INTRODUCTION.
Sect. 1.—Of the Classificatory Sciences.
THE horizon of the sciences spreads wider and wider before us, as we advance in our task of taking a survey of the vast domain. We have seen that the existence of Chemistry as a science which declares the ingredients and essential constitution of all kinds of bodies, implies the existence of another corresponding science, which shall divide bodies into kinds, and point out steadily and precisely what bodies they are which we have analysed. But a science thus dividing and defining bodies, is but one member of an order of sciences, different from those which we have hitherto described; namely, of the classificatory sciences. Such sciences there must be, not only having reference to the bodies with which chemistry deals, but also to all things respecting which we aspire to obtain any general knowledge, as, for instance, plants and animals. Indeed it will be found, that it is with regard to these latter objects, to organized beings, that the process of scientific classification has been most successfully exercised; while with regard to inorganic substances, the formation of a satisfactory system of arrangement has been found extremely difficult; nor has the necessity of such a system been recognised by chemists so distinctly and constantly as it ought to be. The best exemplification of these branches of knowledge, of which we now have to speak, will, therefore, be found in the organic world, in Botany and Zoology; but we will, in the first place, take a brief view of the science which classifies inorganic bodies, and of which Mineralogy is hitherto the very imperfect representative.
The principles and rules of the Classificatory Sciences, as well as of those of the other orders of sciences, must be fully explained when we come to treat of the Philosophy of the Sciences; and cannot be introduced here, where we have to do with history only. But I may observe very briefly, that with the process of classing, is joined the process of naming;—that names imply classification;—and that even the rudest and earliest application of language presupposes a distribution of objects according to their kinds;—but that such a spontaneous [314] and unsystematic distribution cannot, in the cases we now have to consider, answer the purposes of exact and general knowledge. Our classification of objects must be made consistent and systematic, in order to be scientific; we must discover marks and characters, properties and conditions, which are constant in their occurrence and relations; we must form our classes, we must impose our names, according to such marks. We can thus, and thus alone, arrive at that precise, certain, and systematic knowledge, which we seek; that is, at science. The object, then, of the classificatory sciences is to obtain fixed characters of the kinds of things; and the criterion of the fitness of names is, that they make general propositions possible.
I proceed to review the progress of certain sciences on these principles, and first, though briefly, the science of Mineralogy.
Sect. 2.—Mineralogy as the Analytico-classificatory Science.
Mineralogy, as it has hitherto been cultivated, is, as I have already said, an imperfect representative of the department of human knowledge to which it belongs. The attempts at the science have generally been made by collecting various kinds of information respecting mineral bodies; but the science which we require is a complete and consistent classified system of all inorganic bodies. For chemistry proceeds upon the principle that the constitution of a body invariably determines its properties; and, consequently, its kind: but we cannot apply this principle, except we can speak with precision of the kind of a body, as well as of its composition. We cannot attach any sense to the assertion, that “soda or baryta has a metal for its base,” except we know what a metal is, or at least what properties it implies. It may not be, indeed it is not, possible, to define the kinds of bodies by words only; but the classification must proceed by some constant and generally applicable process; and the knowledge which has reference to the classification will be precise as far as this process is precise, and vague as far as this is vague.
There must be, then, as a necessary supplement to Chemistry, a Science of those properties of bodies by which we divide them into kinds. Mineralogy is the branch of knowledge which has discharged the office of such a science, so far as it has been discharged; and, indeed, Mineralogy has been gradually approaching to a clear consciousness of her real place, and of her whole task; I shall give the history of some of the advances which have thus been made. They are, principally, [315] the establishment and use of External Characters, especially of Crystalline Form, as a fixed character of definite substances; and the attempts to bring into view the connexion of Chemical Constitution and External Properties, made in the shape of mineralogical Systems; both those in which chemical methods of arrangement are adopted, and those which profess to classify by the natural-history method.
CRYSTALLOGRAPHY.
CHAPTER I.
Prelude to the Epoch of De Lisle and Haüy.
OF all the physical properties of bodies, there is none so fixed, and in every way so remarkable, as this;—that the same chemical compound always assumes, with the utmost precision, the same geometrical form. This identity, however, is not immediately obvious; it is often obscured by various mixtures and imperfections in the substance; and even when it is complete, it is not immediately recognized by a common eye, since it consists, not in the equality of the sides or faces of the figures, but in the equality of their angles. Hence it is not surprising that the constancy of form was not detected by the early observers. Pliny says,[1] “Why crystal is generated in a hexagonal form, it is difficult to assign a reason; and the more so, since, while its faces are smoother than any art can make them, the pyramidal points are not all of the same kind.” The quartz crystals of the Alps, to which he refers, are, in some specimens, very regular, while in others, one side of the pyramid becomes much the largest; yet the angles remain constantly the same. But when the whole shape varied so much, the angles also seemed to vary. Thus Conrad Gessner, a very learned naturalist, who, in 1564, published at Zurich his work, De rerum Fossilium, Lapidum et Gemmarum maxime, Figuris, says,[2] “One crystal differs from another in its angles, and consequently in its figure.” And Cæsalpinus, who, as we shall [find], did so much in establishing fixed characters in botany, was led by some of his general views to disbelieve the fixity of the form of crystals. In his work De Metallicis, published at Nuremberg in 1602, he says,[3] “To ascribe to inanimate bodies a definite form, does not appear consentaneous to reason; for it is the office of organization to produce a definite form;” [317] an opinion very natural in one who had been immersed in the study of the general analogies of the forms of plants. But though this is excusable in Cæsalpinus, the rejection of this definiteness of form a hundred years later, when its existence had been proved, and its laws developed by numerous observers, cannot be ascribed to anything but strong prejudice; yet this was the course taken by no less a person than Buffon. “The form of crystallization,” says he,[4] “is not a constant character, but is more equivocal and more variable than any other of the characters by which minerals are to be distinguished.” And accordingly, he makes no use of this most important feature in his history of minerals. This strange perverseness may perhaps be ascribed to the dislike which Buffon is said to have entertained for Linnæus, who had made crystalline form a leading character of minerals.
[1] Nat. Hist. xxvii. 2.
[2] p. 25.
[3] p. 97.
[4] Hist. des Min. p. 343.
It is not necessary to mark all the minute steps by which mineralogists were gradually led to see clearly the nature and laws of the fixity of crystalline forms. These forms were at first noticed in that substance which is peculiarly called rock-crystal or quartz; and afterwards in various stones and gems, in salts obtained from various solutions, and in snow. But those who observed the remarkable regular figures which these substances assume, were at first impelled onwards in their speculations by the natural tendency of the human mind to generalize and guess, rather than to examine and measure. They attempted to snatch at once the general laws of geometrical regularity of these occurrences, or to connect them with some doctrine concerning formative causes. Thus Kepler,[5] in his Harmonics of the World, asserts a “formatrix facultas, which has its seat in the entrails of the earth, and, after the manner of a pregnant woman, expresses the five regular geometrical solids in the forms of gems.” But Philosophers, in the course of time, came to build more upon observation, and less upon abstract reasonings. Nicolas Steno, a Dane, published, in 1669, a dissertation De Solido intra Solidum Naturaliter contento, in which he says,[6] that though the sides of the hexagonal crystal may vary, the angles are not changed. And Dominic Gulielmini, in a Dissertation on Salts, published in 1707, says,[7] in a true inductive spirit, “Nature does not employ all figures, but only certain ones of those which are possible; and of these, the determination is not to be fetched from the brain, or proved à priori, but obtained by experiments and observations.” And [318] he speaks[8] with entire decision on this subject: “Nevertheless since there is here a principle of crystallization, the inclination of the planes and of the angles is always constant.” He even anticipates, very nearly, the views of later crystallographers as to the mode in which crystals are formed from elementary molecules. From this time, many persons labored and speculated on this subject; as Cappeller, whose Prodromus Crystallographiæ appeared at Lucern in 1723; Bourguet, who published Lettres Philosophiques sur la Formation de Sels et de Cristaux, at Amsterdam, in 1792; and Henckel, the “Physicus” of the Elector of Saxony, whose Pyritologia came forth in 1725. In this last work we have an example of the description of the various forms of special classes of minerals, (iron pyrites, copper pyrites, and arsenic pyrites;) and an example of the enthusiasm which this apparently dry and laborious study can excite: “Neither tongue nor stone,” he exclaims,[9] “can express the satisfaction which I received on setting eyes upon this sinter covered with galena; and thus it constantly happens, that one must have more pleasure in what seems worthless rubbish, than in the purest and most precious ores, if we know aught of minerals.”
[5] Linz. 1619, p. 161.
[6] p. 69.
[7] p. 19.
[8] p. 83.
[9] p. 343.
Still, however, Henckel[10] disclaims the intention of arranging minerals according to their mathematical forms; and this, which may be considered as the first decided step in the formation of crystallographic mineralogy, appears to have been first attempted by Linnæus. In this attempt, however, he was by no means happy; nor does he himself appear to have been satisfied. He begins his preface by saying, “Lithology is not what I plume myself upon.” (Lithologia mihi cristas non eriget.) Though his sagacity, as a natural historian, led him to see that crystalline form was one of the most definite, and therefore most important, characters of minerals, he failed in profiting by this thought, because, in applying it, he did not employ the light of geometry, but was regulated by what appeared to him resemblances, arbitrarily selected, and often delusive.[11] Thus he derived the form of pyrites from that of vitriol;[12] and brought together alum and diamond on account of their common octohedral form. But he had the great merit of animating to this study one to whom, more perhaps than to any other person, it owes its subsequent progress; I mean Romé de Lisle. “Instructed,” this writer says, in his preface to his Essais de Crystallographie, “by the works of the celebrated Von Linnée, how [319] greatly the study of the angular form of crystals might become interesting, and fitted to extend the sphere of our mineralogical knowledge, I have followed them in all their metamorphoses with the most scrupulous attention.” The views of Linnæus, as to the importance of this character, had indeed been adopted by several others; as John Hill, the King’s gardener at Kew, who, in 1777, published his Spathogenesia; and Grignon, who, in 1775, says, “These crystallizations may give the means of finding a new theory of the generation of crystalline gems.”
[10] p. 167.
[11] Marx. Gesch. p. 97.
[12] Syst. Nat. vi. p. 220.
The circumstance which threw so much difficulty in the way of those who tried to follow out his thought was, that in consequence of the apparent irregularity of crystals, arising from the extension or contraction of particular sides of the figure, each kind of substance may really appear under many different forms, connected with each other by certain geometrical relations. These may be conceived by considering a certain fundamental form to be cut into new forms in particular ways. Thus if we take a cube, and cut off all the eight corners, till the original faces disappear, we make it an octohedron; and if we stop short of this, we have a figure of fourteen faces, which has been called a cubo-octohedron. The first person who appears distinctly to have conceived this truncation of angles and edges, and to have introduced the word, is Démeste;[13] although Wallerius[14] had already said, in speaking of the various crystalline forms of calcspar, “I conceive it would be better not to attend to all differences, lest we be overwhelmed by the number.” And Werner, in his celebrated work On the External Characters of Minerals,[15] had formally spoken of truncation, acuation, and acumination, or replacement by a plane, an edge, a point respectively, (abstumpfung, zuschärfung, zuspitzung,) as ways in which the forms of crystals are modified and often disguised. He applied this process in particular to show the connexion of the various forms which are related to the cube. But still the extension of the process to the whole range of minerals and other crystalline bodies, was due to Romé de Lisle.
[13] Lettres, 1779, i. 48.
[14] Systema Mineralogicum, 1772–5, i. 143.
CHAPTER II.
Epoch of Romé De Lisle and Haüy.—Establishment of the Fixity of Crystalline Angles, and the Simplicity of the Laws of Derivation.
WE have already seen that, before 1780, several mineralogists had recognized the constancy of the angles of crystals, and had seen (as Démeste and Werner,) that the forms were subject to modifications of a definite kind. But neither of these two thoughts was so apprehended and so developed, as to supersede the occasion for a discoverer who should put forward these principles as what they really were, the materials of a new and complete science. The merit of this step belongs jointly to Romé de Lisle and to Haüy. The former of these two men had already, in 1772, published an Essai de Crystallographie, in which he had described a number of crystals. But in this work his views are still rude and vague; he does not establish any connected sequence of transitions in each kind of substance, and lays little or no stress on the angles. But in 1783, his ideas[16] had reached a maturity which, by comparison, excites our admiration. In this he asserts, in the most distinct manner, the invariability of the angles of crystals of each kind, under all the changes of relative dimension which the faces may undergo;[17] and he points out that this invariability applies only to the primitive forms, from each of which many secondary forms are derived by various changes.[18] Thus we cannot deny him the merit of having taken steady hold on both the handles of this discovery, though something still remained for another to do. Romé pursues his general ideas into detail with great labor and skill. He gives drawings of more than five hundred regular forms (in his first work he had inserted only one hundred and ten; Linnæus only knew forty); and assigns them to their proper substances; for instance, thirty to calcspar, and sixteen to felspar. He also invented and used a goniometer. We cannot doubt that he would have been [321] looked upon as a great discoverer, if his fame had not been dimmed by the more brilliant success of his contemporary Haüy.
[16] Cristallographie, ou Description de Formes propres à tous les Corps du Règne Minéral. 3 vols. and 1 vol. of plates.
[17] p. 68.
[18] p. 73.
Réné-Just Haüy is rightly looked upon as the founder of the modern school of crystallography; for all those who have, since him, pursued the study with success, have taken his views for their basis. Besides publishing a system of crystallography and of mineralogy, far more complete than any which had yet appeared, the peculiar steps in the advance which belong to him are, the discovery of the importance of cleavage, and the consequent expression of the laws of derivation of secondary from primary forms, by means of the decrements of the successive layers of integrant molecules.
The latter of these discoveries had already been, in some measure, anticipated by Bergman, who had, in 1773, conceived a hexagonal prism to be built up by the juxtaposition of solid rhombs on the planes of a rhombic nucleus.[19] It is not clear[20] whether Haüy was acquainted with Bergman’s Memoir, at the time when the cleavage of a hexagonal prism of calcspar, accidentally obtained, led him to the same conception of its structure. But however this might be, he had the indisputable credit of following out this conception with all the vigor of originality, and with the most laborious and persevering earnestness; indeed he made it the business of his life. The hypothesis of a solid, built up of small solids, had this peculiar advantage in reference to crystallography; it rendered a reason of this curious fact;—that a certain series of forms occur in crystals of the same kind, while other forms, apparently intermediate between those which actually occur, are rigorously excluded. The doctrine of decrements explained this; for by placing a number of regularly-decreasing rows of equal solids, as, for instance, of bricks, upon one another, we might form a regular equal-sided triangle, as the gable of a house; and if the breadth of the gable were one hundred bricks, the height of the triangle might be one hundred, or fifty, or twenty-five; but it would be found that if the height were an intermediate number, as fifty-seven, or forty-three, the edge of the wall would become irregular; and such irregularity is assumed to be inadmissible in the regular structure of crystals. Thus this mode of conceiving crystals allows of certain definite secondary forms, and no others.
[19] De Formis Crystallorum. Nov. Act. Reg. Soc. Sc. Ups. 1773.
[20] Traité de Minér. 1822, i. 15.
The mathematical deduction of the dimensions and proportions [322] of these secondary forms;—the invention of a notation to express them;—the examination of the whole mineral kingdom in accordance with these views;—the production of a work[21] in which they are explained with singular clearness and vivacity;—are services by which Haüy richly earned the admiration which has been bestowed upon him. The wonderful copiousness and variety of the forms and laws to which he was led, thoroughly exercised and nourished the spirit of deduction and calculation which his discoveries excited in him. The reader may form some conception of the extent of his labors, by being told—that the mere geometrical propositions which he found it necessary to premise to his special descriptions, occupy a volume and a half of his work;—that his diagrams are nearly a thousand in number;—that in one single substance (calcspar) he has described forty-seven varieties of form;—and that he has described one kind of crystal (called by him fer sulfuré parallélique) which has one hundred and thirty-four faces.
[21] Traité de Minéralogie, 1801, 5 vols.
In the course of a long life, he examined, with considerable care, all the forms he could procure of all kinds of mineral; and the interpretation which he gave of the laws of those forms was, in many cases, fixed, by means of a name applied to the mineral in which the form occurred; thus, he introduced such names as équiaxe, métastatique, unibinaire, perihexahèdre, bisalterne, and others. It is not now desirable to apply separate names to the different forms of the same mineral species, but these terms answered the purpose, at the time, of making the subjects of study more definite. A symbolical notation is the more convenient mode of designating such forms, and such a notation Haüy invented; but the symbols devised by him had many inconveniences, and have since been superseded by the systems of other crystallographers.
Another of Haüy’s leading merits was, as we have already intimated, to have shown, more clearly than his predecessors had done, that the crystalline angles of substances are a criterion of the substances; and that this is peculiarly true of the angles of cleavage;—that is, the angles of those edges which are obtained by cleaving a crystal in two different directions;—a mode of division which the structure of many kinds of crystals allowed him to execute in the most complete manner. As an instance of the employment of this criterion, I may mention his separation of the sulphates of baryta and strontia, which had [323] previously been confounded. Among crystals which in the collections were ranked together as “heavy spar,” and which were so perfect as to admit of accurate measurement, he found that those which were brought from Sicily, and those of Derbyshire, differed in their cleavage angle by three degrees and a half. “I could not suppose,” he says,[22] “that this difference was the effect of any law of decrement; for it would have been necessary to suppose so rapid and complex a law, that such an hypothesis might have been justly regarded as an abuse of the theory.” He was, therefore, in great perplexity. But a little while previous to this, Klaproth had discovered that there is an earth which, though in many respects it resembles baryta, is different from it in other respects; and this earth, from the place where it was found (in Scotland), had been named Strontia. The French chemists had ascertained that the two earths had, in some cases, been mixed or confounded; and Vauquelin, on examining the Sicilian crystals, found that their base was strontia, and not, as in the Derbyshire ones, baryta. The riddle was now read; all the crystals with the larger angle belong to the one, all those with the smaller, to the other, of these two sulphates; and crystallometry was clearly recognized as an authorized test of the difference of substances which nearly resemble each other.
[22] Traité, ii. 320.
Enough has been said, probably, to enable the reader to judge how much each of the two persons, now under review, contributed to crystallography. It would be unwise to compare such contributions to science with the great discoveries of astronomy and chemistry; and we have seen how nearly the predecessors of Romé and Haüy had reached the point of knowledge on which these two crystallographers took their stand. But yet it is impossible not to allow, that in these discoveries, which thus gave form and substance to the science of crystallography, we have a manifestation of no common sagacity and skill. Here, as in other discoveries, were required ideas and facts;—clearness of geometrical conception which could deal with most complex relations of form; a minute and extensive acquaintance with actual crystals; and the talent and habit of referring these facts to the general ideas. Haüy, in particular, was happily endowed for his task. Without being a great mathematician, he was sufficiently a geometer to solve all the problems which his undertaking demanded; and though the mathematical reasoning might have been made more compendious [324] by one who was more at home in mathematical generalization, probably this could hardly have been done without making the subject less accessible and less attractive to persons moderately disciplined in mathematics. In all his reasonings upon particular cases, Haüy is acute and clear; while his general views appear to be suggested rather by a lively fancy than by a sage inductive spirit: and though he thus misses the character of a great philosopher, the vivacity of style, and felicity and happiness of illustration, which grace his book, and which agree well with the character of an Abbé of the old French monarchy, had a great and useful influence on the progress of the subject.
Unfortunately Romé de Lisle and Haüy were not only rivals, but in some measure enemies. The former might naturally feel some vexation at finding himself, in his later years (he died in 1790), thrown into shade by his more brilliant successor. In reference to Haüy’s use of cleavage, he speaks[23] of “innovators in crystallography, who may properly be called crystalloclasts.” Yet he adopted, in great measure, the same views of the formation of crystals by laminæ,[24] which Haüy illustrated by the destructive process at which he thus sneers. His sensitiveness was kept alive by the conduct of the Academy of Sciences, which took no notice of him and his labors;[25] probably because it was led by Buffon, who disliked Linnæus, and might dislike Romé as his follower; and who, as we have [seen], despised crystallography. Haüy revenged himself by rarely mentioning Romé in his works, though it was manifest that his obligations to him were immense; and by recording his errors while he corrected them. More fortunate than his rival, Haüy was, from the first, received with favor and applause. His lectures at Paris were eagerly listened to by persons from all quarters of the world. His views were, in this manner, speedily diffused; and the subject was soon pursued, in various ways, by mathematicians and mineralogists in every country of Europe.
[23] Pref. p. xxvii.
[24] T. ii. p. 21.
[25] Marx. Gesch. d. Cryst. 130.
CHAPTER III.
Reception and Corrections of the Hauïan Crystallography.
I HAVE not hitherto noticed the imperfections of the crystallographic views and methods of Haüy, because my business in the last section [325] was to mark the permanent additions he made to the science. His system did, however, require completion and rectification in various points; and in speaking of the crystallographers of the subsequent time, who may all be considered as the cultivators of the Hauïan doctrines, we must also consider what they did in correcting them.
The three main points in which this improvement was needed were;—a better determination of the crystalline forms of the special substances;—a more general and less arbitrary method of considering crystalline forms according to their symmetry; and a detection of more general conditions by which the crystalline angle is regulated. The first of these processes may be considered as the natural sequel of the Hauïan epoch: the other two must be treated as separate steps of discovery.
When it appeared that the angle of natural or of cleavage faces could be used to determine the differences of minerals, it became important to measure this angle with accuracy. Haüy’s measurements were found very inaccurate by many succeeding crystallographers: Mohs says[26] that they are so generally inaccurate, that no confidence can be placed in them. This was said, of course, according to the more rigorous notions of accuracy to which the establishment of Haüy’s system led. Among the persons who principally labored in ascertaining, with precision, the crystalline angles of minerals, were several Englishmen, especially Wollaston, Phillips, and Brooke. Wollaston, by the invention of his Reflecting Goniometer, placed an entirely new degree of accuracy within the reach of the crystallographer; the angle of two faces being, in this instrument, measured by means of the reflected images of bright objects seen in them, so that the measure is the more accurate the more minute the faces are. In the use of this instrument, no one was more laborious and successful than William Phillips, whose power of apprehending the most complex forms with steadiness and clearness, led Wollaston to say that he had “a geometrical sense.” Phillips published a Treatise on Mineralogy, containing a great collection of such determinations; and Mr. Brooke, a crystallographer of the same exact and careful school, has also published several works of the same kind. The precise measurement of crystalline angles must be the familiar employment of all who study crystallography; and, therefore, any further enumeration of those [326] who have added in this way to the stock of knowledge, would be superfluous.
[26] Marx. p. 153.
Nor need I dwell long on those who added to the knowledge which Haüy left, of derived forms. The most remarkable work of this kind was that of Count Bournon, who published a work on a single mineral (calcspar) in three quarto volumes.[27] He has here given representations of seven hundred forms of crystals, of which, however, only fifty-six are essentially different. From this example the reader may judge what a length of time, and what a number of observers and calculators, were requisite to exhaust the subject.
[27] Traité complet de la Chaux Carbonatée et d’Aragonite, par M. le Comte de Bournon. London, 1808.
If the calculations, thus occasioned, had been conducted upon the basis of Haüy’s system, without any further generalization, they would have belonged to that process, the natural sequel of inductive discoveries, which we call deduction; and would have needed only a very brief notice here. But some additional steps were made in the upward road to scientific truth, and of these we must now give an account.
CHAPTER IV.
Establishment of the Distinction of Systems of Crystallization.—Weiss and Mohs.
IN Haüy’s views, as generally happens in new systems, however true, there was involved something that was arbitrary, something that was false or doubtful, something that was unnecessarily limited. The principal points of this kind were;—his having made the laws of crystalline derivation depend so much upon cleavage;—his having assumed an atomic constitution of bodies as an essential part of his system; and his having taken a set of primary forms, which, being selected by no general view, were partly superfluous, and partly defective.
How far evidence, such as has been referred to by various philosophers, has proved, or can prove, that bodies are constituted of indivisible atoms, will be more fully examined in the work which treats of the Philosophy of this subject. There can be little doubt that the [327] portion of Haüy’s doctrine which most riveted popular attention and applause, was his dissection of crystals, in a manner which was supposed to lead actually to their ultimate material elements. Yet it is clear, that since the solids given by cleavage are, in many cases, such as cannot make up a solid space, the primary conception of a necessary geometrical identity between the results of division and the elements of composition, which is the sole foundation of the supposition that crystallography points out the actual elements, disappears on being scrutinized: and when Haüy, pressed by this difficulty, as in the case of fluor-spar, put his integrant octohedral molecules together, touching by the edges only, his method became an empty geometrical diagram, with no physical meaning.
The real fact, divested of the hypothesis which was contained in the fiction of decrements, was, that when the relation of the derivative to the primary faces is expressed by means of numerical indices, these numbers are integers, and generally very small ones; and this was the form which the law gradually assumed, as the method of derivation was made more general and simple by Weiss and others.
“When, in 1809, I published my Dissertation,” says Weiss,[28] “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. While I sought,” he adds, referring to certain doctrines of general philosophy which he and others entertained, “a dynamical ground for this, instead of the untenable atomistic view, I found that, out of my primitive forms, there was gradually unfolded to my hands, that which really governs them, and is not affected by their casual fluctuations, the fundamental relations of those Dimensions according to which a multiplicity of internal oppositions, necessarily and mutually interdependent, are developed in the mass, each having its own polarity; so that the crystalline character is co-extensive with these polarities.”
[28] Mem. Acad. Berl. 1816, p. 307.
The “Dimensions” of which Weiss here speaks, are the Axes of Symmetry of the crystal; that is, those lines in reference to which, every face is accompanied by other faces, having like positions and properties. Thus a rhomb, or more properly a rhombohedron,[29] of [328] calcspar may be placed with one of its obtuse corners uppermost, so that all the three faces which meet there are equally inclined to the vertical line. In this position, every derivative face, which is obtained by any modification of the faces or edges of the rhombohedron, implies either three or six such derivative faces; for no one of the three upper faces of the rhombohedron has any character or property different from the other two; and, therefore, there is no reason for the existence of a derivative from one of these primitive faces, which does not equally hold for the other primitive faces. Hence the derivative forms will, in all cases, contain none but faces connected by this kind of correspondence. The axis thus made vertical will be an Axis of Symmetry, and the crystal will consist of three divisions, ranged round this axis, and exactly resembling each other. According to Weiss’s nomenclature, such a crystal is “three-and-three-membered.”
[29] I use this name for the solid figure, since rhomb has always been used for a plane figure.
But this is only one of the kinds of symmetry which crystalline forms may exhibit. They may have three axes of complete and equal symmetry at right angles to each other, as the cube and the regular octohedron;—or, two axes of equal symmetry, perpendicular to each other and to a third axis, which is not affected with the same symmetry with which they are; such a figure is a square pyramid;—or they may have three rectangular axes, all of unequal symmetry, the modifications referring to each axis separately from the other two.
These are essential and necessary distinctions of crystalline form; and the introduction of a classification of forms founded on such relations, or, as they were called, Systems of Crystallization, was a great improvement upon the divisions of the earlier crystallographers, for those divisions were separated according to certain arbitrarily-assumed primary forms. Thus Romé de Lisle’s fundamental forms were, the tetrahedron, the cube, the octohedron, the rhombic prism, the rhombic octohedron, the dodecahedron with triangular faces: Haüy’s primary forms are the cube, the rhombohedron, the oblique rhombic prism, the right rhombic prism, the rhombic dodecahedron, the regular octohedron, tetrahedron, and six-sided prism, and the bipyramidal dodecahedron. This division, as I have already said, errs both by excess and defect, for some of these primary forms might be made derivatives from others; and no solid reason could be assigned why they were not. Thus the cube may be derived from the tetrahedron, by truncating the edges; and the rhombic dodecahedron again from the cube, by truncating its edges; while the square pyramid could not be legitimately identified with the derivative of any of these forms; for if we were to [329] derive it from the rhombic prism, why should the acute angles always suffer decrements corresponding in a certain way to those of the obtuse angles, as they must do in order to give rise to a square pyramid?
The introduction of the method of reference to Systems of Crystallization has been a subject of controversy, some ascribing this valuable step to Weiss, and some to Mohs.[30] It appears, I think, on the whole, that Weiss first published works in which the method is employed; but that Mohs, by applying it to all the known species of minerals, has had the merit of making it the basis of real crystallography. Weiss, in 1809, published a Dissertation On the mode of investigating the principal geometrical character of crystalline forms, in which he says,[31] “No part, line, or quantity, is so important as the axis; no consideration is more essential or of a higher order than the relation of a crystalline plane to the axis;” and again, “An axis is any line governing the figure, about which all parts are similarly disposed, and with reference to which they correspond mutually.” This he soon followed out by examination of some difficult cases, as Felspar and Epidote. In the Memoirs of the Berlin Academy,[32] for 1814–15, he published An Exhibition of the natural Divisions of Systems of Crystallization. In this Memoir, his divisions are as follows:—The regular system, the four-membered, the two-and-two-membered, the three-and-three-membered, and some others of inferior degrees of symmetry. These divisions are by Mohs (Outlines of Mineralogy, 1822), termed the tessular, pyramidal, prismatic, and rhombohedral systems respectively. Hausmann, in his Investigations concerning the Forms of Inanimate Nature,[33] makes a nearly corresponding arrangement;—the isometric, monodimetric, trimetric, and monotrimetic; and one or other of these sets of terms have been adopted by most succeeding writers.
[30] Edin. Phil. Trans. 1823, vols. xv. and xvi.
[31] pp. 16, 42.
[32] Ibid.
[33] Göttingen, 1821.
In order to make the distinctions more apparent, I have purposely omitted to speak of the systems which arise when the prismatic system loses some part of its symmetry;—when it has only half or a quarter its complete number of faces;—or, according to Mohs’s phraseology, when it is hemihedral or tetartohedral. Such systems are represented by the singly-oblique or doubly-oblique prism; they are termed by Weiss two-and-one-membered, and one-and-one-membered; by other writers, Monoklinometric, and Triklinometric Systems. There are also other [330] peculiarities of Symmetry, such, for instance, as that of the plagihedral faces of quartz, and other minerals.
The introduction of an arrangement of crystalline forms into systems, according to their degree of symmetry, was a step which was rather founded on a distinct and comprehensive perception of mathematical relations, than on an acquaintance with experimental facts, beyond what earlier mineralogists had possessed. This arrangement was, however, remarkably confirmed by some of the properties of minerals which attracted notice about the time now spoken of, as we shall see in the next chapter.
~Additional material in the [3rd edition].~
CHAPTER V.
Reception and Confirmation of the Distinction of Systems of Crystallization.
DIFFUSION of the Distinction of Systems.—The distinction of systems of crystallization was so far founded on obviously true views, that it was speedily adopted by most mineralogists. I need not dwell on the steps by which this took place. Mr. Haidinger’s translation of Mohs was a principal occasion of its introduction in England. As an indication of dates, bearing on this subject, perhaps I may be allowed to notice, that there appeared in the Philosophical Transactions for 1825, A General Method of Calculating the Angles of Crystals, which I had written, and in which I referred only to Haüy’s views; but that in 1826,[34] I published a Memoir On the Classification of Crystalline Combinations, founded on the methods of Weiss and Mohs, especially the latter; with which I had in the mean time become acquainted, and which appeared to me to contain their own evidence and recommendation. General methods, such as was attempted in the Memoir just quoted, are part of that process in the history of sciences, by which, when the principles are once established, the mathematical operation of deducing their consequences is made more and more general and symmetrical: which we have seen already exemplified in the history of celestial mechanics after the time of Newton. It does not enter into our plan, to dwell upon the various steps in this way [331] made by Levy, Naumann, Grassmann, Kupffer, Hessel, and by Professor Miller among ourselves. I may notice that one great improvement was, the method introduced by Monteiro and Levy, of determining the laws of derivation of forces by means of the parallelisms of edges; which was afterwards extended so that faces were considered as belonging to zones. Nor need I attempt to enumerate (what indeed it would be difficult to describe in words) the various methods of notation by which it has been proposed to represent the faces of crystals, and to facilitate the calculations which have reference to them.
[34] Camb. Trans. vol. ii. p. 391.
[2nd Ed.] [My Memoir of 1825 depended on the views of Haüy in so far as that I started from his “primitive forms;” but being a general method of expressing all forms by co-ordinates, it was very little governed by these views. The mode of representing crystalline forms which I proposed seemed to contain its own evidence of being more true to nature than Haüy’s theory of decrements, inasmuch as my method expressed the faces at much lower numbers. I determine a face by means of the dimensions of the primary form divided by certain numbers; Haüy had expressed the face virtually by the same dimensions multiplied by numbers. In cases where my notation gives such numbers as (3, 4, 1), (1, 3, 7), (5, 1, 19), his method involves the higher numbers (4, 3, 12), (21, 7, 3), (19, 95, 5). My method however has, I believe, little value as a method of “calculating the angles of crystals.”
M. Neumann, of Königsberg, introduced a very convenient and elegant mode of representing the position of faces of crystals by corresponding points on the surface of a circumscribing sphere. He gave (in 1823) the laws of the derivation of crystalline faces, expressed geometrically by the intersection of zones, (Beiträge zur Krystallonomie.) The same method of indicating the position of faces of crystals was afterwards, together with the notation, re-invented by M. Grassmann, (Zur Krystallonomie und Geometrischen Combinationslehre, 1829.) Aiding himself by the suggestions of these writers, and partly adopting my method, Prof. Miller has produced a work on Crystallography remarkable for mathematical elegance and symmetry; and has given expressions really useful for calculating the angles of crystalline faces, (A Treatise on Crystallography. Cambridge, 1839.)]
Confirmation of the Distinction of Systems by the Optical Properties of Minerals.—Brewster.—I must not omit to notice the striking confirmation which the distinction of systems of crystallization received from optical discoveries, especially those of Sir D. Brewster. Of the [332] history of this very rich and beautiful department of science, we have already given some account, in speaking of [Optics]. The first facts which were noticed, those relating to double refraction, belonged exclusively to crystals of the rhombohedral system. The splendid phenomena of the rings and lemniscates produced by dipolarizing crystals, were afterwards discovered; and these were, in 1817, classified by Sir David Brewster, according to the crystalline forms to which they belong. This classification, on comparison with the distinction of Systems of Crystallization, resolved itself into a necessary relation of mathematical symmetry: all crystals of the pyramidal and rhombohedral systems, which from their geometrical character have a single axis of symmetry, are also optically uniaxal, and produce by dipolarization circular rings; while the prismatic system, which has no such single axis, but three unequal axes of symmetry, is optically biaxal, gives lemniscates by dipolarized light, and according to Fresnel’s theory, has three rectangular axes of unequal elasticity.
[2nd Ed.] [I have placed Sir David Brewster’s arrangement of crystalline forms in this chapter, as an event belonging to the confirmation of the distinctions of forms introduced by Weiss and Mohs; because that arrangement was established, not on crystallographical, but on optical grounds. But Sir David Brewster’s optical discovery was a much greater step in science than the systems of the two German crystallographers; and even in respect to the crystallographical principle, Sir D. Brewster had an independent share in the discovery. He divided crystalline forms into three classes, enumerating the Hauïan “primitive forms” which belonged to each; and as he found some exceptions to this classification, (such as idocrase, &c.,) he ventured to pronounce that in those substances the received primitive forms were probably erroneous; a judgment which was soon confirmed by a closer crystallographical scrutiny. He also showed his perception of the mineralogical importance of his discovery by publishing it, not only in the Phil. Trans. (1818), but also in the Transactions of the Wernerian Society of Natural History. In a second paper inserted in this later series, read in 1820, he further notices Mohs’s System of Crystallography, which had then recently appeared, and points out its agreement with his own.
Another reason why I do not make his great optical discovery a cardinal point in the history of crystallography is, that as a crystallographical system it is incomplete. Although we are thus led to distinguish the tessular and the prismatic systems (using Mohs’s terms) [333] from the rhombohedral and the square prismatic, we are not led to distinguish the latter two from each other; inasmuch as they have no optical difference of character. But this distinction is quite essential in crystallography; for these two systems have faces formed by laws as different as those of the other two systems.
Moreover, Weiss and Mohs not only divided crystalline forms into certain classes, but showed that by doing this, the derivation of all the existing forms from the fundamental ones assumed a new aspect of simplicity and generality; and this was the essential part of what they did.
On the other hand, I do not think it is too much to say as I have elsewhere said[35] that “Sir D. Brewster’s optical experiments must have led to a classification of crystals into the above systems, or something nearly equivalent, even if crystals had not been so arranged by attention to their forms.”]
[35] Philosophy of the Inductive Sciences, B. viii. C. iii. Art. 3.
Many other most curious trains of research have confirmed the general truth, that the degree and kind of geometrical symmetry corresponds exactly with the symmetry of the optical properties. As an instance of this, eminently striking for its singularity, we may notice the discovery of Sir John Herschel, that the plagihedral crystallization of quartz, by which it exhibits faces twisted to the right or the left, is accompanied by right-handed or left-handed circular polarization respectively. No one acquainted with the subject can now doubt, that the correspondence of geometrical and optical symmetry is of the most complete and fundamental kind.
[2nd Ed.] [Our knowledge with respect to the positions of the optical axes of the oblique prismatic crystals is still imperfect. It appears to be ascertained that, in singly oblique crystals, one of the axes of optical elasticity coincides with the rectangular crystallographic axis. In doubly oblique crystals, one of the axes of optical elasticity is, in many cases, coincident with the axis of a principal zone. I believe no more determinate laws have been discovered.]
Thus the highest generalization at which mathematical crystallographers have yet arrived, may be considered as fully established; and the science of Crystallography, in the condition in which these place it, is fit to be employed as one of the members of Mineralogy, and thus to fill its appropriate place and office.
~Additional material in the [3rd edition].~ [334]
CHAPTER VI.
Correction of the Law of the same Angle for the same Substance.
DISCOVERY of Isomorphism. Mitscherlich.—The discovery of which we now have to speak may appear at first sight too large to be included in the history of crystallography, and may seem to belong rather to chemistry. But it is to be recollected that crystallography, from the time of its first assuming importance in the hands of Haüy, founded its claim to notice entirely upon its connexion with chemistry; crystalline forms were properties of something; but what that something was, and how it might be modified without becoming something else, no crystallographer could venture to decide, without the aid of chemical analysis. Haüy had assumed, as the general result of his researches, that the same chemical elements, combined in the same proportions, would always exhibit the same crystalline form; and reciprocally, that the same form and angles (except in the obvious case of the tessular system, in which the angles are determined by its being the tessular system,) implied the same chemical constitution. But this dogma could only be considered as an approximate conjecture; for there were many glaring and unexplained exceptions to it. The explanation of several of these was beautifully described by the discovery that there are various elements which are isomorphous to each other; that is, such that one may take the place of another without altering the crystalline form; and thus the chemical composition may be much changed, while the crystallographic character is undisturbed.
This truth had been caught sight of, probably as a guess only, by Fuchs as early as 1815. In speaking of a mineral which had been called Gehlenite, he says, “I hold the oxide of iron, not for an essential component part of this genus, but only as a vicarious element, replacing so much lime. We shall find it necessary to consider the results of several analyses of mineral bodies in this point of view, if we wish, on the one hand, to bring them into agreement with the doctrine of chemical proportions, and on the other, to avoid unnecessarily splitting up genera.” In a lecture On the Mutual Influence of [335] Chemistry and Mineralogy,[36] he again draws attention to his term vicarious (vicarirende), which undoubtedly expresses the nature of the general law afterwards established by Mitscherlich in 1822.
[36] Munich, 1820.
But Fuchs’s conjectural expression was only a prelude to Mitscherlich’s experimental discovery of isomorphism. Till many careful analyses had given substance and signification to this conception of vicarious elements, it was of small value. Perhaps no one was more capable than Berzelius of turning to the best advantage any ideas which were current in the chemical world; yet we find him,[37] in 1820, dwelling upon a certain vague view of these cases,—that “oxides which contain equal doses of oxygen must have their general properties common;” without tracing it to any definite conclusions. But his scholar, Mitscherlich, gave this proposition a real crystallographical import. Thus he found that the carbonates of lime (calcspar,) of magnesia, of protoxide of iron, and of protoxide of manganese, agree in many respects of form, while the homologous angles vary through one or two degrees only; so again the carbonates of baryta, strontia, lead, and lime (arragonite), agree nearly; the different kinds of felspar vary only by the substitution of one alkali for another; the phosphates are almost identical with the arseniates of several bases. These, and similar results, were expressed by saying that, in such cases, the bases, lime, protoxide of iron, and the rest, are isomorphous; or in the latter instance, that the arsenic and phosphoric acids are isomorphous.
[37] Essay on the Theory of Chemical Proportions, p. 122.
Since, in some of these cases, the substitution of one element of the isomorphous group for another does alter the angle, though slightly, it has since been proposed to call such groups plesiomorphous.
This discovery of isomorphism was of great importance, and excited much attention among the chemists of Europe. The history of its reception, however, belongs, in part, to the classification of minerals; for its effect was immediately to metamorphose the existing chemical systems of arrangement. But even those crystallographers and chemists who cared little for general systems of classification, received a powerful impulse by the expectation, which was now excited, of discovering definite laws connecting chemical constitution with crystalline form. Such investigations were soon carried on with great activity. Thus, at a recent period, Abich analysed a number of tessular minerals, spinelle, pleonaste, gahnite, franklinite, and chromic iron oxide; and [336] seems to have had some success in giving a common type to their chemical formulæ, as there is a common type in their crystallization.
[2nd Ed.] [It will be seen by the above account that Prof. Mitscherlich’s merit in the great discovery of Isomorphism is not at all narrowed by the previous conjectures of M. Fuchs. I am informed, moreover, that M. Fuchs afterwards (in Schweigger’s Journal) retracted the opinions he had put forward on this subject.]
Dimorphism.—My business is, to point out the connected truths which have been obtained by philosophers, rather than insulated difficulties which still stand out to perplex them. I need not, therefore, dwell on the curious cases of dimorphism; cases in which the same definite chemical compound of the same elements appears to have two different forms; thus the carbonate of lime has two forms, calcspar and arragonite, which belong to different systems of crystallization. Such facts may puzzle us; but they hardly interfere with any received general truths, because we have as yet no truths of very high order respecting the connexion of chemical constitution and crystalline form. Dimorphism does not interfere with isomorphism; the two classes of facts stand at the same stage of inductive generalization, and we wait for some higher truth which shall include both, and rise above them.
[2nd Ed.] [For additions to our knowledge of the Dimorphism of Bodies, see Professor Johnstone’s valuable Report on that subject in the Reports of the British Association for 1837. Substances have also been found which are trimorphous. We owe to Professor Mitscherlich the discovery of dimorphism, as well as of isomorphism: and to him also we owe the greater part of the knowledge to which these discoveries have led.]
CHAPTER VII.
Attempts to Establish the Fixity of other Physical Properties.—Werner.
THE reflections from which it appeared, (at the end of the last [Book],) that in order to obtain general knowledge respecting bodies, we must give scientific fixity to our appreciation of their properties, applies to their other properties as well as to their crystalline [337] form. And though none of the other properties have yet been referred to standards so definite as that which geometry supplies for crystals, a system has been introduced which makes their measures far more constant and precise than they are to a common undisciplined sense.
The author of this system was Abraham Gottlob Werner, who had been educated in the institutions which the Elector of Saxony had established at the mines of Freiberg. Of an exact and methodical intellect, and of great acuteness of the senses, Werner was well fitted for the task of giving fixity to the appreciation of outward impressions; and this he attempted in his Dissertation on the external Characters of Fossils, which was published at Leipzig in 1774. Of the precision of his estimation of such characters, we may judge from the following story, told by his biographer Frisch.[38] One of his companions had received a quantity of pieces of amber, and was relating to Werner, then very young, that he had found in the lot one piece from which he could extract no signs of electricity. Werner requested to be allowed to put his hand in the bag which contained these pieces, and immediately drew out the unelectrical piece. It was yellow chalcedony, which is distinguishable from amber by its weight and coldness.
[38] Werner’s Leben, p. 26.
The principal external characters which were subjected by Werner to a systematic examination were color, lustre, hardness, and specific gravity. His subdivisions of the first character (Color), were very numerous; yet it cannot be doubted that if we recollect them by the eye, and not by their names, they are definite and valuable characters, and especially the metallic colors. Breithaupt, merely by the aid of this character, distinguished two new compounds among the small grains found along with the grains of platinum, and usually confounded with them. The kinds of Lustre, namely, glassy, fatty, adamantine, metallic, are, when used in the same manner, equally valuable. Specific Gravity obviously admits of a numerical measure; and the Hardness of a mineral was pretty exactly defined by the substances which it would scratch, and by which it was capable of being scratched.
Werner soon acquired a reputation as a mineralogist, which drew persons from every part of Europe to Freiberg in order to hear his lectures; and thus diffused very widely his mode of employing external characters. It was, indeed, impossible to attend so closely to [338] these characters as the Wernerian method required, without finding that they were more distinctive than might at first sight be imagined; and the analogy which this mode of studying Mineralogy established between that and other branches of Natural History, recommended the method to those in whom a general inclination to such studies was excited. Thus Professor Jameson of Edinburgh, who had been one of the pupils of Werner at Freiberg, not only published works in which he promulgated the mineralogical doctrines of his master, but established in Edinburgh a “Wernerian Society,” having for its object the general cultivation of Natural History.
Werner’s standards and nomenclature of external characters were somewhat modified by Mohs, who, with the same kinds of talents and views, succeeded him at Freiberg. Mohs reduced hardness to numerical measure by selecting ten known minerals, each harder than the other in order, from talc to corundum and diamond, and by making the place which these minerals occupy in the list, the numerical measure of the hardness of those which are compared with them. The result of the application of this fixed measurement and nomenclature of external characters will appear in the History of Classification, to which we now proceed.
SYSTEMATIC MINERALOGY.
CHAPTER VIII.
Attempts at the Classification of Minerals.
Sect. 1.—Proper object of Classification.
THE fixity of the crystalline and other physical properties of minerals is turned to account by being made the means of classifying such objects. To use the language of Aristotle,[39] Classification is the architectonic science, to which Crystallography and the Doctrine of External Characters are subordinate and ministerial, as the art of the bricklayer and carpenter are to that of the architect. But classification itself is useful only as subservient to an ulterior science, which shall furnish us with knowledge concerning things so classified. To classify is to divide and to name; and the value of the Divisions which we thus make, and of the names which we give them, is this;—that they render exact knowledge and general propositions possible. Now the knowledge which we principally seek concerning minerals is a knowledge of their chemical composition; the general propositions to which we hope to be led are such as assert relations between their intimate constitution and their external attributes. Thus our Mineralogical Classification must always have an eye turned towards Chemistry. We cannot get rid of the fundamental conviction, that the elementary composition of bodies, since it fixes their essence, must determine their properties. Hence all mineralogical arrangements, whether they profess it or not, must be, in effect, chemical; they must have it for their object to bring into view a set of relations, which, whatever else they may be, are at least chemical relations. We may begin with the outside, but it is only in order to reach the inner [340] structure. We may classify without reference to chemistry; but if we do so, it is only that we may assert chemical propositions with reference to our classification.
[39] Eth. Nicom. i. 2.
But, as we have [already] attempted to show, we not only may, but we must classify, by other than chemical characters, in order to be able to make our classification the basis of chemical knowledge. In order to assert chemical truths concerning bodies, we must have the bodies known by some tests not chemical. The chemist cannot assert that Arragonite does or does not contain Strontia, except the mineralogist can tell him whether any given specimen is or is not Arragonite. If chemistry be called upon to supply the definitions as well as the doctrines of mineralogy, the science can only consist of identical propositions.
Yet chemistry has been much employed in mineralogical classifications, and, it is generally believed, with advantage to the science: How is this consistent with what has been said?
To this the answer is, that when this has been done with advantage, the authority of external characters, as well as of chemical constitution, has really been brought into play. We have two sets of properties to compare, chemical and physical; to exhibit the connexion of these is the object of scientific mineralogy. And though this connexion would be most distinctly asserted, if we could keep the two sets of properties distinct, yet it may be brought into view in a great degree, by classifications in which both are referred to as guides. Since the governing principle of the attempts at classification is the conviction that the chemical constitution and the physical properties have a definite relation to each other, we appear entitled to use both kinds of evidence, in proportion as we can best obtain each; and then the general consistency and convenience of our system will be the security for its containing substantial knowledge, though this be not presented in a rigorously logical or systematic form.
Such mixed systems of classification, resting partly on chemical and partly on physical characters, naturally appeared as the earliest attempts in this way, before the two members of the subject had been clearly separated in men’s minds; and these systems, therefore, we must first give an account of.
Sect. 2.—Mixed Systems of Classification.
Early Systems.—The first attempts at classifying minerals went upon the ground of those differences of general aspect which had been [341] recognized in the formation of common language; as earths, stones, metals. But such arrangements were manifestly vague and confused; and when chemistry had advanced to power and honor, her aid was naturally called in to introduce a better order. “Hiarne and Bromell were, as far as I know,” says[40] Cronstedt, “the first who founded any mineral system upon chemical principles; to them we owe the three known divisions of the most simple mineral bodies; viz., the calcarei, vitrescentes, and apyri.” But Cronstedt’s own Essay towards a System of Mineralogy, published in Swedish in 1758, had perhaps more influence than any other, upon succeeding systems. In this, the distinction of earths and stones, and also of vitrescent and non-vitrescent earths (apyri), is rejected. The earths are classed as calcareous, siliceous, argillaceous, and the like. Again, calcareous earth is pure (calc spar), or united with acid of vitriol (gypsum), or united with the muriatic add (sal ammoniac), and the like. It is easy to see that this is the method, which, in its general principle, has been continued to our own time. In such methods, it is supposed that we can recognize the substance by its general appearance, and on this assumption, its place in the system conveys to us chemical knowledge concerning it.
[40] Mineralogy, Pref. p. viii.
But as the other branches of Natural History, and especially Botany, assumed a systematic form, many mineralogists became dissatisfied with this casual and superficial mode of taking account of external characters; they became convinced, that in Mineralogy as in other sciences, classification must have its system and its rules. The views which Werner ascribes to his teacher, Pabst van Ohain,[41] show the rise of those opinions which led through Werner to Mohs: “He was of opinion that a natural mineral system must be constructed by chemical determinations, and external characters at the same time (methodus mixta); but that along with this, mineralogists ought also to construct and employ what he called an artificial system, which might serve us as a guide (loco indicis) how to introduce newly-discovered fossils into the system, and how to find easily and quickly those already known and introduced.” Such an artificial system, containing not the grounds of classification, but marks for recognition, was afterwards attempted by Mohs, and termed by him the Characteristic of his system.
[41] Frisch. Werner’s Leben, p. 15.
Werner’s System.—But, in the mean time, Werner’s classification had an extensive reign, and this was still a mixed system. Werner himself, indeed, never published a system of mineralogy. “We might [342] almost imagine,” Cuvier says,[42] “that when he had produced his nomenclature of external characters, he was affrighted with his own creation; and that the reason of his writing so little after his first essay, was to avoid the shackles which he had imposed upon others.” His system was, indeed, made known both in and out of Germany, by his pupils; but in consequence of Werner’s unwillingness to give it on his own authority, it assumed, in its published forms, the appearance of an extorted secret imperfectly told. A Notice of the Mineralogical Cabinet of Mine-Director Pabst von Ohain, was, in 1792, published by Karsten and Hoffman, under Werner’s direction; and conveyed by example, his views of mineralogical arrangement; and[43] in 1816 his Doctrine of Classification was surreptitiously copied from his manuscript, and published in a German Journal, termed The Hesperus. But it was only in 1817, after his death, that there appeared Werner’s Last Mineral System, edited from his papers by Breithaupt and Köhler: and by this time, as we shall soon see, other systems were coming forwards on the stage.
[42] Cuv. El. ii. 314.
[43] Frisch. p. 52.
A very slight notice of Werner’s arrangement will suffice to show that it was, as we have termed it, a Mixed System. He makes four great Classes of fossils, Earthy, Saline, Combustible, Metallic: the earthy fossils are in eight Genera—Diamond, Zircon, Silica, Alumina, Talc, Lime, Baryta, Hallites. It is clear that these genera are in the main chemical, for chemistry alone can definitely distinguish the different Earths which characterize them. Yet the Wernerian arrangement supposed the distinctions to be practically made by reference to those external characters which the teacher himself could employ with such surpassing skill. And though it cannot be doubted, that the chemical views which prevailed around him had a latent influence on his classification in some cases, he resolutely refused to bend his system to the authority of chemistry. Thus,[44] when he was blamed for having, in opposition to the chemists, placed diamond among the earthy fossils, he persisted in declaring that, mineralogically considered, it was a stone, and could not be treated as anything else.
[44] Frisch. p. 62.
This was an indication to that tendency, which, under his successor, led to a complete separation of the two grounds of classification. But before we proceed to this, we must notice what was doing at this period in other parts of Europe.
Haüy’s System.—Though Werner, on his own principles, ought to [343] have been the first person to see the immense value of the most marked of external characters, crystalline form, he did not, in fact, attach much importance to it. Perhaps he was in some measure fascinated by a fondness for those characters which he had himself systematized, and the study of which did not direct him to look for geometrical relations. However this may be, the glory of giving to Crystallography its just importance in Mineralogy is due to France: and the Treatise of Haüy, published in 1801, is the basis of the best succeeding works of mineralogy. In this work, the arrangement is professedly chemical; and the classification thus established is employed as the means of enunciating crystallographic and other properties. “The principal object of this Treatise,” says the author,[45] “is the exposition and development of a method founded on certain principles, which may serve as a frame-work for all the knowledge which Mineralogy can supply, aided by the different sciences which can join hands with her and march on the same line.” It is worthy of notice, as characteristic of this period of Mixed Systems, that the classification of Haüy, though founded on principles so different from the Wernerian ones, deviates little from it in the general character of the divisions. Thus, the first Order of the first Class of Haüy is Acidiferous Earthy Substances; the first genus is Lime; the species are, Carbonate of Lime, Phosphate of Lime, Fluate of Lime, Sulphate of Lime, and so on.
[45] Disc. Prél. p. xvii.
Other Systems.—Such mixed methods were introduced also into this country, and have prevailed, we may say, up to the present time. The Mineralogy of William Phillips, which was published in 1824, and which was an extraordinary treasure of crystallographic facts, was arranged by such a mixed system; that is, by a system professedly chemical; but, inasmuch as a rigid chemical system is impossible, and the assumption of such a one leads into glaring absurdities, the system was, in this and other attempts of the same kind, corrected by the most arbitrary and lax application of other considerations.
It is a curious example of the difference of national intellectual character, that the manifest inconsistencies of the prevalent systems, which led in Germany, as we shall see, to bold and sweeping attempts at reform, produced in England a sort of contemptuous despair with regard to systems in general;—a belief that no system could be consistent or useful;—and a persuasion that the only valuable knowledge is the accumulation of particular facts. This is not the place to [344] explain how erroneous and unphilosophical such an opinion is. But we may notice that while such a temper prevails among us, our place in this science can never be found in advance of that position which we are now considering as exemplified in the period of Werner and Haüy. So long as we entertain such views respecting the objects of Mineralogy, we can have no share in the fortunes of the succeeding period of its history, to which I now proceed.
CHAPTER IX.
Attempts at the Reform of Mineralogical Systems.—Separation of the Chemical and Natural History Methods.
Sect. 1.—Natural History System of Mohs.
THE chemical principle of classification, if pursued at random, as in the cases just spoken of leads to results at which a philosophical spirit revolts; it separates widely substances which are not distinguishable; joins together bodies the most dissimilar; and in hardly any instance does it bring any truth into view. The vices of classifications like that of Haüy could not long be concealed; but even before time had exposed the weakness of his system, Haüy himself had pointed out, clearly and without reserve,[46] that a chemical system is only one side of the subject, and supposes, as its counterpart, a science of external characters. In the mean time, the Wernerians were becoming more and more in love with the form which they had given to such a science. Indeed, the expertness which Werner and his scholars acquired in the use of external characters, justified some partiality for them. It is related of him,[47] that, by looking at a piece of iron-ore, and poising it in his hand, he was able to tell, almost precisely, the proportion of pure metal which it contained. And in the last year of his life,[48] he had marked out, as the employment of the ensuing winter, the study of the system of Berzelius, with a view to find out the laws of combination as disclosed by external characters. In the same spirit, his pupil [345] Breithaupt[49] attempted to discover the ingredients of minerals by their peculiarities of crystallization. The persuasion that there must be some connexion between composition and properties, transformed itself, in their minds, into a belief that they could seize the nature of the connexion by a sort of instinct.
[46] See his Disc. Prél.
[47] Frisch. Werner’s Leben, p. 78.
[48] Frisch. 3.
[49] Dresdn. Auswahl, vol. ii. p. 97.
This opinion of the independency of the science of external characters, and of its sufficiency for its own object, at last assumed its complete form in the bold attempt to construct a system which should borrow nothing from chemistry. This attempt was made by Frederick Mohs, who had been the pupil of Werner, and was afterwards his successor in the school of Freiberg; and who, by the acute and methodical character of his intellect, and by his intimate knowledge of minerals, was worthy of his predecessor. Rejecting altogether all divisions of which the import was chemical, Mohs turned for guidance, or at least for the light of analogy, to botany. His object was to construct a Natural System of mineralogy. What the conditions and advantages of a natural system of any province of nature are, we must delay to explain till we have before us, in botany, a more luminous example of such a scheme. But further; in mineralogy, as in botany, besides the Natural System, by which we form our classes, it is necessary to have an Artificial System by which we recognize them;—a principle which, we have seen, had already taken root in the school of Freiberg. Such an artificial system Mohs produced in his Characteristic of the Mineral Kingdom, which was published at Dresden in 1820; and which, though extending only to a few pages, excited a strong interest in Germany, where men’s minds were prepared to interpret the full import of such a work. Some of the traits of such a “Characteristic” had, indeed, been previously drawn by others; as for example, by Haüy, who notices that each of his Classes has peculiar characters. For instance, his First Class (acidiferous substances,) alone possesses these combinations of properties; “division into a regular octohedron, without being able to scratch glass; specific gravity above 3·5, without being able to scratch glass.” The extension of such characters into a scheme which should exhaust the whole mineral kingdom, was the undertaking of Mohs.
Such a collection of marks of classes, implied a classification previously established, and accordingly, Mohs had created his own mineral system. His aim was to construct it, as we shall hereafter see that other natural systems are constructed, by taking into account all the [346] resemblances and differences of the objects classified. It is obvious that to execute such a work, implied a most intimate and universal acquaintance with minerals;—a power of combining in one vivid survey the whole mineral kingdom. To illustrate the spirit in which Professor Mohs performed his task, I hope I may be allowed to refer to my own intercourse with him. At an early period of my mineralogical studies, when the very conception of a Natural System was new to me, he, with great kindliness of temper, allowed me habitually to propose to him the scruples which arose in my mind, before I could admit principles which appeared to me then so vague and indefinite; and answered my objections with great patience and most instructive clearness. Among other difficulties, I one day propounded to him this;—“You have published a Treatise on Mineralogy, in which you have described all the important properties of all known minerals. On your principles, then, it ought to be possible, merely by knowing the descriptions in your book, and without seeing any minerals, to construct a natural system; and this natural system ought to turn out identical with that which you have produced, by so careful an examination of the minerals themselves.” He pondered a moment, and then he answered, “It is true; but what an enormous imagination (einbildungskraft, power of inward imagining), a man must have for such a work!” Vividness of conception of sensible properties, and the steady intuition (anschauung) of objects, were deemed by him, and by the Wernerian school in general, to be the most essential conditions of complete knowledge.
It is not necessary to describe Mohs’s system in detail; it may sufficiently indicate its form to state that the following substances, such as I before gave as examples of other arrangements, calcspar, gypsum, fluor spar, apatite, heavy spar, are by Mohs termed respectively, Rhombohedral Lime Haloide, Gyps Haloide, Octohedral Fluor Haloide, Rhombohedral Fluor Haloide, Prismatic Hal Baryte. These substances are thus referred to the Orders Haloide, and Baryte; to Genera Lime Haloide, Fluor Haloide, Hal Baryte; and the Species is an additional particularization.
Mohs not only aimed at framing such a system, but was also ambitious of giving to all minerals Names which should accord with the system. This design was too bold to succeed. It is true, that a new nomenclature was much needed in mineralogy: it is true, too, that it was reasonable to expect, from an improved classification, an improved nomenclature, such as had been so happily obtained in botany by the [347] reform of Linnæus. But besides the defects of Mohs’s system, he had not prepared his verbal novelties with the temperance and skill of the great botanical reformer. He called upon mineralogists to change the name of almost every mineral with which they were acquainted; and the proposed appellations were mostly of a cumbrous form, as the above example may serve to show. Such names could have obtained general currency, only after a general and complete acceptance of the system; and the system did not possess, in a sufficient degree, that evidence which alone could gain it a home in the belief of philosophers,—the coincidence of its results with those of Chemistry. But before I speak finally of the fortunes of the Natural-history System, I will say something of the other attempt which was made about the same time to introduce a Reform into Mineralogy from the opposite extremity of the science.
Sect. 2.—Chemical System of Berzelius and others.
If the students of external characters were satisfied of the independence of their method, the chemical analysts were naturally no less confident of the legitimate supremacy of their principles: and when the beginning of the present century had been distinguished by the establishment of the theory of definite proportions, and by discoveries which pointed to the electro-chemical theory, it could not appear presumption to suppose, that the classification of bodies, so far as it depended on chemistry, might be presented in a form more complete and scientific than at any previous time.
The attempt to do this was made by the great Swedish chemist Jacob Berzelius. In 1816, he published his Essay to establish a purely Scientific System of Mineralogy, by means of the Application of the Electro-chemical Theory and the Chemical Doctrine of Definite Proportions. It is manifest that, for minerals which are constituted by the law of Definite Proportions, this constitution must be a most essential part of their character. The electro-chemical theory was called in aid, in addition to the composition, because, distinguishing the elements of all compounds as electro-positive and electro-negative, and giving to every element a place in a series, and a place defined by the degree of these relations, it seemed to afford a rigorous and complete principle of arrangement. Accordingly, Berzelius, in his First System, arranged minerals according to their electro-positive element, and the elements according to their electro-positive rank; [348] and supposed that he had thus removed all that was arbitrary and vague in the previous chemical systems of mineralogy.
Though the attempt appeared so well justified by the state of chemical science, and was so plausible in its principle, it was not long before events showed that there was some fallacy in these specious appearances. In 1820, Mitscherlich discovered Isomorphism: by that discovery it appeared that bodies containing very different electro-positive elements could not be distinguished from each other; it was impossible, therefore, to put them in distant portions of the classification;—and thus the first system of Berzelius crumbled to pieces.
But Berzelius did not so easily resign his project. With the most unhesitating confession of his first failure, but with undaunted courage, he again girded himself to the task of rebuilding his edifice. Defeated at the electro-positive position, he now resolved to make a stand at the electro-negative element. In 1824, he published in the Transactions of the Swedish Academy, a Memoir On the Alterations in the Chemical Mineral System, which necessarily follow from the Property exhibited by Isomorphous Bodies, of replacing each other in given Proportions. The alteration was, in fact, an inversion of the system, with an attempt still to preserve the electro-chemical principle of arrangement. Thus, instead of arranging metallic minerals according to the metal, under iron, copper, &c., all the sulphurets were classed together, all the oxides together, all the sulphates together, and so in other respects. That such an order was a great improvement on the preceding one, cannot be doubted; but we shall see, I think, that as a strict scientific system it was not successful. The discovery of isomorphism, however, naturally led to such attempts. Thus Gmelin also, in 1825, published a mineral system,[50] which, like that of Berzelius, founded its leading distinctions on the electro-negative, or, as it was sometimes termed, the formative element of bodies; and, besides this, took account of the numbers of atoms or proportions which appear in the composition of the body; distinguishing, for instance, Silicates, as simple silicates, double silicates, and so on, to quintuple silicate (Pechstein) and sextuple silicate (Perlstein). In like manner, Nordenskiöld devised a system resting on the same bases, taking into account also the crystalline form. In 1824, Beudant published his Traité Elémentaire de Minéralogie, in which he professes to found his arrangement on the electro-negative element, and on Ampère’s circular [349] arrangement of elementary substances. Such schemes exhibit rather a play of the mere logical faculty, exercising itself on assumed principles, than any attempt at the real interpretation of nature. Other such pure chemical systems may have been published, but it is not necessary to accumulate instances. I proceed to consider their result.
[50] Zeitsch. der Min. 1825, p. 435.
Sect. 3.—Failure of the Attempts at Systematic Reform.
It may appear presumptuous to speak of the failure of those whom, like Berzelius and Mohs, we acknowledge as our masters, at a period when, probably, they and some of their admirers still hold them to have succeeded in their attempt to construct a consistent system. But I conceive that my office as an historian requires me to exhibit the fortunes of this science in the most distinct form of which they admit, and that I cannot evade the duty of attempting to seize the true aspect of recent occurrences in the world of science. Hence I venture to speak of the failure of both the attempts at framing a pure scientific system of mineralogy,—that founded on the chemical, and that founded on the natural-history principle; because it is clear that they have not obtained that which alone we could, according to the views here presented, consider as success,—a coincidence of each with the other. A Chemical System of arrangement, which should bring together, in all cases, the substances which come nearest each other in external properties;—a Natural-history System, which should be found to arrange bodies in complete accordance with their chemical constitution:—if such systems existed, they might, with justice, claim to have succeeded. Their agreement would be their verification. The interior and exterior system are the type and the antitype, and their entire correspondence would establish the mode of interpretation beyond doubt. But nothing less than this will satisfy the requisitions of science. And when, therefore, the chemical and the natural-history system, though evidently, as I conceive, tending towards each other, are still far from coming together, it is impossible to allow that either method has been successful in regard to its proper object.
But we may, I think, point out the fallacy of the principles, as well as the imperfection of the results, of both of those methods. With regard to that of Berzelius, indeed, the history of the subject obviously betrays its unsoundness. The electro-positive principle was, in a very short time after its adoption, proved and acknowledged to be utterly untenable: what security have we that the electro-negative element is [350] more trustworthy? Was not the necessity of an entire change of system, a proof that the ground, whatever that was, on which the electro-chemical principle was adopted, was an unfounded assumption? And, in fact, do we not find that the same argument which was allowed to be fatal to the First System of Berzelius, applies in exactly the same manner against the Second? If the electro-positive elements be often isomorphous, are not the electro-negative elements sometimes isomorphous also? for instance, the arsenic and phosphoric acids. But to go further, what is the ground on which the electro-chemical arrangement is adopted? Granted that the electrical relations of bodies are important; but how do we come to know that these relations have anything to do with mineralogy? How does it appear that on them, principally, depend those external properties which mineralogy must study? How does it appear that because sulphur is the electro-negative part of one body, and an acid the electro-negative part of another, these two elements similarly affect the compounds? How does it appear that there is any analogy whatever in their functions? We allow that the composition must, in some way, determine the classified place of the mineral,—but why in this way?
I do not dwell on the remark which Berzelius himself[51] makes on Nordenskiöld’s system;—that it assumes a perfect knowledge of the composition in every case; although, considering the usual discrepancies of analyses of minerals, this objection must make all pure chemical systems useless. But I may observe, that mineralogists have not yet determined what characters are sufficiently affixed to determine a species of minerals. We have seen that the ancient notion of the composition of a species, has been unsettled by the discovery of isomorphism. The tenet of the constancy of the angle is rendered doubtful by cases of plesiomorphism. The optical properties, which are so closely connected with the crystalline, are still so imperfectly known, that they are subject to changes which appear capricious and arbitrary. Both the chemical and the optical mineralogists have constantly, of late, found occasion to separate species which had been united, and to bring together those which had been divided. Everything shows that, in this science, we have our classification still to begin. The detection of that fixity of characters, on which a right establishment of species must rest, is not yet complete, great as the progress is which we have made, by acquiring a knowledge of the laws of crystallization and of [351] definite chemical constitution. Our ignorance may surprise us; but it may diminish our surprise to recollect, that the knowledge which we seek is that of the laws of the physical constitution of all bodies whatever; for to us, as mineralogists, all chemical compounds are minerals.
[51] Jahres Bericht. viii. 188.
The defect of the principle of the natural-history classifiers may be thus stated:—in studying the external characters of bodies, they take for granted that they can, without any other light, discover the relative value and importance of those characters. The grouping of Species into a Genus, of Genera into an Order, according to the method of this school, proceeds by no definite rules, but by a latent talent of appreciation,—a sort of classifying instinct. But this course cannot reasonably be expected to lead to scientific truth; for it can hardly be hoped, by any one who looks at the general course of science, that we shall discover the relation between external characters and chemical composition, otherwise than by tracing their association in cases where both are known. It is urged that in other classificatory sciences, in botany, for example, we obtain a natural classification from external characters without having recourse to any other source of knowledge. But this is not true in the sense here meant. In framing a natural system of botany, we have constantly before our eyes the principles of physiology; and we estimate the value of the characters of a plant by their bearing on its functions,—by their place in its organization. In an unorganic body, the chemical constitution is the law of its being; and we shall never succeed in framing a science of such bodies but by studiously directing our efforts to the interpretation of that law.
On these grounds, then, I conceive, that the bold attempts of Mohs and of Berzelius to give new forms to mineralogy, cannot be deemed successful in the manner in which their authors aspired to succeed. Neither of them can be marked as a permanent reformation of the science. I shall not inquire how far they have been accepted by men of science, for I conceive that their greatest effect has been to point out improvements which might be made in mineralogy without going the whole length either of the pure chemical, or of the pure natural-history system.
Sect. 4.—Return to Mixed Systems with Improvements.
In spite of the efforts of the purists, mineralogists returned to mixed systems of classification; but these systems are much better than they were before such efforts were made. [352]
The Second System of Berzelius, though not tenable in its rigorous form, approaches far nearer than any previous system to a complete character, bringing together like substances in a large portion of its extent. The System of Mohs also, whether or not unconsciously swayed by chemical doctrines, forms orders which have a community of chemical character; thus, the minerals of the order Haloide are salts of oxides, and those of the order Pyrites are sulphurets of metals. Thus the two methods appear to be converging to a common centre; and though we are unable to follow either of them to this point of union, we may learn from both in what direction we are to look for it. If we regard the best of the pure systems hitherto devised as indications of the nature of that system, perfect both as a chemical and as a natural-history system, to which a more complete condition of mineralogical knowledge may lead us, we may obtain, even at present, a tolerably good approximation to a complete classification; and such a one, if we recollect that it must be imperfect, and is to be held as provisional only, may be of no small value and use to us.
The best of the mixed systems produced by this compromise again comes from Freiberg, and was published by Professor Naumann in 1828. Most of his orders have both a chemical character and great external resemblances. Thus his Haloides, divided into Unmetallic and Metallic, and these again into Hydrous and Anhydrous, give good natural groups. The most difficult minerals to arrange in all systems are the siliceous ones. These M. Naumann calls Silicides, and subdivides them into Metallic, Unmetallic, and Amphoteric or mixed; and again, into Hydrous and Anhydrous. Such a system is at least a good basis for future researches; and this is, as we have said, all that we can at present hope for. And when we recollect that the natural-history principle of classification has begun, as we have already seen, to make its appearance in our treatises of chemistry, we cannot doubt that some progress is making towards the object which I have pointed out. But we know not yet how far we are from the end. The combination of chemical, crystallographical, physical and optical properties into some lofty generalization, is probably a triumph reserved for future and distant years.
Conclusion.—The history of Mineralogy, both in its successes and by its failures, teaches us this lesson;—that in the sciences of classification, the establishment of the fixity of characters, and the discovery of such characters as are fixed, are steps of the first importance in the progress of these sciences. The recollection of this maxim may aid us in [353] shaping our course through the history of other sciences of this kind; in which, from the extent of the subject, and the mass of literature belonging to it, we might at first almost despair of casting the history into distinct epochs and periods. To the most prominent of such sciences, Botany, I now proceed.
~Additional material in the [3rd edition].~