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tain a knowledge of the minerals themselves, and how it was chiefly this unpleasant experience at Werner's lectures which afterward caused me to work out another quite opposite method in teaching mineralogy.

It seems to me the natural way of beginning, to let the pupil first examine the mineral, without at the time enlightening bim with any oral explanation whatever. In this way he receives a first simple impression on the senses. If this impression is remembered, he may then be told the names of the minerals examined.*

It is important to begin with instructing in external characteristics, because this instruction communicates the results of the most thorough analysis of the general idea into its constituents. It would be wrong to begin by making the pupil observe in one mineral the weight alone, in another only the color or only the hardness; for such a method would break up the quiet, thoughtful, receptive mood proper to obtain an apprehension of the total idea.

But after having mastered this total idea of the mineral, the pupil must, especially if he desires to compare it with similar minerals, and to distinguish it from them, reduce this idea to its constituent peculiarities, even to the varying modifications of these peculiarities. For instance, on comparing gold with iron pyrites he will find both yellow; but there is a great difference between the pure, clear yellow of gold, and the pale whitish of the pyrites. He finds gold to be soft and malleable, while the brittle pyrites will give off to steel abundant sparks, large and smelling of sulphur, &c.

Thus, by a careful comparison of the separate peculiarities of both minerals, their great difference will clearly appear; whereas, without such a process, only an indistinct notion of them would be had. Indeed, there are many minerals of which the general idea would lead into great errors without a closer analysis of their qualities. Thus, the student would be much more likely to class a beautiful yellow polished crystal along with the topaz than to rank it as similar to a piece of insignificant, opaque, homely, white quartz, though the latter is its proper place.

Werner's theory of external marks is very simple, and quite sufficient to enable mining officials to deal with the minerals which they are likely to meet with. These officers can not go into delicate investigations. For example, the purely scientific mineralogist determines the specific gravity of a mineral by means of a fine balance. The specific gravity of water is taken as the unit, and that of the mineral is reckoned from it, and carried out to three or four decimal

• The commencement of mineralogical instruction is entirely like that of geognosy and bot. any; in every case, a vivid and permanent impression should be had of the total idea before any analysis of it.

places. The specific gravity of water being thus 1,000, that of gold is 19,258. The miner can not usually attempt so accurate a determination ; but he can make that wbich Werner gives. He makes five grades of specific gravity; and very judiciously taught his pupils to determine these, without balances, by poising the substance in the hand. He required them to be able to say only “Gold belongs among the extraordinarily heavy minerals ; "* not that "its specific gravity is 19,258."

What Werner did not require from mining officers we can still less require of new beginners in mineralogy; they must first learn to estimate specific gravities by the hand.

Werner's mode of dealing with other points was similar. He treated his subject exhaustively, but was very far from giving a delicately accurate physical description of every separate item; nor will he be found to furnish a mathematically developed crystallography.t

As crystallization is one of the most important, if not the most important, characteristics of a mineral, I shall devote a little space to it.

The angles of crystals are mathematically true and unvarying ; but the size of the side varies infinitely, without affecting the angles. Thus, for instance, we seldom find a cubic crystal with six equal sides; but the right angles of its sides and corners are invariable.I

The beginner will find his study of the polyhedral crystals much perplexed by these variations of the size of the surfaces; and, to assist him, he is usually furnished with models, in which the corresponding sides are made equal. His model for the cube, for instance, has six equal squares; that of the octahedron, eight equal and equilateral triangles.

Above all, the beginner should be drilled in the recognition of crystals by the eye; and his perceptions of their beautiful symmetry, and of the various relations connected with this symmetry, should be trained.

I can not here set forth the details of the method which I should recommend in teaching mineralogy. I shall only observe, in general, that the teacher must be careful not to carry the pupil too soon from the use of his senses to the mathematical part of his study.ll It is enough for the beginner to know that the cube has six sides, twelve edges, and eight corners. But that the edge, that the diagonal of a side, and the axis of the crystal, are to each other as the square roots of 1, 2, and 3, is a fact with which he has no business ; nor has it any thing to do with the recognition of natural crystals. Nor need he be given the use of certain mathematical aids. He should describe the twelve edges of a cube standing on a horizontal surface thus : four horizontal edges above, four below, and four vertical ones.

This class includes minerals whose specific gravity is over 6,000. f it is not meant that the teacher ought to restrict himself entirely to Werner's theory of the external marks; there are many points (in crystallography especially) which must be made more clear and definite than he made them. But, like Werner, the teacher must never lose sight of the elementary attitude.

More will hereafter be said on this point. $ On this point I refer to the chapter on Geometry, and to my " A B C-Book of Crystallo. graphy," (A B C-Buch der Krystallkunde.)

|| What here follows may be used as additional to what was said above of the relation be. tween mathematical and elementary instruction in natural science.

But he should not say, out of Euclid, "There are six quadrilateral surfaces, and the cube has therefore 6 X 42=12 edges. That such a calculation does not afford a full description of its form appears from crystals, whose surfaces consist of equal numbers of sides, but not of sides of the same form. Vesuvianite, (das Leuzitæder,] for instance, has a surface of twenty-four trapeziums, and therefore 24 x 4-2=48 edges; but twenty-four of these are entirely different from the other twenty-four.

A beginner, if he understands subtraction, can by another formula ascertain very easily the number of angles of a body, of which he has not the slightest knowledge through his senses. This is, that the number of angles of a body equals that of its edges, diminished by that of its surfaces less two.* If, therefore, I tell the beginner that a certain body has 540 edges and 182 surfaces, he can instantly say by his formula that it has 540-180=360 angles. But, if I give him the body itself, he is not in the least able to forin such an idea of it as to determine that some of its angles are formed from six surfaces, &c. He may perhaps not even be able to state, without first reasoning with himself, how many surfaces, edges, and angles there are in a cube. In short, his formula serves him, according to the familiar German proverb, as an asses' bridge. He neither understands it nor what he discovers by its means; and the readiness with which he ascertains results by its use hinders him from strenuous labors to discover the right thing in the right way.

But how, is the next question, shall the pupil learn to analyze the external marks of minerals—to consider the mineral with reference to each individual characteristic? I reply: The best introduction to this knowledge is to take him through a collection arranged by external marks; in which each group, as far as possible, shall lie before him in the order of its colors, crystallization, &c. The teacher will need to give but very little aid-only to put into words what the pupil sees, or to require the more advanced pupils to do it themselves.

*A=E-(S-2) From this, E or $ can be determined, if the number of angles and sur. laces, or of edges and angles, is given.

This investigation of the collection should follow the general theory of external marks ; which is indeed only an arrangement of the characteristics which the pupil has learned to know from the examination of single species.* When the pupil has in this way attained a moderate degree of skill, in the objects and technics of the study, then, and not before he is prepared to read mineralogies. Where the mineralogical author has translated minerals and species into words, a pupil thus trained can translate the words back again into minerals. Every word is to him a living incantation, which awakes the slumbering ideas previously impressed upon his mind.

But, in order that each word may awaken the corresponding conception in the mind, all ambiguity must, as we have already shown, be avoided, and only one fixed term be used for each mineral and each characteristic. This was what Werner meant by his “Be not facile in choice of words, in order that you may agree in things.” And the converse is true: Be not facile in selecting things, in order that

you may agree in words. To understand words is only possible when things are understood. The utmost definiteness in terms, the most accurate expression, will be useless to the scholar, unless the most definite corresponding impressions exist in his mind, to be called up again by those expressions-by words. “No description," says Forster, in his “Views on the Lower Rhine,(Ansichten vom Niederrhein,)“ will convey to another what my own eyes bave received directly from the object, unless he has something with which to compare that object. The botanist may describe to you a rose with the most appropriate terms of his science, may name all its parts even to the smallest, may state their relative size, form, position, substance, surface, and coloring-in short, he may give you such a description as, if you had the rose before you, would leave nothing to desire—and yet it would be impossible, if you had never seen a rose, for him thus to call up an image of it which should correspond with the original. No painter would dare undertake to paint from description a flower which he had never seen. But take but a single look, one single observation with the senses, and its image is indelibly imprinted upon the mind.” Can any one doubt whether Forster is right, or that learned man who flattered himself that he had so perfectly described a certain cabinet of antiquities that it might safely be entirely destroyed, because a skillful sculptor could completely restore it from his description? If Forster is right, which I do not doubt, then it must needs be admitted that the endeavor is utterly foolish to teach a knowledge of minerals by mere oral instruction and reading of books.

* For further delails on this point see Appendix II.

I have thus endeavored to describe the method of my instructions in mineralogy, and its reasons; and to show how the pupil may be gradually carried onward, from his first silent and simple observation of nature, to a full and intelligent comprehension and description of minerals and all their peculiarities.* It remains to offer some observations on the traits of pupils.

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There is a universal method of instruction, applicable to all pupils, and based upon the nature of its subject, which is the same for all pupils, and upon the universal qualities of human character. I have hitherto discussed this method, which was that followed by me in teaching mineralogy.

It is usually thought that he who is master of a department of study is a qualified teacher of it; too little regard being had to his knowledge of his pupils. And thus many teachers are deficient in an understanding of the universal relation that exists between the pupil and the study, and in the skill in teaching which depends upon that understanding

the universal method. I soon learned, however, not usually instructing by the ordinary method of lectures, how little there is in common in mineralogical instruction and in the universal method. I found pupils of so distinctly different and even opposite characters that I saw plainly that it was impossible to instruct them all in the same way. And the longer I taught the more I felt the necessity of studying the peculiarities of pupils with the same attention which is usually devoted only to the subject of instruction; that the teacher of natural history should be able to draw up as good a monograph upon single scholars as upon single species. But in order to pay attention to each individual pupil, and to be able to instruct him in a proper manner, the teacher must be such a master of his subject that no difficulty will rise to embarrass him while he is teaching. In this mode of regarding each single pupil I have had many experiences, bad and good; of which I will here mention a few.

And, first, the bad ones.

Complaints are made of inactive muscles, of weak arms, shoulders, and legs; but much more complaint should be made of imperfect senses, and especially of eyes dulled almost to entire insensibility. This I have found, to my sorrow, in many pupils, particularly the older ones. And no wonder. Brought up in the city, among books, their eyes were directed to almost nothing except reading and writing,

*It is only after having reached this point that they should take up mineralogical chemistry,

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