If such an identification or comparison be not intended, the use of the same word in two different senses can only lead to confusion; and the proper course, recommended by all the best analogies of scientific history, is to adopt a peculiar term for that peculiar relation on which chemical composition depends. The word Affinity, even if it were not rigorously proper according to its common meaning, still, being simple, familiar, and well established in this very usage, is much to be preferred before any other.

But further, there are some analogies drawn from the common meaning of this word, which appear to recommend it as suitable for the office which it has to discharge. For common mechanical attractions and {20} repulsions, the forces by which one body considered as a whole acts upon another external to it, are, as we have said, to be distinguished from those more intimate ties by which the parts of each body are held together. Now this difference is implied, if we compare the former relations, the attractions and repulsions, to alliances and wars between States, and the latter, the internal union of particles, to those bonds of affinity which connect the citizens of the same state with one another, and especially to the ties of Family. We have seen that Boerhaave compares the union of two elements of a compound to their marriage; 'we must allow,' says an eminent chemist of our own time[19\6], 'that there is some truth in this poetical comparison.' It contains this truth,--that the two become one to most intents and purposes, and that the Unit thus formed (the Family) is not a mere juxtaposition of the component parts. And thus the Idea of Affinity as the peculiar principle of chemical composition, is established among chemists, and designated by a familiar and appropriate name.

[Note 19\6: Dumas, Leçons de Phil. Chim. p. 363.]

5. Analysis is possible.--We must, however, endeavour to obtain a further insight into this Idea, thus fixed and named. We must endeavour to extricate, if not from the Idea itself, from the processes by which it has obtained acceptation and currency among chemists, some principles which may define its application, some additional specialities in the relations which it implies. This we shall proceed to do.

The Idea of Affinity, as already explained, implies a disposition to combine. But this combination is to be understood as admitting also of a possibility of separation. Synthesis implies Analysis as conceivable: or to recur to the image which we have already used, Divorce is possible when the Marriage has taken place.

That there is this possibility, is a conviction implied in all the researches of chemists, ever since the true notion of composition began to predominate in their investigations. One of the first persons who clearly {21} expressed this conviction was Mayow, an English physician, who published his Medico-Physical Tracts in 1674. The first of them De Sale-Nitro et Spiritu Nitro-Aerio, contains a clear enunciation of this principle. After showing how, in the combinations of opposite elements, as acid and alkali, their properties entirely disappear, and a new substance is formed not at all resembling either of the ingredients, he adds[20\6], 'Although these salts thus mixed appear to be destroyed it is still possible for them to be separated from each other, with their powers still entire.' He proceeds to exemplify this, and illustrates it by the same image which I have already alluded to: 'Salia acida a salibus volatilibus discedunt, ut cum sale fixo tartari, tanquam sponso magis idoneo, conjugium strictius ineunt.' This idea of a synthesis which left a complete analysis still possible, was opposed to a notion previously current, that when two heterogeneous bodies united together and formed a third body, the two constituents were entirely destroyed, and the result formed out of their ruins[21\6]. And this conception of Synthesis and Analysis, as processes which are possible successively and alternately, and each of which supposes the possibility of the other, has been the fundamental and regulative principle of the operations and speculations of analytical chemistry from the time of Mayow to the present day.

[Note 20\6: Cap. xiv. p. 233.]

[Note 21\6: Thomson's Chemistry, iii. 8.]

6. Affinity is Elective.--When the idea of chemical affinity, or disposition to unite, was brought into view by the experiments and reasonings of chemists, they found it necessary to consider this disposition as elective;--each element chose one rather than another of the elements which were presented to it, and quitted its union with one to unite with another which it preferred. This has already appeared in the passage just quoted from Mayow. He adds in the same strain, 'I have no doubt that fixed salts choose one acid rather than another, in order that they may coalesce with it {22} in a more intimate union.'--'Nullus dubito salia fixa acidum unum præ aliis eligere, ut cum eodem arctiore unione coalescant.' The same thought is expressed and exemplified by other chemists: they notice innumerable cases in which, when an ingredient is combined with a liquid, if a new substance be immersed which has a greater affinity for the liquid, the liquid combines with the new substance by election, and the former **ingredient is precipitated. Thus Stahl says[22\6], 'In spirit of nitre dissolve silver; put in copper and the silver is thrown down; put in iron and the copper goes down; put in zinc, the iron precipitates; put in volatile alkali, the zinc is separated; put in fixed alkali, the volatile quits its hold.'--As may be seen in this example, we have in such cases, not only a preference, but a long gradation of preferences. The spirit of nitre will combine with silver, but it prefers copper; prefers iron more; zinc still more; volatile alkali yet more; fixed alkali the most.

[Note 22\6: Zymotechnia, 1697, p. 117.]

The same thing was proved to obtain with regard to each element; and when this was ascertained, it became the object of chemists to express these degrees of preference, by lists in which substances were arranged according to their disposition to unite with another substance. In this manner was formed Geoffroy's Table of Affinities (1718), which we have already mentioned. This Table was further improved by other writers, as Gellert (1751) and Limbourg (1761). Finally Bergman improved these Tables still further, taking into account not only the order of affinities of each element for others, but the sum of the tendencies to unite of each two elements, which sum, he held, determined the resulting combination when several elements were in contact with each other.

7. As we have stated in the History[23\6], when the doctrine of elective affinities had assumed this very definite and systematic form, it was assailed by Berthollet, who maintained, in his Essai de Statique {23} Chimique, (1803,) that chemical affinities are not elective:--that, when various elements are brought together, their combinations do not depend upon the kind of elements alone, but upon the quantity of each which is present, that which is most abundant always entering most largely into the resulting compounds. It may seem strange that it should be possible, at so late a period of the science, to throw doubt upon a doctrine which had presided over and directed its progress so long. Proust answered Berthollet, and again maintained that chemical affinity is elective. I have, in the History, given the judgment of Berzelius upon this controversy. 'Berthollet,' he says, 'defended himself with an acuteness which makes the reader hesitate in his judgment; but the great mass of facts finally decided the point in favour of Proust.' I may here add the opinion pronounced upon this subject by Dr. Turner[24\6]: 'Bergman erred in supposing the result of the chemical action to be in every case owing to elective affinity [for this power is modified in its effects by various circumstances]: but Berthollet ran into the opposite extreme in declaring that the effects formerly ascribed to that power are never produced by it. That chemical attraction is exerted between different bodies with different degrees of energy, is, I apprehend, indisputable.' And he then proceeds to give many instances of differences in affinity which cannot be accounted for by the operation of any modifying causes. Still more recently, M. Dumas has taken a review of this controversy; and, speaking with enthusiasm of the work of Berthollet, as one which had been of inestimable service to himself in his early study of chemistry, he appears at first disposed to award to him the victory in this dispute. But his final verdict leaves undamaged the general principle now under our consideration, that chemical affinity is elective. 'For my own part,' he says[25\6], 'I willingly admit the notions of Berthollet when we have to do with acids or {24} with bases, of which the energy is nearly equal: but when bodies endued with very energetic affinities are in presence of other bodies of which the affinities are very feeble, I propose to adopt the following rule: In a solution, everything remaining dissolved, the strong affinities satisfy themselves, leaving the weak affinities to arrange matters with one another. The strong acids take the strong bases, and the weak acids can only unite with the weak bases. The known facts are perfectly in accordance with this practical rule.' It is obvious that this recognition of a distinction between strong and weak affinities, which operates to such an extent as to determine entirely the result, is a complete acknowledgement of the Elective nature of Affinity, as far as any person acquainted with chemical operations could contend for it. For it must be allowed by all, that solubility, and other collateral circumstances, influence the course of chemical combinations, since they determine whether or not there shall take place that contact of elements without which affinity cannot possibly operate.

[Note 23\6: Hist. Ind. Sc. b. xiv. c. iii.]

[Note 24\6: Chemistry, p. 199. 6th edition.]

[Note 25\6: Leçons de Philosophie Chimique, p. 386.]

8. Affinity is Definite as to quantity.--In proportion as chemists obtained a clearer view of the products of the laboratory as results of the composition of elements, they saw more and more clearly that these results were definite; that one element not only preferred to combine with another of a certain kind, but also would combine with it to a certain extent and no further, thus giving to the result not an accidental and variable, but a fixed and constant character. Thus salts being considered as the result of the combination of two opposite principles, acid and alkali, and being termed neutral when these principles exactly balanced each other, Rouelle (who was Royal Professor at Paris in 1742) admits of neutral salts with excess of acid, neutral salts with excess of base, and perfect neutral salts. Beaume maintained[26\6] against him that there were no salts except those perfectly neutral, the other classes being the results of mixture and imperfect {25} combination. But this question was not adequately treated till chemists made every experiment with the balance in their hands. When this was done, they soon discovered that, in each neutral salt, the proportional weights of the ingredients which composed it were always the same. This was ascertained by Wenzel, whose Doctrine of the Affinities of Bodies appeared in 1777. He not only ascertained that the proportions of elements in neutral chemical compounds are definite, but also that they are reciprocal; that is, (to express his results in a manner now employed by chemists), that if A, a certain weight of a certain acid, neutralize m, a certain weight of a certain base, and B, a certain weight of a certain other acid, neutralize n, a certain weight of a certain other base; the compound of A and n will also be neutral; as also that of B and m. The same views were again presented by Richter in 1792, in his Principles of the Measure of Chemical Elements. And along with these facts, that of the combination of elements in multiple proportions being also taken into account, the foundations of the Atomic Theory were laid; and that Theory was propounded in 1803 by Mr. Dalton. That theory, however, rests upon the Idea of Substance, as well as upon that Idea of Chemical Affinity which we are here considering; and the discussion of its evidence and truth must be for the present deferred.

[Note 26\6: Dumas, Phil. Chim. p. 198.]

9. The two principles just explained,--that Affinity is Definite as to the Kind, and as to the Quantity of the elements which it unites,--have here been stated as results of experimental investigation. That they could never have been clearly understood, and therefore never firmly established, without laborious and exact experiments, is certain; but yet we may venture to say that being once fully known, they may seem to thoughtful men to possess an evidence beyond that of mere experiment. For how, in fact, can we conceive combinations, otherwise than as definite in kind and quantity? If we were to suppose each element ready to combine with any other indifferently, and indifferently in any quantity, we should have a world in {26} which all would be confusion and indefiniteness. There would be no fixed kinds of bodies. Salts, and stones, and ores, would approach to and graduate into each other by insensible degrees. Instead of this, we know that the world consists of bodies distinguishable from each other by definite differences, capable of being classified and named, and of having general propositions asserted concerning them. And as we cannot conceive a world in which this should not be the case, it would appear that we cannot conceive a state of things in which the laws of the combination of elements should not be of that definite and measured kind which we have above asserted.

This will, perhaps, appear more clearly by stating our fundamental convictions respecting chemical composition in another form, which I shall, therefore, proceed to do.

10. Chemical Composition determines Physical Properties.--However obscure and incomplete may be our conception of the internal powers by which the ultimate particles of bodies are held together, it involves, at least, this conviction:--that these powers are what determine bodies to be bodies, and therefore contain the reason of all the properties which, as bodies, they possess. The forces by which the particles of a body are held together, also cause it to be hard or soft, heavy or light, opake or transparent, black or red; for if these forces are not the cause of these peculiarities, what can be the cause? By the very supposition which we make respecting these forces, they include all the relations by which the parts are combined into a whole, and therefore they, and they only, must determine all the attributes of the whole. The foundation of all our speculations respecting the intimate constitution of bodies must be this principle, that their composition determines their properties.

Accordingly we find our chemists reasoning from this principle with great confidence, even in doubtful cases. Thus Davy, in his researches concerning the diamond, says: 'That some chemical difference must exist between the hardest and most beautiful of the {27} gems and charcoal, between a non-conductor and a conductor of electricity, it is scarcely possible to doubt: and it seems reasonable to expect that a very refined or perfect chemistry will confirm the analogies of nature; and show that bodies cannot be the same in their composition or chemical nature, and yet totally different in their chemical properties.' It is obvious that the principle here assumed is so far from being a mere result of experience, that it is here appealed to to prove that all previous results of experience on this subject must be incomplete and inaccurate; and that there must be some chemical difference between charcoal and diamond, though none had hitherto been detected.

11. In what manner, according to what rule, the chemical composition shall determine the kind of the substance, we cannot reasonably expect to determine by mere conjecture or assumption, without a studious examination of natural bodies and artificial compounds. Yet even in the most recent times, and among men of science, we find that an assumption of the most arbitrary character has in one case been mixed up with this indisputable principle, that the elementary composition determines the kind of the substance. In the classification of minerals, one school of mineralogists have rightly taken it as their fundamental principle that the chemical composition shall decide the position of the mineral in the system. But they have appended to this principle, arbitrarily and unjustifiably, the maxim that the element which is largest in quantity shall fix the class of the substance. To make such an assumption is to renounce, at once, all hope of framing a system which shall be governed by the resemblances of the things classified; for how can we possibly know beforehand that fifty-five per cent, of iron shall give a substance its predominant properties, and that forty-five per cent, shall not? Accordingly, the systems of mineralogical arrangement which have been attempted in this way, (those of Haüy, Phillips, and others,) have been found inconsistent with themselves, ambiguous, and incapable of leading to any general truths. {28}

12. Chemical Composition and Crystalline Form correspond.--Thus the physical properties of bodies depend upon their chemical composition, but in a manner which a general examination of bodies with reference to their properties and their composition can alone determine. We may, however, venture to assert further, that the more definite the properties are, the more distinct may we expect to find this dependence. Now the most definite of the properties of bodies are those constant properties which involve relations of space; that is, their figure. We speak not, however, of that external figure, derived from external circumstances, which, so far from being constant and definite, is altogether casual and arbitrary; but of that figure which arises from their internal texture, and which shows itself not only in the regular forms which they spontaneously assume, but in the disposition of the parts to separate in definite directions, and no others. In short, the most definite of the properties of perfect chemical compounds is their crystalline structure; and therefore it is evident that the crystalline structure of each body, and the forms which it affects, must be in a most intimate dependence upon its chemical composition.

Here again we are led to the brink of another theory;--that of crystalline structure, which has excited great interest among philosophers ever since the time of Haüy. But this theory involves, besides that idea of chemical composition with which we are here concerned, other conceptions, which enter into the relations of figure. These conceptions, governed principally by the Idea of Symmetry, must be unfolded and examined before we can venture to discuss any theory of crystallization: and we shall proceed to do this as soon as we have first duly considered the Idea of Substance and its consequences.

{{29}} CHAPTER III.

OF THE IDEA OF SUBSTANCE.

1. Axiom of the Indestructibility of Substance.--WE now come to an Idea of which the history is very different from those of which we have lately been speaking. Instead of being gradually and recently brought into a clear light, as has been the case with the Ideas of Polarity and Affinity, the Idea of Substance has been entertained in a distinct form from the first periods of European speculation. That this is so, is proved by our finding a principle depending upon this Idea current as an axiom among the early philosophers of Greece:--namely, that nothing can be produced out of nothing. Such an axiom, more fully stated, amounts to this: that the substance of which a body consists is incapable of being diminished (and consequently incapable of being augmented) in quantity, whatever apparent changes it may undergo. Its forms, its distribution, its qualities, may vary, but the substance itself is identically the same under all these variations.

The axiom just spoken of was the great principle of the physical philosophy of the Epicurean school, as it must be of every merely material philosophy. The reader of Lucretius will recollect the emphasis with which it is repeatedly asserted in his poem: E nilo nil gigni, in nilum nil posse reverti; Nought comes of nought, nor ought returns to nought.

Those who engaged in these early attempts at physical speculation were naturally much pleased with the clearness which was given to their notions of change, composition, and decomposition, by keeping steadily hold of the Idea of Substance, as marked by this {30} fundamental axiom. Nor has its authority ever ceased to be acknowledged. A philosopher was asked[27\6], What is the weight of smoke? He answered, 'Subtract the weight of the ashes from the weight of the wood which is burnt, and you have the weight of the smoke.' This reply would be assented to by all; and it assumes as incontestable that even under the action of fire, the material, the substance, does not perish, but only changes its form.

[Note 27\6: Kant, Kritik der R. V. p. 167.]

This principle of the indestructibility of substance might easily be traced in many reasonings and researches, ancient and modern. For instance, when the chemist works with the retort, he places the body on which he operates in one part of an inclosed cavity, which, by its bendings and communications, separates at the same time that it confines, the products which result from the action of fire: and he assumes that this process is an analysis of the body into its ingredients, not a creation of anything which did not exist before, or a destruction of anything which previously existed. And he assumes further, that the total quantity of the substance thus analysed is the sum of the quantities of its ingredients. This principle is the very basis of chemical speculation, as we shall hereafter explain more fully.

2. The Idea of Substance.--The axiom above spoken of depends upon the Idea of Substance, which is involved in all our views of external objects. We unavoidably assume that the qualities and properties which we observe are properties of things;--that the adjective implies a substantive;--that there is, besides the external characters of things, something of which they are the characters. An apple which is red, and round, and hard, is not merely redness, and roundness, and hardness: these circumstances may all alter while the apple remains the same apple. Behind or under the appearances which we see, we conceive something of which we think; or, to use the metaphor which obtained currency among the ancient philosophers, the {31} attributes and qualities which we observe are supported by and inherent in something: and this something is hence called a substratum or substance,--that which stands beneath the apparent qualities and supports them.

That we have such an Idea, using the term 'Idea' in the sense in which I have employed it throughout these disquisitions, is evident from what has been already said. The Axiom of the Indestructibility of Substance proves the existence of the Idea of Substance, just as the Axioms of Geometry and Arithmetic prove the existence of the Ideas of Space and Number. In the case of Substance, as of space or number, the ideas cannot be said to be borrowed from experience, for the axioms have an authority of a far more comprehensive and demonstrative character than any which experience can bestow. The axiom that nothing can be produced from nothing and nothing destroyed, is so far from being a result of experience, that it is apparently contradicted by the most obvious observation. It has, at first, the air of a paradox; and by those who refer to it, it is familiarly employed to show how fallacious common observation is. The assertion is usually made in this form;--that nothing is created and nothing annihilated, notwithstanding that the common course of our experience appears to show the contrary. The principle is not an empirical, but a necessary and universal truth;--is collected, not from the evidence of our senses, but from the operation of our ideas. And thus the universal and undisputed authority of the axiom proves the existence of the Idea of Substance.

3. Locke's Denial of the Idea of Substance.--I shall not attempt to review the various opinions which have been promulgated respecting this Idea: but it may be worth our while to notice briefly the part which it played in the great controversy concerning the origin of our ideas which Locke's Essay occasioned. Locke's object was to disprove the existence of all ideas not derived from Sensation or Reflection: and since the idea of substance as distinct from external qualities, is {32} manifestly not derived directly from sensation, nor by any very obvious or distinct process from reflection, Locke was disposed to exclude the idea as much as possible. Accordingly, in his argumentation against Innate Ideas[28\6], he says plainly, 'the idea of substance, which we neither have nor can have by sensation or reflection.' And the inference which he draws is, 'that we have no such clear idea at all.' What then, it may be asked, do we mean by the word substance? This also he answers, though somewhat strangely, 'We signify nothing by the word substance, but only an uncertain supposition of we know not what, i. e. of something whereof we have no particular distinct positive idea, which we take to be the substratum, or support, of those ideas we know.' That while he indulged in this tautological assertion of our ignorance and uncertainty, he should still have been compelled to acknowledge that the word substance had some meaning, and should have been driven to explain it by the identical metaphors of 'substratum' and 'support,' is a curious proof how impossible it is entirely to reject this idea.

[Note 28\6: Essay, b. i. c. iv. s. 18.]

But as we have already seen, the supposition of the existence of substance is so far from being uncertain, that it carries with it irresistible conviction, and substance is necessarily conceived as something which cannot be produced or destroyed. It may be easily supposed, therefore, that when the controversy between Locke and his assailants came to this point, he would be in some difficulty. And, indeed, though with his accustomed skill in controversy, he managed to retain a triumphant tone, he was driven from his main points. Thus he repels the charge that he took the being of substance to be doubtful[29\6]. He says, 'Having everywhere affirmed and built upon it that man is a substance, I cannot be supposed to question or doubt of the being of substance, till I can question or doubt of my own being.' He attempts to make a stand by saying that being of things does not depend upon our {33} ideas; but if he had been asked how, without having an idea of substance, he knew substance to be, it is difficult to conceive what answer he could have made. Again, he had said that our idea of substance arises from our 'accustoming ourselves to suppose' a substratum of qualities. Upon this his adversary, Bishop Stillingfleet, very properly asks, Is this custom grounded upon true reason or no? To which Locke replies, that it is grounded upon this: That we cannot conceive how simple ideas of sensible qualities should subsist alone; and therefore we suppose them to exist in, and to be supported by some common subject, which support we denote by the name substance. Thus he allows, not only that we necessarily assume the reality of substance, but that we cannot conceive qualities without substance; which are concessions so ample as almost to include all that any advocate for the Idea of Substance need desire.

[Note 29\6: Essay, b. ii. c. ii. and First Letter to the Bishop of Worcester.]

Perhaps Locke, and the adherents of Locke, in denying that we have an idea of substance in general, were latently influenced by finding that they could not, by any effort of mind, call up any image which could be considered as an image of substance in general. That in this sense we have no idea of substance, is plain enough; but in the same sense we have no idea of space in general, or of time, or number, or cause, or resemblance. Yet we certainly have such a power of representing to our minds space, time, number, cause, resemblance, as to arrive at numerous truths by means of such representations. These general representations I have all along called Ideas, nor can I discover any more appropriate word; and in this sense, we have also, as has now been shown, an Idea of Substance.

4. Is all Material Substance heavy?--The principle that the quantity of the substance of any body remains unchanged by our operations upon it, is, as we have said, of universal validity. But then the question occurs, how are we to ascertain the quantity of substance, and thus, to apply the principle in particular cases. In the case above mentioned, where {34} smoke was to be weighed, it was manifestly assumed that the quantity of the substance might be known by its weight; and that the total quantity being unchanged, the total weight also would remain the same. Now on what grounds do we make this assumption? Is all material substance heavy? and if we can assert this to be so, on what grounds does the truth of the assertion rest? These are not idle questions of barren curiosity; for in the history of that science (Chemistry) to which the Idea of Substance is principally applicable, nothing less than the fate of a comprehensive and long established theory (the Phlogiston theory) depended upon the decision of this question. When it was urged that the reduction of a metal from a calcined to a metallic form could not consist in the addition of phlogiston, because the metal was lighter than the calx had been; it was replied by some, that this was not conclusive, for that phlogiston was a principle of levity, diminishing the weight of the body to which it was added. This reply was, however, rejected by all the sounder philosophers, and the force of the argument finally acknowledged. But why was this suggestion of a substance having no weight, or having absolute levity, repudiated by the most reflective reasoners? It is assumed, it appears, that all matter must be heavy; what is the ground of this assumption?

The ground of such an assumption appears to be the following. Our idea of substance includes in it this:--that substance is a quantity capable of addition; and thus capable of making up, by composition, a sum equal to all its parts. But substance, and the quantity of substance, can be known to us only by its attributes and qualities. And the qualities which are capable constantly and indefinitely of increase and diminution by increase and diminution of the parts, must be conceived inseparable from the substance. For the qualities, if removable from the substance at all, must be removable by some operation performed upon the substance; and by the idea of substance, all such operations are only equivalent to separation, junction, and union of parts. Hence those characters {35} which thus universally increase and diminish by addition and subtraction of the things themselves, belong to the substance of the things. They are measures of its quantity, and are not merely its separable qualities.

The weight of bodies is such a character. However we compound or divide bodies, we compound and divide their weight in the same manner. We may dismember a body into the minutest parts; but the sum of the weights of the parts is always equal to the whole weight of the body. The weight of a body can be in no way increased or diminished, except by adding something to it or taking something from it. If we bake a brick, we do not conceive that the change of colour or of hardness, implies that anything has been created or destroyed. It may easily be that the parts have only assumed a new arrangement; but if the brick have lost weight, we suppose that something (moisture for instance) has been removed elsewhere.

Thus weight is apprehended as essential to matter. In considering the dismemberment or analysis of bodies, we assume that there must be some criterion of the quantity of substance; and this criterion can possess no other properties than their weight possesses. If we assume an element which has no weight, or the weight of which is negative, as some of the defenders of phlogiston attempted to do, we put an end to all speculation on such subjects. For if weight is not the criterion of the quantity of one element, phlogiston for instance, why is weight the criterion of the quantity of any other element? We may, by the same right, assume any other real or imaginary element to have levity instead of gravity; or to have a peculiar intensity of gravity which makes its weight no index of its quantity. In short, if we do this, we deprive of all possibility of application our notions of element, analysis, and composition; and violate the postulates on which the questions are propounded which we thus attempt to decide.

We must, then, take a constant and quantitative property of matter, such as weight is, to be an index {36} of the quantity of matter or of substance to which it belongs. I do not here speak of the question which has sometimes been proposed, whether the weight or the inertia of bodies be the more proper measure of the quantity of matter. For the measure of inertia is regulated by the same assumption as that of substance:--that the quantity of the whole must be equal to the quantity of all the parts: and inertia is measured by weight, for the same reason that substance is so.

Having thus established the certainty, and ascertained the interpretation of the fundamental principle which the Idea of Substance involves, we are prepared to consider its application in the science upon which it has a peculiar bearing.

{{37}} NOTE TO CHAPTER III.

[3rd Ed.]--[THE doctrine here propounded, that All Matter is Heavy, has been opposed by Sir William Hamilton of Edinburgh. (Works of Reid, note, p. 853.) This writer is a man of unquestionable acuteness and of very extensive reading; but his acuteness shows itself in barren ontological distinctions, which appear to me to be of the same character as the speculations of the eminent Schoolmen of the most sterile periods of the dark ages. That he should have no conception of progressive or inductive science is not wonderful, when we recollect that he holds, as an important part of his philosophy, that the study of mathematics perverts and obscures the mind. But it may be of some interest to consider his objections to the doctrine here maintained.

He says, 1st, that our reasoning assumes that we must necessarily have it in our power to ascertain the Quantity of Matter; whereas this may be a problem out of the reach of human determination.

To this I reply, that my reasoning does assume that there is a science, or sciences, which make assertions concerning the Quantity of Matter: Mechanics and Chemistry are such sciences. My assertion is, that to make such sciences possible, Quantity of Matter must be proportional to Weight. If my opponent deny that Mechanics and Chemistry can exist as sciences, he may invalidate my proof; but not otherwise.

2. He says that there are two conceivable ways of estimating the Quantity of Matter: by the Space occupied, and by the Weight or Inertia; and that I assume the second measure gratuitously.

To which I reply, that the most elementary steps in Mechanics and in Chemistry contradict the notion that {38} the Quantity of Matter is proportionate to the Space. They proceed necessarily on a distinction between Space and Matter:--between mere Extension and material Substance.

3. He allows that we cannot make the Extension of a body the measure of the Quantity of Matter, because, he says, we do not know if 'the compressing force' is such as to produce 'the closest compression.' That is, he assumes a compressing force, assumes a closest compression, assumes a peculiar (and very improbable) atomic hypothesis; and all this to supply a reason why we are not to believe the first simple principle of Mechanics and Chemistry.

4. He speaks of 'a series of apparent fluids (as Light or its vehicle, the Calorific, the Electro-galvanic, and Magnetic agents) which we can neither denude of their character of substance, nor clothe with the attribute of weight.'

To which my reply is, that precisely because I cannot 'clothe' these agents with the attribute of Weight, I do 'denude them of the character of Substance.' They are not substances, but agencies. These Imponderable Agents are not properly called 'Imponderable Fluids.' This I conceive that I have proved; and the proof is not shaken by denying the conclusion without showing any defect in the reasoning.

5. Finally, my critic speaks about 'a logical canon,' and about 'a criterion of truth, subjectively necessary and objectively certain;' which matters I shall not waste the reader's time by discussing.]

{{39}} CHAPTER IV.

APPLICATION OF THE IDEA OF SUBSTANCE IN CHEMISTRY.

1. A Body is Equal to the Sum of its Elements.--FROM the earliest periods of chemistry the balance has been familiarly used to determine the proportions of the ingredients and of the compound; and soon after the middle of the last century, this practice was so studiously followed, that Wenzel and Richter were thereby led to the doctrine of Definite Proportions. But yet the full value and significance of the balance, as an indispensable instrument in chemical researches, was not understood till the gaseous, as well as solid and fluid ingredients were taken into the account. When this was done, it was found that the principle, that the whole is equal to the sum of its parts, of which, as we have seen, the necessary truth, in such cases, flows from the idea of substance, could be applied in the most rigorous manner. And conversely, it was found that by the use of the balance, the chemist could decide, in doubtful cases, which was a whole, and which were parts.

For chemistry considers all the changes which belong to her province as compositions and decompositions of elements; but still the question may occur, whether an observed change be the one or the other. How can we distinguish whether the process which we contemplate be composition or decomposition?--whether the new body be formed by addition of a new, or subtraction of an old element? Again; in the case of decomposition, we may inquire, What are the ultimate limits of our analysis? If we decompound bodies into others more and more simple, how far can we carry this succession {40} of processes? How far can we proceed in the road of analysis? And in our actual course, what evidence have we that our progress, as far as it has gone, has carried us from the more complex to the more simple?

To this we reply, that the criterion which enables us to distinguish, decidedly and finally, whether our process have been a mere analysis of the proposed body into its ingredients, or a synthesis of some of them with some new element, is the principle stated above, that the weight of the whole is equal to the weight of all the parts. And no process of chemical analysis or synthesis can be considered complete till it has been verified by this fact;--by finding that the weight of the compound is the weight of its supposed ingredients; or, that if there be an element which we think we have detached from the whole, its loss is betrayed by a corresponding diminution of weight.

I have already noticed what an important part this principle has played in the great chemical controversy which ended in the establishment of the oxygen theory. The calcination of a metal was decided to be the union of oxygen with the metal, and not the separation of phlogiston from it, because it was found that in the process of calcination, the weight of the metal increased, and increased exactly as much as the weight of ambient air diminished. When oxygen and hydrogen were exploded together, and a small quantity of water was produced, it was held that this was really a synthesis of water, because, when very great care was taken with the process, the weight of the water which resulted was equal to the weight of the gases which disappeared.

2. Lavoisier.--It was when gases came to be considered as entering largely into the composition of liquid and solid bodies, that extreme accuracy in weighing was seen to be so necessary to the true understanding of chemical processes. It was in this manner discovered by Lavoisier and his contemporaries that oxygen constitutes a large ingredient of calcined metals, of acids, and of water. A countryman of Lavoisier[30\6] {41} has not only given most just praise to that great philosopher for having constantly tested all his processes by a careful and skilful use of the balance, but has also claimed for him the merit of having introduced the maxim, that in chemical operations nothing is created and nothing lost. But I think it is impossible to deny that this maxim is assumed in all the attempts at analysis made by his contemporaries, as well as by him. This maxim is indeed included in any clear notion of analysis: it could not be the result of the researches of any one chemist, but was the governing principle of the reasonings of all. Lavoisier, however, employed this principle with peculiar assiduity and skill. In applying it, he does not confine himself to mere additions and subtractions of the quantities of ingredients; but often obtains his results by more complex processes. In one of his investigations he says, 'I may consider the ingredients which are brought together, and the result which is obtained as an algebraical equation; and if I successively suppose each of the quantities of this equation to be unknown, I can obtain its value from the rest: and thus I can rectify the experiment by the calculation, and the calculation by the experiment. I have often taken advantage of this method, in order to correct the first results of my experiments, and to direct me in repeating them with proper precautions.'

[Note 30\6: M. Dumas, Leçons de la Philosophie Chimique. 1837. p. 157.]

The maxim, that the whole is equal to the sum of all its parts, is thus capable of most important and varied employment in chemistry. But it may be applied in another form to the exclusion of a class of speculations which are often put forwards.

3. Maxim respecting Imponderable Elements.--Several of the phenomena which belong to bodies, as heat, light, electricity, magnetism, have been explained hypothetically by assuming the existence of certain fluids; but these fluids have never been shown to have weight. Hence such hypothetical fluids have been termed imponderable elements. It is however plain, that so long as these fluids appear to be without weight, they are not elements of bodies in the same {42} sense as those elements of which we have hitherto been speaking. Indeed we may with good reason doubt whether those phenomena depend upon transferable fluids at all. We have seen strong reason to believe that light is not matter, but only motion; and the same thing appears to be probable with regard to heat. Nor is it at all inconceivable that a similar hypothesis respecting electricity and magnetism should hereafter be found tenable. Now if heat, light, and those other agents, be not matter, they are not elements in such a sense as to be included in the principle referred to above, That the body is equal to the sum of its elements. Consequently the maxim just stated, that in chemical operations nothing is created, nothing annihilated, does not apply to Light and Heat. They are not things. And whether heat can be produced where there was no heat before, and light struck out from darkness, the ideas of which we are at present treating do not enable us to say. In reasoning respecting chemical synthesis and analysis therefore, we shall only make confusion by attempting to include in our conception the Light and Heat which are produced and destroyed. Such phenomena may be very proper subjects of study, as indeed they undoubtedly are; but they cannot be studied to advantage by considering them as sharing the nature of composition and decomposition.

Again: in all attempts to explain the processes of nature, the proper course is, first to measure the facts with precision, and then to endeavour to understand their cause. Now the facts of chemical composition and decomposition, the weights of the ingredients and of the compounds, are facts measurable with the utmost precision and certainty. But it is far otherwise with the light and heat which accompany chemical processes. When combustion, deflagration, explosion, takes place, how can we measure the light or the heat? Even in cases of more tranquil action, though we can apply the thermometer, what does the thermometer tell us respecting the quantity of the heat? Since then we have no measure which is of any value as {43} regards such circumstances in chemical changes, if we attempt to account for these phenomena on chemical principles, we introduce, into investigations in themselves perfectly precise and mathematically rigorous, another class of reasonings, vague and insecure, of which the only possible effect is to vitiate the whole reasoning, and to make our conclusions inevitably erroneous.

We are led then to this maxim: that imponderable fluids are not to be admitted as chemical elements of bodies[31\6].

[Note 31\6: See the answer to Sir William Hamilton's objections, at the end of the last chapter.

Since we are thus warned by a sound view of the nature of science, from considering chemical affinity as having any hold upon imponderable elements, we are manifestly still more decisively prohibited from supposing mechanical impulse or pressure to have any effect upon such elements. To make this supposition, is to connect the most subtle and incorporeal objects which we know in nature by the most gross material ties. This remark seems to be applicable to M. Poisson's hypothesis that the electric fluid is retained at the surface of bodies by the pressure of the atmosphere.]

4. It appears, I think, that our best and most philosophical chemists have proceeded upon this principle in their investigations. In reasoning concerning the constitution of bodies and the interpretation of chemical changes, the attempts to include in these interpretations the heat or cold produced, by the addition or subtraction of a certain hypothetical 'caloric,' have become more and more rare among men of science. Such statements, and the explanations often put forwards of the light and heat which appear under various circumstances in the form of fire, must be considered as unessential parts of any sound theory. Accordingly we find Mr. Faraday gradually relinquishing such views. In January, 1834, he speaks generally of an hypothesis of this kind[32\6]: 'I cannot refrain from recalling here the beautiful idea put forth, I believe by Berzelius, in his development of his views of the electro-chemical theory of affinity, that the heat and light evolved during cases of powerful combination {44} are the consequence of the electric discharge which is at that moment taking place.' But in April of the same year[33\6], he observes, that in the combination of oxygen and hydrogen to produce water, electric powers to a most enormous amount are for the time active, but that the flame which is produced gives but feeble traces of such powers. 'Such phenomena,' therefore, he adds, 'may not, cannot, be taken as evidences of the nature of the action; but are merely incidental results, incomparably small in relation to the forces concerned, and supplying no information of the way in which the particles are active on each other, or in which their forces are finally arranged.'

[Note 32\6: Researches, 870.]

[Note 33\6: Researches, 960.]

In pursuance of this maxim, we must consider as an unessential part of the oxygen theory that portion of it, much insisted upon by its author at the time, in which when sulphur, for instance, combined with oxygen to produce sulphuric acid, the combustion was accounted for by means of the caloric which was supposed to be liberated from its combination with oxygen.

5. Controversy of the Composition of Water.--There is another controversy of our times to which we may with great propriety apply the maxim now before us. After the glory of having first given a true view of the composition of water had long rested tranquilly upon the names of Cavendish and Lavoisier, a claim was made in favour of James Watt as the real author of this discovery by his son, (Mr J. Watt,) and his eulogist, (M. Arago[34\6]). It is not to our purpose here to discuss the various questions which have arisen on this subject respecting priority of publication, and respecting the translation of opinions published at one time into the language of another period. But if we look at Watt's own statement of his views, given soon after those of Cavendish had been published, we shall perceive that it is marked by a violation of this maxim: we shall find that he does admit imponderable fluids {45} as chemical elements; and thus shows a vagueness and confusion in his idea of chemical composition. With such imperfection in his views, it is not surprising that Watt, not only did not anticipate, but did not apprehend quite precisely the discovery of Cavendish and Lavoisier. Watt's statement of his views is as follows[35\6]:--'Are we not authorized to conclude that water is composed of dephlogisticated air and phlogiston deprived of part of their latent or elementary heat; that dephlogisticated or pure air is composed of water deprived of its phlogiston and united to elementary heat and light; and that the latter are contained in it in a latent state, so as not to be sensible to the thermometer or to the eye; and if light be only a modification of heat, or a circumstance attending it, or a component part of the inflammable air, then pure or dephlogisticated air is composed of water deprived of its phlogiston and united to elementary heat?'

[Note 34\6: Éloge de James Watt, Annuaire du Bur. des Long. 1839.]

[Note 35\6: Phil. Trans. 1784, p. 332.]

When we compare this doubtful and hypothetical statement, involving so much that is extraneous and heterogeneous, with the conclusion of Cavendish, in which there is nothing hypothetical or superfluous, we may confidently assent to the decision which has been pronounced by one[36\6] of our own time in favour of Cavendish. And we may with pleasure recognize, in this enlightened umpire, a due appreciation of the value of the maxim on which we are now insisting. 'Cavendish,' says Mr. Vernon Harcourt, 'pared off {46} from the hypotheses their theories of combustion, and affinities of imponderable for ponderable matter, as complicating chemical with physical considerations.'

[Note 36\6: The Rev. W. Vernon Harcourt, Address to the British Association, 1839.--Since the first edition of this work was published, and also since the second edition of the History of the Inductive Sciences, Mr. Watt's correspondence bearing upon the question of the Composition of Water has been published by Mr. Muirhead. I do not find, in this publication, any reason for withdrawing what I have stated in the text above: but with reference to the statement in the History, it appears that Mr. Cavendish's claim to the discovery was not uncontested in his own time. Mr. Watt had looked at the composition of water, as a problem to be solved, perhaps more distinctly than Mr. Cavendish had done; and he conceived himself wronged by Mr. Cavendish's putting forwards his experiment as the first solution of this problem.]

6. Relation of Heat to Chemistry.--But while we thus condemn the attempts to explain the thermotical phenomena of chemical processes by means of chemical considerations, it may be asked if we are altogether to renounce the hope of understanding such phenomena? It is plain, it may be said, that heat generated in chemical changes is always a very important circumstance, and can sometimes be measured, and perhaps reduced to laws; are we prohibited from speculating concerning the causes of such circumstances and such laws? And to this we reply, that we may properly attempt to connect chemical with thermotical processes, so far as we have obtained a clear and probable view of the nature of the thermotical processes. When our theory of Thermotics is tolerably complete and certain, we may with propriety undertake to connect it with our theory of Chemistry. But at present we are not far enough advanced in our knowledge of heat to make this attempt with any hope of success. We can hardly expect to understand the part which heat plays in the union of two bodies, when we cannot as yet comprehend in what manner it produces the liquefaction or vaporization of one body. We cannot look to account for Gay Lussac and Dalton's Law, that all gases expand equally by heat, till we learn how heat causes a gas to expand. We cannot hope to see the grounds of Dulong and Petit's Law, that the specific heat of all atoms is the same, till we know much more, not only about atoms, but about specific heat. We have as yet no thermotical theory which even professes to account for all the prominent facts of the subject[37\6]: and the theories which have been proposed are of the most diverse kind. Laplace assumes particles of bodies surrounded by atmospheres of caloric[38\6]; Cauchy makes heat consist in longitudinal vibrations of the ether of which transverse vibrations {47} produce light: in Ampère's theory[39\6], heat consists in the vibrations of the particles of bodies. And so long as we have nothing more certain in our conceptions of heat than the alternative of these and other precarious hypotheses, how can we expect to arrive at any real knowledge, by connecting the results of such hypotheses with the speculations of Chemistry, of which science the theory is at least equally obscure?

[Note 37\6: Hist. Ind. Sci. b. x. c. 4.]

[Note 38\6: Ib.]

[Note 39\6: Hist. Ind. Sci. b. x. c. 4.]

The largest attempts at chemical theory have been made in the form of the Atomic Theory, to which I have just had occasion to allude. I must, therefore, before quitting the subject, say a few words respecting this theory.

{{48}} CHAPTER V.

THE ATOMIC THEORY.

1. The Atomic Theory considered on Chemical Grounds.--WE have already seen that the combinations which result from chemical affinity are definite, a certain quantity of one ingredient uniting, not with an uncertain, but with a certain quantity of another ingredient. But it was found, in addition to this principle, that one ingredient would often unite with another in different proportions, and that, in such cases, these proportions are multiples one of another. In the three salts formed by potassa with oxalic acid, the quantities of acid which combine with the same quantity of alkali are exactly in the proportion of the numbers 1, 2, 4. And the same rule of the existence of multiple proportions is found to obtain in other cases.

It is obvious that such results will be accounted for, if we suppose that the base and the acid consist each of numerous definite equal particles, and that the formation of the salts above mentioned consists in the combination of one particle of the base with one particle of acid, with two particles of acid, and with four particles of acid, respectively. But further; as we have already stated, chemical affinity is not only definite, but reciprocal. The proportions of potassa and soda which form neutral salts being 590 and 391 in one case, they are so in all cases. These numbers represent proportions of weight in which the two bases, potassa and soda, enter into analogous combinations; 590 of potassa is equivalent to 391 of soda. These facts with regard to combination are still expressed by the above supposition of equal particles, assuming that the weights of a {49} particle of potassa and of soda are in the proportion of 590 to 391.

But we pursue our analysis further. We find that potassa is a compound of a metallic base, potassium, and of oxygen, in the proportion of 490 to 100; we suppose, then, that the particle of potassa consists of a particle of potassium and a particle of oxygen; and these latter particles, since we see no present need to suppose them divided, potassium and oxygen being simple bodies, we may call atoms, and assume to be indivisible. And by supposing all simple bodies to consist of such atoms, and compounds to be formed by the union of two, or three, or more of such atoms, we explain the occurrence of definite and multiple proportions, and we construct the Atomic Theory.

2. Hypothesis of Atoms.--So far as the assumption of such atoms as we have spoken of serves to express those laws of chemical composition which we have referred to, it is a clear and useful generalization. But if the Atomic Theory be put forwards (and its author, Dr. Dalton, appears to have put it forwards with such an intention,) as asserting that chemical elements are really composed of atoms, that is, of such particles not further divisible, we cannot avoid remarking, that for such a conclusion, chemical research has not afforded, nor can afford, any satisfactory evidence whatever. The smallest observable quantities of ingredients, as well as the largest, combine according to the laws of proportions and equivalence which have been cited above. How are we to deduce from such facts any inference with regard to the existence of certain smallest possible particles? The Theory, when dogmatically taught as a physical truth, asserts that all observable quantities of elements are composed of proportional numbers of particles which can no further be subdivided; but all which observation teaches us is, that if there be such particles, they are smaller than the smallest observable quantities. In chemical experiment, at least, there is not the slightest positive evidence for the existence of such atoms. The assumption of indivisible particles, smaller than the smallest {50} observable, which combine, particle with particle, will explain the phenomena; but the assumption of particles bearing this proportion, but not possessing the property of indivisibility, will explain the phenomena at least equally well. The decision of the question, therefore, whether the Atomic Hypothesis be the proper way of conceiving the chemical combinations of substances, must depend, not upon chemical facts, but upon our conception of Substance. In this sense the question is an ancient and curious controversy, and we shall hereafter have to make some remarks upon it.

3. Chemical Difficulties of the Hypothesis.--But before doing this, we may observe that there is no small difficulty in reconciling this hypothesis with the facts of chemistry. According to the theory, all salts, compounded of an acid and a base, are analogous in their atomic constitution; and the number of atoms in one such compound being known or assumed, the number of atoms in other salts may be determined. But when we proceed in this course of reasoning to other bodies, as metals, we find ourselves involved in difficulties. The protoxide of iron is a base which, according to all analogy, must consist of one atom of iron and one of oxygen: but the peroxide of iron is also a base, and it appears by the analysis of this substance that it must consist of two-thirds of an atom of iron and one atom of oxygen. Here, then, our indivisible atoms must be divisible, even upon chemical grounds. And if we attempt to evade this difficulty by making the peroxide of iron consist of two atoms of iron and three of oxygen, we have to make a corresponding alteration in the theoretical constitution of all bodies analogous to the protoxide; and thus we overturn the very foundation of the theory. Chemical facts, therefore, not only do not prove the Atomic Theory as a physical truth, but they are not, according to any modification yet devised of the theory, reconcileable with its scheme.

Nearly the same conclusions result from the attempts to employ the Atomic Hypothesis in expressing another important chemical law;--the law of the {51} combinations of gases according to definite proportions of their volumes, experimentally established by Gay Lussac[40\6]. In order to account for this law, it has been very plausibly suggested that all gases, under the same pressure, contain an equal number of atoms in the same space; and that when they combine, they unite atom to atom. Thus one volume of chlorine unites with one volume of hydrogen, and forms hydrochloric acid[41\6]. But then this hydrochloric acid occupies the space of the two volumes; and therefore the proper number of particles cannot be supplied, and the uniform distribution of atoms in all gases maintained, without dividing into two each of the compound particles, constituted of an atom of chlorine and an atom of hydrogen. And thus in this case, also, the Atomic Theory becomes untenable if it be understood to imply the indivisibility of the atoms.

[Note 40\6: Hist. Ind. Sc. b. xiv. c. 8.]

[Note 41\6: Dumas, Phil. Chim. 263.]

In all these attempts to obtain distinct physical conception of chemical union by the aid of the Atomic Hypothesis, the atoms are conceived to be associated by certain forces of the nature of mechanical attractions. But we have already seen[42\6] that no such mode of conception can at all explain or express the facts of chemical combination; and therefore it is not wonderful that when the Atomic Theory attempts to give an account of chemical relations by contemplating them under such an aspect, the facts on which it grounds itself should be found not to authorize its positive doctrines; and that when these doctrines are tried upon the general range of chemical observation, they should prove incapable of even expressing, without self-contradiction, the laws of phenomena.

[Note 42\6: See Chapter I. of this book.]

4. Grounds of the Atomic Doctrine.--Yet the doctrine of atoms, or of substance as composed of indivisible particles, has in all ages had great hold upon the minds of physical speculators; nor would this doctrine ever have suggested itself so readily, or have been maintained so tenaciously, as the true mode of {52} conceiving chemical combinations, if it had not been already familiar to the minds of those who endeavour to obtain a general view of the constitution of nature. The grounds of the assumption of the atomic structure of substance are to be found rather in the idea of substance itself, than in the experimental laws of chemical affinity. And the question of the existence of atoms, thus depending upon an idea which has been the subject of contemplation from the very infancy of philosophy, has been discussed in all ages with interest and ingenuity. On this very account it is unlikely that the question, so far as it bears upon chemistry, should admit of any clear and final solution. Still it will be instructive to look back at some of the opinions which have been delivered respecting this doctrine.

5. Ancient Prevalence of the Atomic Doctrine.--The doctrine that matter consists of minute, simple, indivisible, indestructible particles as its ultimate elements, has been current in all ages and countries, whenever the tendency of man to wide and subtle speculations has been active. I need not attempt to trace the history of this opinion in the schools of Greece and Italy. It was the leading feature in the physical tenets of the Epicureans, and was adopted by their Roman disciples, as the poem of Lucretius copiously shows us. The same tenet had been held at still earlier periods, in forms more or less definite, by other philosophers. It is ascribed to Democritus, and is said to have been by him derived from Leucippus. But this doctrine is found also, we are told[43\6], among the speculations of another intellectual and acute race, the Hindoos. According to some of their philosophical writers, the ultimate elements of matter are atoms, of which it is proved by certain reasonings, that they are each one-sixth of one of the motes that float in the sunbeam.

[Note 43\6: By Mr. Colebrook. Asiatic Res. 1824.]

This early prevalence of controversies of the widest and deepest kind, which even in our day remain undecided, has in it nothing which need surprize us; or, at least, it has in it nothing which is not in conformity {53} with the general course of the history of philosophy. As soon as any ideas are clearly possessed by the human mind, its activity and acuteness in reasoning upon them are such, that the fundamental antitheses and ultimate difficulties which belong to them are soon brought into view. The Greek and Indian philosophers had mastered completely the Idea of Space, and possessed the Idea of Substance in tolerable distinctness. They were, therefore, quite ready, with their lively and subtle minds, to discuss the question of the finite and infinite divisibility of matter, so far as it involved only the ideas of space and of substance, and this accordingly they did with great ingenuity and perseverance.

But the ideas of Space and of Substance are far from being sufficient to enable men to form a complete general view of the constitution of matter. We must add to these ideas, that of mechanical Force with its antagonist Resistance, and that of the Affinity of one kind of matter for another. Now the former of these ideas the ancients possessed in a very obscure and confused manner; and of the latter they had no apprehension whatever. They made vague assumptions respecting the impact and pressure of atoms on each other; but of their mutual attraction and repulsion they never had any conception, except of the most dim and wavering kind; and of an affinity different from mere local union they did not even dream. Their speculations concerning atoms, therefore, can have no value for us, except as a part of the history of science. If their doctrines appear to us to approach near to the conclusions of our modern philosophy, it must be because our modern philosophy is that philosophy which has not fully profited by the additional light which the experiments and meditations of later times have thrown upon the constitution of matter.

6. Bacon.--Still, when modern philosophers look upon the Atomic Theory of the ancients in a general point of view merely, without considering the special conditions which such a theory must fulfil, in order to represent the discoveries of modern times, they are {54} disposed to regard it with admiration. Accordingly we find Francis Bacon strongly expressing such a feeling. The Atomic Theory is selected and dwelt upon by him as the chain which connects the best parts of the physical philosophy of the ancient and the modern world. Among his works is a remarkable dissertation On the Philosophy of Democritus, Parmenides, and Telesius: the last mentioned of whom was one of the revivers of physical science in modern times. In this work he speaks of the atomic doctrine of Democritus as a favourable example of the exertions of the undisciplined intellect. 'Hæc ipsa placita, quamvis paulo emendatiora, talia sunt qualia esse possunt illa quæ ab intellectu sibi permisso, nec continenter et gradatim sublevato, profecta videntur.'--'These doctrines, thus [in an ancient fable] presented in a better form, are such glimpses of truth as can be obtained by the intellect left to its own natural impulses, and not ascending by successive and connected steps,' [as the Baconian philosophy directs]. 'Accordingly,' he adds, 'the doctrine of Atoms, from its going a step beyond the period in which it was advanced, was ridiculed by the vulgar, and severely handled in the disputations of the learned, notwithstanding the profound acquaintance with physical science by which its author was allowed to be distinguished, and from which he acquired the character of a magician.'

'However,' he continues, 'neither the hostility of Aristotle, with all his skill and vigour in disputation, (though, like the Ottoman sultans, he laboured to destroy all his brother philosophers that he might rest undisputed master of the throne of science,) nor the majestic and lofty authority of Plato, could effect the subversion of the doctrine of Democritus. And while the opinions of Plato and Aristotle were rehearsed with loud declamation and professorial pomp in the schools, this of Democritus was always held in high honour by those of a deeper wisdom, who followed in silence a severer path of contemplation. In the days of Roman speculation it kept its ground and its favour; Cicero everywhere speaks of its author with the {55} greatest praise; and Juvenal, who, like poets in general, probably expressed the prevailing judgment of his time, proclaims his merit as a noble exception to the general stupidity of his countrymen. . . . . Cujus prudentia monstrat Magnos posse viros et magna exempla daturos Vervecum in patriâ crassoque sub aere nasci.

'The destruction of this philosophy was not effected by Aristotle and Plato, but by Genseric and Attila, and their barbarians. For then, when human knowledge had suffered shipwreck, those fragments of the Aristotelian and Platonic philosophy floated on the surface like things of some lighter and emptier sort, and so were preserved; while more solid matters went to the bottom, and were almost lost in oblivion.'

7. Modern Prevalence of the Atomic Doctrine.--It is our business here to consider the doctrine of Atoms only in its bearing upon existing physical sciences, and I must therefore abstain from tracing the various manifestations of it in the schemes of hypothetical cosmologists;--its place among the vortices of Descartes, its exhibition in the monads of Leibnitz. I will, however, quote a passage from Newton to show the hold it had upon his mind.

At the close of his Opticks he says, 'All these things being considered, it seems probable to me that God, in the beginning, formed matter in solid, massy, hard, impenetrable, moveable particles, of such sizes and figures, and with such other properties, and in such proportions to space, as most conduced to the end for which He formed them; and that the primitive particles, being solids, are incomparably harder than any porous bodies compounded of them, even so very hard as never to wear or break in pieces; no ordinary power being able to divide what God had made one in the first creation. While the particles continue entire, they may compose bodies of one and the same nature and texture in all ages: but should they wear away or break in pieces, the nature of things depending on them would be changed. Water and earth composed {56} of old worn particles and fragments of particles would not be of the same nature and texture now with water and earth composed of entire particles in the beginning. And therefore that nature may be lasting, the changes of corporeal things are to be placed only in the various separations and new associations and motions of these permanent particles; compounded bodies being apt to break, not in the midst of solid particles, but where those particles are laid together and only touch in a few points.'

We shall hereafter see how extensively the atomic doctrine has prevailed among still more recent philosophers. Not only have the chemists assumed it as the fittest form for exhibiting the principles of multiple proportions; but the physical mathematicians, as Laplace and Poisson, have made it the basis of their theories of heat, electricity, capillary action; and the crystallographers have been supposed to have established both the existence and the arrangement of such ultimate molecules.

In the way in which it has been employed by such writers, the hypothesis of ultimate particles has been of great use, and is undoubtedly permissible. But when we would assert this theory, not as a convenient hypothesis for the expression or calculation of the laws of nature, but as a philosophical truth respecting the constitution of the universe, we find ourselves checked by difficulties of reasoning which we cannot overcome, as well as by conflicting phenomena which we cannot reconcile. I will attempt to state briefly the opposing arguments on this question.

8. Arguments for and against Atoms.--The leading arguments on the two sides of the question, in their most general form, may be stated as follows:

For the Atomic Doctrine.--The appearances which nature presents are compounded of many parts, but if we go on resolving the larger parts into smaller, and so on successively, we must at last come to something simple. For that which is compound can be so no otherwise than by composition of what is simple; and if we suppose all composition to be removed, which {57} hypothetically we may do, there can remain nothing but a number of simple substances, capable of composition, but themselves not compounded. That is, matter being dissolved, resolves itself into atoms.

Against the Atomic Doctrine.--Space is divisible without limit, as may be proved by Geometry; and matter occupies space, therefore matter is divisible without limit, and no portion of matter is indivisible, or an atom.

And to the argument on the other side just stated, it is replied that we cannot even hypothetically divest a body of composition, if by composition we mean the relation of point to point in space. However small be a particle, it is compounded of parts having relation in space.

The Atomists urge again, that if matter be infinitely divisible, a finite body consists of an infinite number of parts, which is a contradiction. To this it is replied, that the finite body consists of an infinite number of parts in the same sense in which the parts are infinitely small, which is no contradiction.

But the opponents of the Atomists not only rebut, but retort this argument drawn from the notion of infinity. Your atoms, they say, are indivisible by any finite force; therefore they are infinitely hard; and thus your finite particles possess infinite properties. To this the Atomists are wont to reply, that they do not mean the hardness of their particles to be infinite, but only so great as to resist all usual natural forces. But here it is plain that their position becomes untenable; for, in the first place, their assumption of this precise degree of hardness in the particles is altogether gratuitous; and in the next place, if it were granted, such particles are not atoms, since in the next moment the forces of nature may be augmented so as to divide the particle, though hitherto undivided.

Such are the arguments for and against the Atomic Theory in its original form. But when these atoms are conceived, as they have been by Newton, and commonly by his followers, to be solid, hard particles exerting attractive and repulsive forces, a new set of {58} arguments come into play. Of these, the principal one may be thus stated: According to the Atomic Theory thus modified, the properties of bodies depend upon the attractions and repulsions of the particles. Therefore, among other properties of bodies, their hardness depends upon such forces. But if the hardness of the bodies depends upon the forces, the repulsion, for instance, of the particles, upon what does the hardness of the particles depend? what progress do we make in explaining the properties of bodies, when we assume the same properties in our explanation? and to what purpose do we assume that the particles are hard?

9. Transition to Boscovich's Theory.--To this difficulty it does not appear easy to offer any reply. But if the hardness and solidity of the particles be given up as an incongruous and untenable appendage to the Newtonian view of the Atomic Theory, we are led to the theory of Boscovich, according to which matter consists not of solid particles, but of mere mathematical centers of force. According to this theory, each body is composed of a number of geometrical points from which emanate forces, following certain mathematical laws in virtue of which the forces become, at certain small distances attractive, at certain other distances repulsive, and at greater distances attractive again. From these forces of the points arise the cohesion of the parts of the same body, the resistance which it exerts against the pressure of another body, and finally the attraction of gravitation which it exerts upon bodies at a distance.

This theory is at least a homogeneous and consistent theory, and it is probable that it may be used as an instrument for investigating and expressing true laws of nature; although, as we have already said, the attempt to identify the forces by which the particles of bodies are bound together with mechanical attraction, appears to be a confusion of two separate ideas[44\6].

[Note 44\6: 'Boscovich's Theory,' that all bodies may be considered as consisting of a mere collection of centers of forces, may be so conceived as possibly to involve an explanation of all the powers which their parts exert, (such powers, namely, as those which produce optical, thermotical and chemical phenomena;) but this theory cannot supply an explanation of the mechanical properties of a body as a whole, especially of its inertia. A collection of mere centers of force can have no inertia. If two bodies are considered as two collections of centers of force, the one attracting the other, there is in this view nothing to limit or determine the velocity with which the one body will approach the other. A world composed of such bodies is not a material world: for matter (as we have already seen in book iii. chapter v.) implies not only force, but something which resists the action of force.]

{59} 10. Use of the Molecular Hypothesis.--In this form, representing matter as a collection of molecules or centers of force, the Atomic Theory has been abundantly employed in modern times as an hypothesis on which calculations respecting the elementary forces of bodies might be conducted. When thus employed it is to be considered as expressing the principle that the properties of bodies depend upon forces emanating from immovable points of their mass. This view of the way in which the properties of bodies are to be treated by the mechanical philosopher was introduced by Newton, and was a natural sequel to the success which he had obtained by reasoning concerning central forces on a large scale. I have already quoted his Preface to the Principia, in which he says, 'Many things induce me to believe that the rest of the phenomena of nature, as well as those of astronomy, may depend upon certain forces by which the particles of bodies, in virtue of causes not yet known, are urged towards each other and cohere in regular figures, or are mutually repelled and recede; and philosophers, knowing nothing of these forces, have hitherto failed in their examination of nature.' Since the time of Newton, this line of speculation has been followed with great assiduity, and by some mathematicians with great success. In particular Laplace has shown that the hypothesis may, in many instances, be made a much closer representation of nature, if we suppose the forces exerted by the particles to decrease so rapidly with the increasing distance from them, that {60} the force is finite only at distances imperceptible to our senses, and vanishes at all remoter points. He has taught the method of expressing and calculating such forces, and he and other mathematicians of his school have applied this method to many of the most important questions of physics; as capillary action, the elasticity of solids, the conduction and radiation of heat. The explanation of many apparently unconnected and curious observed facts by these mathematical theories gives a strong assurance that its essential principles are true. But it must be observed that the actual constitution of bodies as composed of distinct and separate particles is by no means proved by these coincidences. The assumption, in the reasoning, of certain centers of force acting at a distance, is to be considered as nothing more than a method of reducing to calculation that view of the constitution of bodies which supposes that they exert force at every point. It is a mathematical artifice of the same kind as the hypothetical division of a body into infinitesimal parts, in order to find its center of gravity; and no more implies a physical reality than that hypothesis does.

11. Poisson's Inference.--When, therefore, M. Poisson, in his views of Capillary Action, treats this hypothetical distribution of centers of force as if it were a physical fact, and blames Laplace for not taking account of their different distribution at the surface of the fluid and below it[45\6], he appears to push the claims of the molecular hypothesis too far. The only ground for the assumption of separate centers, is that we can thus explain the action of the whole mass. The intervals between the centers nowhere enter into this explanation: and therefore we can have no reason for assuming these intervals different in one part of the fluid and in the other. M. Poisson asserts that the density of the fluid diminishes when we approach very near the surface; but he allows that this diminution is not detected by experiment, and that the formulæ on {61} his supposition, so far as the results go, are identical with those of Laplace. It is clear, then, that his doctrine consists merely in the assertion of the necessary truth of a part of the hypothesis which cannot be put to the test of experiment. It is true, that so long as we have before us the hypothesis of separate centers, the particles very near the surface are not in a condition symmetrical with that of the others: but it is also true that this hypothesis is only a step of calculation. There results, at one period of the process of deduction, a stratum of smaller density at the surface of the fluid; but at a succeeding point of the reasoning the thickness of this stratum vanishes; it has no physical existence.

[Note 45\6: Poisson, Théorie de l'Action Capillaire.]

Thus the molecular hypothesis, as used in such cases, does not differ from the doctrine of forces acting at every point of the mass; and this principle, which is common to both the opposite views, is the true part of each.

12. Wollaston's Argument.--An attempt has been made in another case, but depending on nearly the same arguments, to bring the doctrine of ultimate atoms to the test of observation. In the case of the air, we know that there is a diminution of density in approaching the upper surface of the atmosphere, if it have a surface: but it is held by some that except we allow the doctrine of ultimate molecules, it will not be bounded by any surface, but will extend to an infinite distance. This is the reasoning of Wollaston[46\6]. 'If air consists of any ultimate particles no longer divisible, then must the expansion of the medium composed of them cease at that distance where the force of gravity downwards is equal to the resistance arising from the repulsive force of the medium.' But if there be no such ultimate particles, every stratum will require a stratum beyond it to prevent by its weight a further expansion, and thus the atmosphere {62} must extend to an infinite distance. And Wollaston conceived that he could learn from observation whether the atmosphere was thus diffused through all space; for if so, it must, he argued, be accumulated about the larger bodies of the system, as Jupiter and the Sun, by the law of universal gravitation; and the existence of an atmosphere about these bodies, might, he remarked, be detected by its effects in producing refraction. His result is, that 'all the phenomena accord entirely with the supposition that the earth's atmosphere is of finite extent, limited by the weight of ultimate atoms of definite magnitude, no longer divisible by repulsion of their parts.'

[Note 46\6: Phil. Trans. 1822, p. 89.]

A very little reflection will show us that such a line of reasoning cannot lead to any result. For we know nothing of the law which connects the density with the compressing force, in air so extremely rare as we must suppose it to be near the boundary of the atmosphere. Now there are possible laws of dependence of the density upon the compressing force such that the atmosphere would terminate in virtue of the law without any assumption of atoms. This may be proved by mathematical reasoning. If we suppose the density of air to be as the square root of the compressing force, it will follow that at the very limits of the atmosphere, the strata of equal thickness may observe in their densities such a law of proportion as is expressed by the numbers 7, 5, 3, 1[47\6].

[Note 47\6: For the compressing force on each being as the whole weight beyond it, it will be for the four highest strata, 16, 9, 4 and 1, of which the square roots are as 4, 3, 2, 1, or, as 8, 6, 4, 2; and though these numbers are not exactly as the densities 7, 5, 3, 1, those who are a little acquainted with mathematical reasoning, will see that the difference arises from taking so small a number of strata. If we were to make the strata indefinitely thin, as to avoid error we ought to do, the coincidence would be exact; and thus, according to this law, the series of strata terminates as we ascend, without any consideration of atoms.]

If it be asked how, on this hypothesis, the density of the highest stratum can be as 1, since there is {63} nothing to compress it, we answer that the upper part of the highest stratum compresses the lower, and that the density diminishes continually to the surface, so that the need of compression and the compressing weight vanish together.

The fallacy of concluding that because the height of the atmosphere is finite, the weight of the highest stratum must be finite, is just the same as the fallacy of those who conclude that when we project a body vertically upwards, because it occupies only a finite time in ascending to the highest point, the velocity at the last instant of the ascent must be finite. For it might be said, if the last velocity of ascent be not finite, how can the body describe the last particle of space in a finite time? and the answer is, that there is no last finite particle of space, and therefore no last finite velocity.

13. Permanence of Properties of Bodies.--We have already seen that, in explaining the properties of matter as we find them in nature, the assumption of solid, hard, indestructible particles is of no use or value. But we may remark, before quitting the subject, that Newton appears to have had another reason for assuming such particles, and one well worthy of notice. He wished to express, by means of this hypothesis, the doctrine that the laws of nature do not alter with the course of time. This we have already seen in the quotation from Newton. 'The ultimate particles of matter are indestructible, unalterable, impenetrable; for if they could break or wear, the structure of material bodies now would be different from that which it was when the particles were new.' No philosopher will deny the truth which is thus conveyed by the assertion of atoms; but it is obviously equally easy for a person who rejects the atomic view, to state this truth by saying that the forces which matter exerts do not vary with time, but however modified by the new modifications of its form, are always unimpaired in quantity, and capable of being restored to their former mode of action. {64}

We now proceed to speculations in which the fundamental conceptions may, perhaps, be expressed, at least in some cases, by means of the arrangement of atoms; but in which the philosophy of the subject appears to require a reference to a new Fundamental Idea.

{{65}} BOOK VII.

THE PHILOSOPHY OF MORPHOLOGY, INCLUDING CRYSTALLOGRAPHY.

CRYSTALLIZATION exhibits to us the effects of the natural arrangement of the ultimate particles of various compound bodies; but we are scarcely yet sufficiently acquainted with chemical synthesis and analysis to understand the rationale of this process. The rhomboidal form may arise from the proper position of 4, 6, 8 or 9 globular particles, the cubic form from 8 particles, the triangular form from 3, 6 or 10 particles, the hexahedral prism from 7 particles, &c. Perhaps, in due time we may be enabled to ascertain the number and order of elementary particles, constituting any given compound element, and from that determine the figure which it will prefer on crystallization, and vice versâ.

JOHN DALTON, Chemical Philosophy (1808), p. 210.

{{67}} BOOK VII.

THE PHILOSOPHY OF MORPHOLOGY, INCLUDING CRYSTALLOGRAPHY.

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I. EXPLICATION OF THE IDEA OF SYMMETRY

1. WE have seen in the History of the Sciences, that the principle which I have there termed[1\7] the Principle of Developed and Metamorphosed Symmetry, has been extensively applied in botany and physiology, and has given rise to a province of science termed Morphology. In order to understand clearly this principle, it is necessary to obtain a clear idea of the Symmetry of which we thus speak. But this Idea of Symmetry is applicable in the inorganic, as well as in the organic kingdoms of nature; it is presented to our eyes in the forms of minerals, as well as of flowers and animals; we must, therefore, take it under our consideration here, in order that we may complete our view of Mineralogy, which, as I have repeatedly said, is an essential part of Chemical science. I shall accordingly endeavour to unfold the Idea of Symmetry with which we here have to do.

[Note 1\7: Hist. Ind. Sc. b. xvii. c. vi.]

It will of course be understood that by the term Symmetry I here intend, not that more indefinite attribute of form which belongs to the domain of the fine arts, as when we speak of the 'symmetry' of an edifice {68} or of a sculptured figure, but a certain definite relation or property, no less rigorous and precise than other relations of number and position, which is thus one of the sure guides of the scientific faculty, and one of the bases of our exact science.

2. In order to explain what Symmetry is in this sense, let the reader recollect that the bodies of animals consist of two equal and similar sets of members, the right and the left side;--that some flowers consist of three or of five equal sets of organs, similarly and regularly disposed, as the iris has three straight petals, and three reflexed ones, alternately disposed, the rose has five equal and similar sepals of the calyx, and alternate with these, as many petals of the corolla. This orderly and exactly similar distribution of two, or three, or five, or any other number of parts, is Symmetry; and according to its various modifications, the forms thus determined are said to be symmetrical with various numbers of members. The classification of these different kinds of symmetry has been most attended to in Crystallography, in which science it is the highest and most general principle by which the classes of forms are governed. Without entering far into the technicalities of the subject, we may point out some of the features of such classes.

3. These different kinds of symmetry occur in various ways in the animal, vegetable, and mineral kingdom. Vertebrate animals have a right and a {70} left side exactly alike, and thus possess simple symmetry. The same kind of symmetry (simple symmetry) occurs very largely in the forms of vegetables, as in most leaves, in papilionaceous, personate, and labiate flowers. Among minerals, crystals which possess this symmetry are called oblique-prismatic, and are of very frequent occurrence. The oblong, or two-and-two-membered symmetry belongs to right-prismatic crystals; and may be seen in cruciferous flowers, for though these are cross-shaped, the cross has two longer and two shorter arms, or pairs of arms. The square or tetragonal symmetry occurs in crystals abundantly; to the vegetable world it appears to be less congenial; for though there are flowers with four exactly similar and regularly-disposed petals, as the herb Paris (Paris quadrifolia), these flowers appear, from various circumstances, to be deviations from the usual type of vegetable forms. The trigonal, or three-membered symmetry is found abundantly both in plants and in crystals, while the pentagonal symmetry, on the other hand, though by far the most common among flowers, nowhere occurs in minerals, and does not appear to be a possible form of crystals. This pentagonal form further occurs in the animal kingdom, which the oblong, triangular, and square forms do not. Many of Cuvier's radiate animals appear in this pentagonal form, as echini and pentacrinites, which latter have hence their name.

4. The regular, or as they may be called, the normal types of the vegetable world appear to be the forms which possess triangular and pentagonal symmetry; from these the others may be conceived to be derived, by transformations resulting from the expansion of one or more parts. Thus it is manifest that if in a three-membered or five-membered flower, one of the petals be expanded more than the other, it is immediately reduced from pentagonal or trigonal, to simple symmetry. And the oblong or two-and-two-membered symmetry of the flowers of cruciferous plants, (in which the stamens are four large and two small ones, arranged in regular opposition,) is held by botanists to result {71} from a normal form with ten stamens; Meinecke explaining this by adhesion, and Sprengel by the metamorphosis of the stamens into petals[2\7].

[Note 2\7: Sprengel, Gesch. d. Bot. ii. 304.]

It is easy to see that these various kinds of symmetry include relations both of form and of number, but more especially of the latter kind; and as this symmetry is often an important character in various classes of natural objects, such classes have often curious numerical properties. One of the most remarkable and extensive of these is the distinction which prevails between monocotyledonous and dicotyledonous plants; the number three being the ground of the symmetry of the former, and the number five, of the latter. Thus liliaceous and bulbous plants, and the like, have flowers of three or six petals, and the other organs follow the same numbers: while the vast majority of plants are pentandrous, and with their five stamens have also their other parts in fives. This great numerical distinction corresponding to a leading difference of physiological structure cannot but be considered as a highly curious fact in phytology. Such properties of numbers, thus connected in an incomprehensible manner with fundamental and extensive laws of nature, give to numbers an appearance of mysterious importance and efficacy. We learn from history how strongly the study of such properties, as they are exhibited by the phenomena of the heavens, took possession of the mind of Kepler; perhaps it was this which, at an earlier period, contributed in no small degree to the numerical mysticism of the Pythagoreans in antiquity, and of the Arabians and others in the middle ages. In crystallography, numbers are the primary characters in which the properties of substances are expressed;--they appear, first, in that classification of forms which depends on the degree of symmetry, that is, upon the number of correspondencies; and next, in the laws of derivation, which, for the most part, appear to be common in their occurrence in proportion to the numerical simplicity of their expression. But the manifestation {72} of a governing numerical relation in the organic world strikes us as more unexpected; and the selection of the number five as the index of the symmetry of dicotyledonous plants and radiated animals, (a number which is nowhere symmetrically produced in inorganic bodies,) makes this a new and remarkable illustration of the constancy of numerical relations. We may observe, however, that the moment one of these radiate animals has one of its five members expanded, or in any way peculiarly modified, (as happens among the echini), it is reduced to the common type of animals simply symmetrical, with a right and left side.

5. It is not necessary to attempt to enumerate all the kinds of Symmetry, since our object is only to explain what Symmetry is, and for this purpose enough has probably been said already. It will be seen, as soon as the notion of Symmetry in general is well apprehended, that it is or includes a peculiar Fundamental Idea, not capable of being resolved into any of the ideas hitherto examined. It may be said, perhaps, that the Idea of Symmetry is a modification or derivative of our ideas of space and number;--that a symmetrical shape is one which consists of parts exactly similar, repeated a certain number of times, and placed so as to correspond with each other. But on further reflection it will be seen that this repetition and correspondence of parts in symmetrical figures are something peculiar; for it is not any repetition or any correspondence of parts to which we should give the name of symmetry, in the manner in which we are now using the term. Symmetrical arrangements may, no doubt, be concerned with space and position, time and number; but there appears to be implied in them a Fundamental Idea of regularity, of completeness, of complex simplicity, which is not a mere modification of other ideas.

6. It is, however, not necessary, in this and in similar cases, to determine whether the idea which we have before us be a peculiar and independent Fundamental Idea or a modification of other ideas, provided we clearly perceive the evidence of those Axioms by {73} means of which the Idea is applied in scientific reasonings. Now in the application of the Idea of Symmetry to crystallography, phytology and zoology, we must have this idea embodied in some principle which asserts more than a mere geometrical or numerical accordance of members. We must have it involved in some vital or productive action, in order that it may connect and explain the facts of the organic world. Nor is it difficult to enunciate such a principle. We may state it in this manner. All the symmetrical members of a natural product are, under like circumstances, alike affected by the natural formative power. The parts which we have termed symmetrical, resemble each other, not only in their form and position, but also in the manner in which they are produced and modified by natural causes. And this principle we assume to be necessarily true, however unknown and inconceivable may be the causes which determine the phenomena. Thus it has not yet been found possible to discover or represent to ourselves, in any intelligible manner, the forces by which the various faces of a crystal are consequent upon its primary form: for the hypothesis of their being built up of integrant molecules, as Haüy held, cannot be made satisfactory. But though the mechanism of crystals is still obscure, there is no doubt as to the principle which regulates their modifications. The whole of crystallography rests upon this principle, that if one of the primary planes or axes be modified in any manner, all the symmetrical planes and axes must be modified in the same manner. And though accidental mechanical or other causes may interfere with the actual exhibition of such faces, we do not the less assume their crystallographical reality, as inevitably implied in the law of symmetry of the crystal[3\7]. And we apply similar considerations to organized beings. We assume that in a regular flower, each of the similar {74} members has the same organization and similar powers of developement; and hence if among these similar parts some are much less developed than others, we consider them as abortive; and if we wish to remove doubts as to what are symmetrical members in such a case, we make the inquiry by tracing the anatomy of these members, or by following them in their earlier states of developement, or in cases where their capabilities are magnified by monstrosity or otherwise. The power of developement may be modified by external causes, and thus we may pass from one kind of symmetry to another; as we have already remarked. Thus a regular flower with pentagonal symmetry, growing on a lateral branch, has one petal nearest to the axis of the plant: if this petal be more or less expanded than the others, the pentagonal symmetry is interfered with, and the flower may change to a symmetry of another kind. But it is easy to see that all such conceptions of expansion, abortion, and any other kind of metamorphosis, go upon the supposition of identical faculties and tendencies in each similar member, in so far as such tendencies have any relation to the symmetry. And thus the principle we have stated above is the basis of that which, in the History, we termed the Principle of Developed and Metamorphosed Symmetry.

[Note 3\7: Some crystalline forms, instead of being holohedral (provided with their whole number of faces), are hemihedral (provided with only half their number of faces). But in these hemihedral forms the half of the faces are still symmetrically suppressed.]

We shall not at present pursue the other applications of this Idea of Symmetry, but we shall consider some of the results of its introduction into Crystallography.

{{75}} CHAPTER II.

APPLICATION OF THE IDEA OF SYMMETRY TO CRYSTALS.

1. MINERALS and other bodies of definite chemical composition often exhibit that marked regularity of form and structure which we designate by terming them Crystals; and in such crystals, when we duly study them, we perceive the various kinds of symmetry of which we have spoken in the previous chapter. And the different kinds of symmetry which we have there described are now usually distinguished from each other, by writers on crystallography. Indeed it is mainly to such writers that we are indebted for a sound and consistent classification of the kinds and degrees of symmetry of which forms are capable. But this classification was by no means invented as soon as mineralogists applied themselves to the study of crystals. These first attempts to arrange crystalline forms were very imperfect; those, for example, of Linnæus, Werner, Romé de Lisle, and Haüy. The essays of these writers implied a classification at once defective and superfluous. They reduced all crystals to one or other of certain fundamental forms; and this procedure might have been a perfectly good method of dividing crystalline forms into classes, if the fundamental forms had been selected so as to exemplify the different kinds of symmetry. But this was not the case. Haüy's fundamental or 'primitive' forms, were, for instance, the following: the parallelepiped, the octahedron, the tetrahedron, the regular hexagonal prism, the rhombic dodecahedron, and the double hexagonal pyramid. Of these, the octahedron, the tetrahedron, the rhombic dodecahedron, all belong to the {76} same kind of symmetry (the TESSULAR systems); also the hexagonal prism and the hexagonal pyramid both belong to the RHOMBIC system; while the parallelepiped is so employed as to include all kinds of symmetry.

It is, however, to be recollected that Haüy, in his selection of primitive forms, not only had an eye to the external form of the crystal and to its degree and kind of regularity, but also made his classification with an especial reference to the cleavage of the mineral, which he considered as a primary element in crystalline analysis. There can be no doubt that the cleavage of a crystal is one of its most important characters: it is a relation of form belonging to the interior, which is to be attended to no less than the form of the exterior. But still, the cleavage is to be regarded only as determining the degree of geometrical symmetry of the body, and not as defining a special geometrical figure to which the body must be referred. To have looked upon it in the latter light, was a mistake of the earlier crystallographic speculators, on which we shall shortly have to remark.

2. I have said that the reference of crystals to Primitive Forms might have been well employed as a mode of expressing a just classification of them. This follows as a consequence from the application of the Principle stated in the last chapter, that all symmetrical members are alike affected. Thus we may take an upright triangular prism as the representative of the rhombic system, and if we then suppose one of the upper edges to be cut off, or truncated, we must, by the Principle of Symmetry, suppose the other two upper edges to be truncated in precisely the same manner. By this truncation we may obtain the upper part of a rhombohedron; and by truncations of the same kind, symmetrically affecting all the analogous parts of the figure, we may obtain any other form possessing three-membered symmetry. And the same is true of any of the other kinds of symmetry, provided we make a proper selection of a fundamental form. And this was really the method employed by Demeste, Werner, and Romé de Lisle. They {77} assumed a Primitive Form, and then conceived other forms, such as they found in nature, to be derived from the Primitive Form by truncation of the edges, acumination of the corners, and the like processes. This mode of conception was a perfectly just and legitimate expression of the general Idea of Symmetry.

3. The true view of the degrees of symmetry was, as I have already said, impeded by the attempts which Haüy and others made to arrive at primitive forms by the light which cleavage was supposed to throw upon the structure of minerals. At last, however, in Germany, as I have narrated in the History of Mineralogy[4\7], Weiss and Mohs introduced a classification of forms implying a more philosophical principle, dividing the forms into Systems; which, employing the terms of the latter writer, we shall call the tessular, the pyramidal or square pyramidal, the prismatic or oblong, and the rhombohedral systems.

[Note 4\7: Hist. Ind. Sc. b. xv. c. iv.]

Of these forms, the three latter may be at once referred to those kinds of symmetry of which we have spoken in the last chapter. The rhombohedral system has triangular symmetry, or is three-membered: the pyramidal has square symmetry, or is four-membered: the prismatic has oblong symmetry, and is two-and-two-membered. But the kinds of symmetry which were spoken of in the former chapter, do not exhaust the idea when applied to minerals. For the symmetry which was there explained was such only as can be exhibited on a surface, whereas the forms of crystals are solid. Not only have the right and left parts of the upper surface of a crystal relations to each other; but the upper surface and the lateral faces of the crystal have also their relations; they may be different, or they may be alike. If we take a cube, and hold it so that four of its faces are vertical, not only are all these four sides exactly similar, so as to give square symmetry; but also we may turn the cube, so that any one of these four sides shall become the top, and still the four sides which are thus made vertical, though {78} not the same which were vertical before, are still perfectly symmetrical. Thus this cubical figure possesses more than square symmetry. It possesses square symmetry in a vertical as well as in a horizontal sense. It possesses a symmetry which has the same relation to a cube which four-membered symmetry has to a square. And this kind of symmetry is termed the cubical or tessular symmetry. All the other kinds of symmetry have reference to an axis, about which the corresponding parts are disposed; but in tessular symmetry the horizontal and vertical axes are also symmetrical, or interchangeable; and thus the figure may be said to have no axis at all.

4. It has already been repeatedly stated that, by the very idea of symmetry, all the incidents of form must affect alike all the corresponding parts. Now in crystals we have, among these incidents, not only external figure, but cleavage, which may be considered as internal figure. Cleavage, then, must conform to the degree of symmetry of the figure. Accordingly cleavage, no less than form, is to be attended to in determining to what system a mineral belongs. If a crystal were to occur as a square prism or pyramid, it would not on that account necessarily belong to the square pyramidal system. If it were found that it was cleavable parallel to one side of the prism, but not in the transverse direction, it has only oblong symmetry; and the equality of the sides which makes it square is only accidental.

Thus no cleavage is admissible in any system of crystallization which does not agree with the degree of symmetry of the system. On the other hand, any cleavage which is consistent with the symmetry of the system, is (hypothetically at least) allowable. Thus in the oblong prismatic system we may have a cleavage parallel to one side only of the prism; or parallel to both, but of different distinctness; or parallel to the two diagonals of the prism but of the same distinctness; or we may have both these cleavages together. In the rhombohedral system, the cleavage may be parallel to the sides of the rhombohedron, as in Calc {79} Spar: or, in the same system, the cleavage, instead of being thus oblique to the axis, may be along the axis in those directions which make equal angles with each other: this cleavage easily gives either a triangular or a hexagonal prism. Again, in the tessular system, the cleavage may be parallel to the surface of the cube, which is thus readily separable into other cubes, as in Galena; or the cleavage may be such as to cut off the solid angle of the cube, and since there are eight of these, such cleavage gives us an octahedron, which, however, may be reduced to a tetrahedron, by rejecting all parallel faces, as being mere repetitions of the same cleavage; this is the case with Fluor Spar: or the cube of the tessular system may be cleavable in planes which truncate all the edges of the cube; and as these are twelve, we thus obtain the dodecahedron with rhombic faces: this occurs in Zinc Blende. And thus we see the origin of Haüy's various primitive forms, the tetrahedron, octahedron, and rhombic dodecahedron, all belonging to the tessular system:--they are, in fact, different cleavage forms of that system.

5. I do not dwell upon other incidents of crystals which have reference to form, nor upon the lustre, smoothness, and striation of the surfaces. To all such incidents the general principle applies, that similar parts are similarly affected; and hence, if any parts are found to be constantly and definitely different from other parts of the same sort, they are not similar parts; and the symmetry is to be interpreted with reference to this difference.

We have now to consider the inferences which have been drawn from these incidents of crystallization, with regard to the intimate structure of bodies.

{{80}} CHAPTER III.

SPECULATIONS FOUNDED UPON THE SYMMETRY OF CRYSTALS.

1. WHEN a crystal, as, for instance, a crystal of Galena, (sulphuret of lead,) is readily divisible into smaller cubes, and these into smaller ones, and so on without limit, it is very natural to represent to ourselves the original cube as really consisting of small cubical elements; and to imagine that it is a philosophical account of the physical structure of such a substance to say that it is made up of cubical molecules. And when the Galena crystal has externally the form of a cube, there is no difficulty in such a conception; for the surface of the crystal is also conceived as made up of the surfaces of its cubical molecules. We conceive the crystal so constituted, as we conceive a wall built of bricks.

But if, as often happens, the Galena crystal be an octahedron, a further consideration is requisite in order to understand its structure, pursuing still the same hypothesis. The mineral is still, as in the other case, readily cleavable into small cubes, having their corners turned to the faces of the octahedron. Therefore these faces can no longer be conceived as made up of the faces of cubical elements of which the whole is constituted. If we suppose a pile of such small cubes to be closely built together, but with decreasing width above, so as to form a pyramid, the face of such a pyramid will no longer be plane; it will consist of a great number of the corners or edges of the small elementary cubes. It would appear at first sight, therefore, that such a face cannot represent the smooth polished surface of a crystal. {81}

But when we come to look more closely, this difficulty disappears. For how large are these elementary cubes? We cannot tell, even supposing they really have any size. But we know that they must be, at any rate, very small; so small as to be inappreciable by our senses, for our senses find no limit to the divisibility of minerals by cleavage. Hence the surface of the pyramid above described would not consist of visible corners or edges, but would be roughened by specks of imperceptible size; or rather, by supposing these specks to become still smaller, the roughness becomes smoothness. And thus we may have a crystal with a smooth surface, made up of small cubes in such a manner that their surfaces are all oblique to the surface of the crystal.

Haüy, struck by some instances in which the supposition of such a structure of crystals appeared to account happily for several of their relations and properties, adopted and propounded it as a general theory. The small elements, of which he supposed crystals to be thus built up, he termed integrant molecules. The form of these molecules might or might not be the same as the primitive form with which his construction was supposed to begin; but there was, at any rate, a close connexion between these forms, since both of them were founded on the cleavage of the mineral. The tenet that crystals are constituted in the manner which I have been describing, I shall call the Theory of Integrant Molecules, and I have now to make some remarks on the grounds of this theory.

2. In the case of which I have spoken, the mineral used as the example, Galena, readily splits into cubes, and cubes are easily placed together so as to fit each other, and fill the space which they occupy. The same is the case in the mineral which suggested to Haüy his theory, namely, Calc Spar. The crystals of this substance are readily divisible into rhombohedrons, a form like a brick with oblique angles; and such bricks can be built together so as to produce crystals of all the immense varieties of form which Calc Spar presents. This kind of masonry is equally possible in many other {82} minerals; but as we go through the mineral kingdom in our survey, we soon find cases which offer difficulties. Some minerals cleave only in two directions, some in one only; in such cases we cannot by cleavage obtain an integrant molecule of definite form; one of its dimensions, at least, must remain indeterminate and arbitrary. Again, in some instances, we have more than three different planes of cleavage, as in Fluor Spar, where we have four. The solid, bounded by four planes, is a tetrahedron; or if we take four pairs of parallel faces, an octahedron. But if we attempt to take either of these forms for our integrant molecule, we are met by this difficulty: that a collection of such forms will not fill space. Perhaps this difficulty will be more readily conceived by the general reader if it be contemplated with reference to plane figures. It will readily be seen that a number of equal squares may be put together so as to fill the space which they occupy; but if we take a number of equal regular octagons, we may easily convince ourselves that no possible arrangement can make them cover a flat space without leaving blank spots between. In like manner octahedrons or tetrahedrons cannot be arranged in solid space so as to fill it. They necessarily leave vacancies. Hence the structure of Fluor Spar, and similar crystals, was a serious obstacle in the way of the theory of integrant molecules. That theory had been adopted in the first instance because portions of the crystal, obtained by cleavage, could be built up into a solid mass; but this ground of the theory failed altogether in such instances as I have described, and hence the theory, even upon the representations of its adherents, had no longer any claim to assent.

The doctrine of Integral Molecules, however, was by no means given up at once, even in such instances. In this and in other subjects, we may observe that a theory, once constructed and carried into detail, has such a hold upon the minds of those who have been in the habit of applying it, that they will attempt to uphold it by introducing suppositions inconsistent with {83} the original foundations of the theory. Thus those who assert the Atomic Theory, reconcile it with facts by taking the halves of atoms; and thus the Theory of Integrant Molecules was maintained for Fluor Spar, by representing the elementary octahedrons of which crystals are built up, as touching each other only by the edges. The contact of surface with surface amongst integrant molecules had been the first basis of the theory; but this supposition being here inapplicable, was replaced by one which made the theory no longer a representation of the facts (the cleavages), but a mere geometrical construction. Although, however, the inapplicability of the theory to such cases was thus, in some degree, disguised to the disciples of Haüy, it was plain that, in the face of such difficulties, the Theory of Integrant Molecules could not hold its place as a philosophical truth. But it still answered the purpose (a very valuable one, and one to which crystallography is much indebted,) of an instrument for calculating the geometrical relations of the parts of crystals to each other: for the integrant molecules were supposed to be placed layer above layer, each layer as we ascend, decreasing by a certain number of molecules and rows of molecules; and the calculation of these laws of decrement was, in fact, the best mode then known of determining the positions of the faces. The Theory of Decrements served to express and to determine, in a great number of the most obvious cases, the laws of phenomena in crystalline forms, though the Theory of Integrant Molecules could not be maintained as a just view of the structure of crystals.

3. The Theory of Integrant Molecules, however, involved this just and important principle: that a true view of the intimate structure of crystals must include and explain the facts of crystallization, that is, crystalline form and cleavage; and that it must take these into account, according to their degree of Symmetry. So far all theories concerning the elements of crystals must agree. And it was soon seen that this was, in reality, all that had been established by the investigations of Haüy and his school. I have already, in the {84} History, quoted Weiss's reflections on making this step. 'When in 1809,' he says[5\7], 'I published my Dissertation, I shared the common opinion as to the necessity of the assumption, and the reality of the existence of a primitive form, at least in a sense not very different from the usual sense of the expression.' He then proceeds to relate that he sought a ground for such an opinion, independent of the doctrine of Atoms, which he, in common with a great number of philosophers of that time in his own country, was disposed to reject, inclining to believe that the properties of bodies were determined by Forces which acted in them, and not by Molecules of which they were composed. He adds, that in pursuing this train of thought, he found, 'that out of his Primitive Forms there was gradually unfolded to his hands that which really governs them, and is not affected by their casual fluctuations; namely, the Fundamental Relations of their Dimensions,' or as we now may call them, Axes of Symmetry. With reference to these Axes, he found, as he goes on to say, that 'a multiplicity of internal Oppositions, necessarily and mutually interdependent, are developed in the crystalline mass, each Relation having its own Polarity; so that the Crystalline Character is co-extensive with these Polarities.' The character of these polarities, whether manifested in crystalline faces, cleavage, or any other incidents of crystallization, is necessarily displayed in the degree and kind of Symmetry which the crystal possesses: and thus this Symmetry, in all our speculations concerning the structure of crystals, necessarily takes the place of that enumeration of Primitive Forms which were rejected as inconsistent with observed facts, and destitute of sound scientific principle.

[Note 5\7: Acad. Berlin. 1816, p. 307.]

I may just notice here what I have stated in the History of Mineralogy[6\7], that the distinction of systems of crystallization, as introduced by Weiss and Mohs, was strikingly confirmed by Sir David Brewster's discoveries respecting the optical properties of minerals. {85} The splendid phenomena which were produced by passing polarized light through crystals, were found to vary according as the crystals were of the Rhombohedral, Square Pyramidal, Oblong Prismatic, or Tessular System. The Optical Symmetry exactly corresponded with the Geometrical Symmetry. In the two former Systems were crystals uniaxal in respect of their optical properties; the oblong prismatic, was biaxal; while in the tessular, the want of a predominant axis prevented the phenomena here spoken of from occurring at all. The optical experiments must have led, and would have led, to a classification of crystals into the above systems or something nearly equivalent, even had they not been already so arranged by attention to their forms.

[Note 6\7: Hist. Ind. Sc. b. xv. c. v.]

4. While in Germany Weiss and Mohs with their disciples, were gradually rejecting what was superfluous in the previous crystallographical hypotheses, philosophers in England were also trying to represent to themselves the constitution of crystals in a manner which should be free from the obviously arbitrary and untenable fictions of the Haüyian school. These attempts, however, were not crowned with much success. One mode of representing the structure of crystals which suggested itself, was to reject the polyhedral forms which Haüy gave to his integrant molecules, and to conceive the elements of crystals as spheres, the properties of the crystal being determined not by the surfaces, but by the position of the elements. This was done by Wollaston, in the Philosophical Transactions for 1813. He applied this view to the tessular system, in which, indeed, the application is not difficult; and he showed that octahedral and tetrahedral figures may be deduced from symmetrical arrangements of equal spherules. But though in doing this, he manifested a perception of the conditions of the problem, he appeared to lose his hold on the real question when he tried to pass on to other systems of crystallization. For he accounted for the rhombohedral system by supposing the spheres changed into spheroids. Such a procedure involved him in a gratuitous and useless hypothesis: for to what purpose do we introduce the {86} arrangement of atoms (instead of their figure,) as a mode of explaining the symmetry of the crystallization, when at the next step we ascribe to the atom, by an arbitrary fiction, a symmetry of figure of the same kind as that which we have to explain? It is just as easy, and as allowable, to assume an elementary rhombohedron, as to assume elementary spheroids, of which the rhombohedrons are constructed.

5. Many hypotheses of the same kind might be adduced, devised both by mineralogists and chemists. But almost all such speculations have been pursued with a most surprising neglect of the principle which obviously is the only sound basis on which they can proceed. The principle is this:--that All hypotheses concerning the arrangement of the elementary atoms of bodies in space must be constructed with reference to the general facts of crystallization. The truth and importance of this principle can admit of no doubt. For if we make any hypothesis concerning the mode of connexion of the elementary particles of bodies, this must be done with the view of representing to ourselves the forces which connect them, and the results of these forces as manifested in the properties of the bodies. Now the forces which connect the particles of bodies so as to make them crystalline, are manifestly chemical forces. It is only definite chemical compounds which crystallize; and in crystals the force of cohesion by which the particles are held together cannot in any way be distinguished or separated from the chemical force by which their elements are combined. The elements are understood to be combined, precisely because the result is a definite, apparently homogeneous substance. The properties of the compound bodies depend upon the elements and their mode of combination; for, in fact, these include everything on which they can depend. There are no other circumstances than these which can affect the properties of a body. Therefore all those properties which have reference to space, namely, the crystalline properties, cannot depend upon anything else than the arrangement of the elementary molecules in space. These {87} properties are the facts which any hypothesis of the arrangement of molecules must explain, or at least render conceivable; and all such hypotheses, all constructions of bodies by supposed arrangements of molecules, can have no other philosophical object than to account for facts of this kind. If they do not do this, they are mere arbitrary geometrical fictions, which cannot be in any degree confirmed or authorised by an examination of nature, and are therefore not deserving of any regard.

6. Those philosophers who have endeavoured to represent the mode in which bodies are constructed by the combination of their chemical atoms, have often undertaken to show, not only that the atoms are combined, but also in what positions and configurations they are combined. And it is truly remarkable, as I have already said, that they have done this, almost in every instance, without any consideration of the crystalline character of the resulting combinations; from which alone we receive any light as to the relation of their elements in space. Thus Dr. Dalton, in his Elements of Chemistry, in which he gave to the world the Atomic Theory as a representation of the doctrine of definite and multiple proportions, also published a large collection of Diagrams, exhibiting what he conceived to be the configuration of the atoms in a great number of the most common combinations of chemical elements. Now these hypothetical diagrams do not in any way correspond, as to the nature of their symmetry, with the compounds, as we find them displaying their symmetry when they occur crystallized. Carbonate of lime has in reality a triangular symmetry, since it belongs to the rhombohedral system; Dr. Dalton's carbonate of lime would be an oblique rhombic prism or pyramid. Sulphate of baryta is really two-and-two membered; Dr. Dalton's diagram makes it two-and-one membered. Alum is really octahedral or tessular; but according to the diagram it could not be so, since the two ends of the atom are not symmetrical. And the same want of correspondence between the facts and the hypothesis runs through the whole {88} system. It need not surprise us that the theoretical arrangement of atoms does not explain the facts of crystallization; for to produce such an explanation would be a second step in science quite as great as the first, the discovery of the atomic theory in its chemical sense. But we may allow ourselves to be surprised that an utter discrepance between all the facts of crystallization and the figures assumed in the theory, did not suggest any doubt as to the soundness of the mode of philosophizing by which this part of the theory was constructed.

7. Some little accordance between the hypothetical arrangements of chemical atoms and the facts of crystallization, does appear to have been arrived at by some of the theorists to whom we here refer, although by no means enough to show a due conviction of the importance of the principle stated above. Thus Wollaston, in the Essay above noticed, after showing that a symmetrical arrangement of equal spherules would give rise to octahedral and other tessular figures, remarks, very properly, that the metals, which are simple bodies, crystallize in such forms. M. Ampère[7\7] also, in 1814, published a brief account of an hypothesis of a somewhat similar nature, and stated himself to have developed this speculation in a Memoir which has not yet, so far as I am aware, been published. In this notice he conceives bodies to be compounded of molecules, which, arranged in a polyhedral form, constitute particles. These representative forms of the particles depend on chemical laws. Thus the particles of oxygen, of hydrogen, and of azote, are composed each of four molecules. Hence it is collected that the particles of nitrous gas are composed of two molecules of oxygen and two of azote; and similar conclusions are drawn respecting other substances. These conclusions, though expressed by means of the polyhedrons thus introduced, are supported by chemical, rather than by crystallographical comparisons. The author does, indeed, appeal to the crystallization of sal {89} ammoniac as an argument[8\7]; but as all the forms which he introduces appear to belong to the tessular system of crystallization, there is, in his reasonings, nothing distinctive; and therefore nothing, crystallographically speaking, of any weight on the side of this theory.

[Note 7\7: Ann. de Chimie, tom. xc. p. 43.]

[Note 8\7: Ann. de Chimie, tom. xc. p. 83.]

8. Any hypothesis which should introduce any principle of chemical order among the actual forms of minerals, would well deserve attention. At first sight, nothing can appear more anomalous than the forms which occur. We have, indeed, one broad fact, which has an encouraging aspect, the tessular forms in which the pure metals crystallize. The highest degree of chemical and of geometrical simplicity coincide: irregularity disappears precisely where it is excluded by the consideration above stated, that the symmetry of chemical composition must determine the symmetry of crystalline form[9\7].

[Note 9\7: Inasmuch as this law, that the simple metals crystallize in tessular forms, is the most signal example of that connexion between the chemical nature of a body and its crystalline form, I in the former Edition stated it with as much generality as I could find any ground for, and I should have been glad if I could have added confirmation of the law, derived from later observations. But the most recent investigations of crystallographers appear to have afforded exceptions rather than examples of the rule. Arsenic and Tellurium are said to be rhombohedral. Antimony, stated by Haüy to be octahedral (and therefore tessular), has been found by more modern observers to be rhombohedral. Tin has been obtained by Professor Miller in beautiful crystals belonging to the pyramidal system. Professor Nöggerath has observed in Zinc, after cooling from fusion, hexagonal cleavage, rendering it probable that the mineral crystallized in rhombohedrons having their axes vertical, like ice. G. Rose conceives it highly probable that Osmium and Iridium are rhombohedral. (Poggendorf. Bd. liv.)

But all the more perfect metals are tessular; namely, Gold, Silver, Mercury, Platinum, Iron, Copper; also Bismuth [?] Perhaps the observation in which the crystallization of Zinc is affected by its position is, on that very account, no sufficient evidence of its free crystallization. We can hardly conceive a collection of perfectly simple, similar particles to crystallize so as to have one pre-eminent axis, without some extraneous action affecting them.]

But if we go on to any other class of crystalline forms, we soon find ourselves lost in our attempts to {90} follow any thread of order. We have indeed many large groups connected by obvious analogies; as the rhombohedral carbonates of lime, magnesia, iron, manganese;--the prismatic carbonates and sulphates of lime, baryta, strontia, lead. But even in these, we cannot form any plausible hypothesis of the arrangement of the elements; and in other cases to which we naturally turn, we can find nothing but confusion. For instance, if we examine the oxides of metals:--those of iron are rhombohedral and tessular; those of copper, tessular; those of tin, of titanium, of manganese, square pyramidal; those of antimony, prismatic; and we have other forms for other substances.

It may be added, that if we take account of the optical properties which, as we have already stated, have constant relations to the crystalline forms, the confusion is still further increased; for the optical dimensions vary in amount, though not in symmetry, where chemistry can trace no difference of composition.

9. We will not quit the subject, however, without noticing the much more promising aspect which it has assumed by the detection of such groups as are referred to in the last article; or in other words, by Mitscherlich's discovery of Isomorphism. According to that discovery, there are various elements which may take the place of each other in crystalline bodies, either without any alteration of the crystalline form, or at most with only a slight alteration of its dimensions. Such a group of elements we have in the earths lime and magnesia, the protoxides of iron and manganese: for the carbonates of all these bases occur crystallized in forms of the rhombohedral system, the characteristic angle being nearly the same in all. Now lime and magnesia, by the discoveries of modern chemistry, are really oxides of metals; and therefore all these carbonates have a similar chemical constitution, while they have also a similar crystalline form. Whether or no we can devise any arrangement of molecules by which this connexion of the chemical and the geometrical property can be represented, we cannot help {91} considering the connexion as an extremely important fact in the constitution of bodies; and such facts are more likely than any other to give us some intelligible view of the relations of the ultimate parts of bodies. The same may be said of all the other isomorphous or plesiomorphous groups[10\7]. For instance, we have a number of minerals which belong to the same system of crystallization, but in which the chemical composition appears at first sight to be very various: namely, spinelle, pleonaste, gahnite, franklinite, chromic iron oxide, magnetic iron oxide: but Abich has shown that all these may be reduced to a common chemical formula;--they are bioxides of one set of bases, combined with trioxides of another set. Perhaps some mathematician may be able to devise some geometrical arrangement of such a group of elements which may possess the properties of the tessular system. Hypothetical arrangements of atoms, thus expressing both the chemical and the crystalline symmetry which we know to belong to the substance, would be valuable steps in analytical science; and when they had been duly verified, the hypotheses might easily be divested of their atomic character.

[Note 10\7: See Hist. Ind. Sc. b. xv. c. vi.]

Thus, as we have already said, mineralogy, understood in its wider sense, as the counterpart of chemistry, has for one of its main objects to discover those Relations of the Elements of bodies which have reference to Space. In this research, the foundation of all sound speculation is the kind and degree of Symmetry of form which we find in definite chemical compounds: and the problem at present before the inquirer is, to devise such arrangements of molecules as shall answer the conditions alike of Chemistry and of Crystallography.

We now proceed to the Classificatory Sciences, of which Mineralogy is one, though hitherto by far the least successful.

{{93}} BOOK VIII.

THE PHILOSOPHY OF THE CLASSIFICATORY SCIENCES.

WHERE a certain apparent difference between things (although perhaps in itself of little moment) answers to we know not what number of other differences, pervading not only their known properties but properties yet undiscovered, it is not optional but imperative to recognise this difference as the foundation of a specific distinction.

JOHN S. MILL, System of Logic, b. 1, ch. vii. § 4.

{{95}} BOOK VIII.

THE PHILOSOPHY OF THE CLASSIFICATORY SCIENCES.

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