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but what if we are convicted of universal ignorance of every thing included in the domain of science? I repeat: Have we effected a perfectly exhaustive investigation of any single existence or fact in nature? Is it not rather the case that every such fact has both its comprehensible and incomprehensible side, and, like the moon, turns one side toward us, sometimes lighter and sometimes darker, but keeps the other always turned from us ? *
Did not Cuvier, so mighty in investigating the laws of the animal creation, yet find each animal a riddle, and was he not thus brought to confess that life was a riddle to him?
When the mineralogist measures and computes, with his utmost accuracy, the primitive rhomboids of calcareous spar, and determines mathematically its relation to the many hundreds of crystallized forms which that mineral offers, does he, for all this, understand these rhomboids ? Can he tell how it is that it becomes possible to split them in three directions, parallel to the three parts of rhombic surfaces, so that each surface of cleavage shall be a perfect plane-polished, and with angles mathematically true? We shall look to him in vain for answers to these questions.
The astronomer, of all men, claims to be the most scientific. He computes with accuracy the movements of planets, and comets, and moons, at vast distances of time and place, and demonstrates the most delicate observation in his astronomical prophecy as the correctness of a problem is demonstrated by the proof. Is there here also room for ignorance? I reply: Count one hundred while the minute-hand of a watch is going from twelve to one, and go on counting at the same rate. You can then predict with certainty that when you have counted six hundred the hand will stand at six, and when you
have counted twelve hundred it will have completed its circuit. But notwithstanding this prediction, you may perhaps never have opened the watch, and may know nothing whatever of its construction or mechanism. Even so is it with the astronomer. However accurately he can compute the path of Jupiter, can he for that reason tell wbat are the essential qualities of Jupiter ?? What man can even answer
*" Because that which may be known of God is manifest in them.” *. For we know in part
but when that which is perfect is come, then that which is in part shall be done a way
now I know in part, but then shall I know even as also I am known.” 1 Newton, who, as we have seen, considered the real essence of all bodies entirely incom prehensible to man, would of course reply that such requirements could not be satisfied The originator of the theory of gravitation, he repeatedly declared that he knew only qualities of gravity, not its essence. Thus he says, “I have explained the phenomena of the heaven and of the sea by the power of gravity, but I have not assigned any cause for gravity." Again, having stated the qualities of gravity, he
* But I have not been able to deduce from the phenomena the cause of these properties of gravity, and I offer no hypothesis." (Princip., I. c., p 676.) And in like manner in the " Optics." (Clarke's ed., 1740, p. 3262) • There are efficient principles, such as gravity, whose existence is testibed to by natural phenomena; but what are the causes of these principles has never been explained. Exery
the question, What is the essential nature of the earth—of this rery earth on which you live? And if any one should pretend to have an answer to it, he may be replied to with the reply of the EarthSpirit in Goethe's Faust:
“Thou art equal to the spirit which thou comprehendest-
Such considerations should not, however, lead to an apathetic despair of understanding any understanding of nature, but should only counteract the illusive notion that man can understand created things in the way in which only God, their creator, can understand them.* To us nature is “ mysteriously revealed.”
But, it may be inquired, what is the value of this discussion in a work on pedagogy ?
I reply: A recognition of the wonderful union of revelation and mystery in nature, and the clearest possible perception of the boundary between them, will exercise a most important influence upon the character of the teacher and upon his study of nature.
The mysteries of nature will direct him in humility and earnestness toward eternity; while he will investigate what is susceptible of being known with conscientious and persevering industry, thanking God for every pleasure which he receives from discovering the beautiful and invariable divine laws.t
And how can this state of feeling and this knowledge in the teacher fail to have the greatest and most excellent influence upon his methods of instruction ?
Any one doubtful as to the goodness of this influence will be convinced of it, if he will examine the bad influence exerted on their scholars by such teachers as are destitute of the knowledge and feeling which give it; who live in a narrow circle of overestimation of themselves. For them there are no mysteries; they can comprehend every thing. And then it most commonly happens that they fail to observe and learn what is really attainable, while they weary themselves in vain over the incomprehensible; and thus, instead of ascertaining divine laws, they hatch out a parcel of chimeras, which in their presumptuous blindness they set up as being those laws. The proverb may well be applied to them, that they make fools of themselves by thinking themselves so wise. And they make their scholars fools.
where the qualities are manifest, but their causes are hidden." And again, “ There are originating causes (principia) of motion, as gravity. But the causes of these I leave to be investigated." • By universal analogy"—(Bacon.) As Kepler repeatedly does.
Beginners are dismayed at the apparent irregularity of crystals. On comparing, for instance, the model of a cube, of six equal sides, with a cubic crystal of fluor spar, whose sides are very unequal, he fancies that, notwithstanding the right angles of the spar, there is by no means as entire a regularity in the natural crystal as in the artificial model.
To remove this error, we may first consider the way in which laws prevail in the vegetable world. When the botanist says of the lily that its blossom has a six-petaled campanulate corolla, six anthers, a sexfid, capsule, &c., a German lily will answer the description as well as a lily from Mount Carmel. And so do the carefully painted lilies in old paintings; they have a six-leaved corolla, six anthers, &c Thus the generic description, which the botanist gives, applies to lilies of all countries and periods. The close adherence to the law is evident; but an ignorant person, on learning so much, might probably conclude that all lilies were all exactly alike, and that accordingly great monotony must prevail throughout the creation. Such was the idea of the electress who denied Leibnitz's assertion that no leaf was precisely like another; but all her endeavors to find two precisely alike were quite in vain. It would be equally impossible to find two lilies exactly alike, though they grew upon the same stem. “The law of the Lord is unchangeable," but their unchangeableness does not produce a disagreeable monotony among the individuals subject to it; but under its protection there prevails an agreeable variety and unconstrained beauty.
This appears still more clearly in the animal kingdom; most of all in the human race. Here the law becomes less and less
apparent, and the freedom of the individual is so prominent that the wicked quito forget the power of God, either over individuals or the race. “ Tho fool hath said in his heart, There is no God," but the pious finds peace in the love of God, and says, “I desire not to be free without Thee; let my will be thine and thine mine."
From this culminating point of revealed freedom and concealed law, to return to the silent mineral world. While the ungodly may fall into the delusion that he is entirely independent and free, we may take the mineral kingdom as the realm of entire dependence. Here we find no notions of freedom.
Freedom, in the moral sense, can be predicated only of men; the freedom, that is, of individual action. But a first suggestion, a dawn of this freedom, an evidence that God desires not a world of wiform puppets, but of free and independent creatures, is revealed in the
realm of nature, by this infinite variety of individuals, included under one and the same generic idea.
And this is true even of the crystals of the mineral kingdom. If we find a crystal prismatic, six-sided, and terminated at each end by a six-sided pyramid, we shall find the number of surfaces, and the angles, invariable; but there is an infinite variety in the size of the sides of the prism and pyramids. No crystal is like another, any more than a leaf. And it is this very variety in size which brings out the beautiful relations* which do not appear from the model, because all its similar surfaces are of equal size.
The pupil's attention should be directed to these relations; and he will thus escape the mistaken idea that the natural crystals, instead of being really like the artificial model, are only attempts to be like it.
It is my heartfelt wish that instruction in natural science, in former periods entirely neglected, may be increasingly given; but that it may be given in the right spirit and in the right way, so that the feelings, senses, and understandings of the young may be trained by it, from their early years, to a clear and ascertained comprehension of the creation—that other Holy Writ.
Any one imagining that such a course of training would enslave the senses, would most wrongfully confuse the right and holy exercise of the senses with their beastly abuse. For the natural philosopher uses his senses to the honor of God; and if he makes them serve base lusts and passions, he will by that means blunt and finally destroy their loftier susceptibilities. Therefore the teacher of natural history must, above all, urge upon his pupils the necessity of holiness; must contend against wicked lusts ; must cultivate in them chaste and pure feelings, and childlike innocence of heart. He must seek to secure for them a consecration such as a divine would properly require in order to the pious study of the Holy Scriptures.
Such a devotional method of investigating the creation takes a more and more spiritual form. Mere mortal and bodily envelopes disappear: and immortal thoughts, rooted in God, awaken and stimulate to a higher life.
Thus also is developed the whole man. In the imaginative period of childhood, the material world, so rich in suggestions, surrounds and enchains him. His senses are being more and more developed, up to the period of adult life; they are the means for influencing his immortal soul. As he reaches the limit of earthly life, they begin to disappear; and we then complain that the powers of our eyes and ears are decaying. But let us not complain; let us herein recognize a token that in the man, his bodily senses sated with the phenomena of this earth, all things are spiritualizing and growing clearer; and that he is thus ripening and adapting himself for a higher life. All earthly things are ended; heaven is opening to us.
* Such as the parallelism of the edges.
Aids for TEACHING MINERALOGY.*_Besides the academical collection at Breslau, I made usc in my instruction there of two smaller ones. The first consisted of only ten cases, containing specimens of all the important groups, and was intended for beginners; not only for their first inspection, but to afford some rough instruction in manipulation. Fiat experimentum in re vili; and accordingly this first collection was of little value; so that any little injury from unskillful handling could do but small harm. After this the pupils came to the second collection, which occupied fifty-four
The specimens were small, but mostly fresh and clean. In going throngh with this collection I mentioned the names of groups; so that the pupils obtained an intelligent and actual list of names, and a general view of all the groups. Some details of colors and crystals were omitted.
It was only after this that I introduced them to the main collection, of three hundred and fifty-five cases. In going through this collection, the pupils might, as in the others, take each specimen in their hands, but must replace it in its paper box. Where it was useless or injurious to take them in the hands, as in examining the colors, for instance, it was of course not practiced. If the pupil has been made acquainted with the careful handling of the specimens, this method does not injure them. The collection is not intended merely for the teacher's scientific investigation, and still less for empty show; but principally for the instruction of the pupils ; which can not be thoroughly done without permitting this handling. This purpose of the collection also decided me not to expend its income for expensive curiosities, or the novelties of the day, which are commonly of very small relative scientific value, and to the beginner of none whatever. In the place of one unimportant scrap of euclase can be bought a large number of instructive crystals of quartz, calcareous spar, &c. This principle is of course not applicable to collections which are not at all, or not entirely, intended for instruction, and which are sufficiently provided with all common specimens, and with incoines.
The chief collection was arranged generally on Werner's plan. According to this, the pupil had to go through the groups according to their separate peculiarities; first according to color, then transparency, then luster, crystallization, &c.
To afford the pupil a scientific gratification as soon as possible, I was accustoined to permit him, if capable, to take some single group, whose crystallization was easy, and go through with it; such as lead glance, fluor spar, &c. Thus he gained a first clear comprehension of the wondrous intelligence that pervades nature. If there were two pupils, perhaps not precisely equal, but of about equal, capacity, I cansed them to go through the collection together; which was beneficial to both. On the contrary, nothing is more harmful than to class together in this way pupils of uncqual capacity. The more capable is impeded, or wearied, by the slow progress of him who less so; and the latter again despairs
* What is here said relntes to my instructions in mineralogy at Breslau. No objection should be minde respecting the richness of the collection there; for something can be done, eren with smaller means.