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are certainly separated, but without regard to the races which cannot be included in any of these classes, and which have been alternately termed Scythian and Allophyllic. Iranian is certainly a less objectionable term for the European nations than Caucasian; but it may be maintained generally, that geographical denominations are very vague when used to express the points of departure of races, more especially where the country which has given its name to the race--as, for instance, Turan (Mawerannahr) has been inhabited at different periods by Indo-Germanic and Finnish, and not by Mongolian tribes.
Whilst we maintain the unity of the human species, we at the same time repel the depressing assumption of superior and inferior races of men. There are nations more susceptible of cultivation, more highly civilized, more ennobled by mental cultivation than others—but none in themselves nobler than others. All are in like degree designed for freedom; a freedom which in the ruder conditions of society belongs only to the individual, but which in social states enjoying political institutions appertains as a right to the whole body of the community.
“ Man,” says W. von Humboldt, regards the earth in all its limits, and the heavens as far as his eye can scan their bright and starry depths, as inwardly his own, given to him as the objects of his contemplation, and as a field for the development of his energies. Even the child longs to pass the hills or the seas which enclose his narrow home; yet when his eager steps have borne him beyond those limits, he pines, like the plant, for his native soil : and it is, by this touching and beautiful attribute of man—this longing for that which is unknown, and this fond remembrance of that which is lost—that he is spared from an exclusive attachment to the present. Thus deeply-rooted in the innermost nature of man, and even enjoined upon him by his highest tendencies—the recognition of the bond of humanity becomes one of the noblest leading principles in the history of mankind.”—HUMBOLDT.
DIVISIONS OF SCIENCE.
The Sciences may be divided into three great classes :those which relate to Number and Quantity, those which relate to Matter, and those which relate to Mind. The first are called the Mathematics, and teach the properties of numbers and of figures; the second are called Natural Philosophy, and teach the properties of the various bodies which we are acquainted with by means of our senses; the third are called Intellectual or Moral Philosophy, and teach the nature of the mind, of the existence of which we have the most perfect evidence in our own reflections; or, in other words, they teach the moral nature of man, both as an individual and as a member of society. Connected with all the Sciences, and subservient to them, though not one of their number, is History, or the record of facts relating to all kinds of knowledge.-BROUGHAM.
DIFFERENCE BETWEEN MATHEMATICAL AND MECHANICAL
All the truths which Natural Philosophy teaches depend upon matter of fact; and that is learnt by observation and experiment, and never could be discovered by reasoning at all. If a man were shut up in a room with pen, ink, and paper, he might by thinking discover any of the truths in arithmetic, algebra, or geometry; it is possible at least; there would be nothing absolutely impossible in his discovering all that is now known of these sciences; and if his memory were as good as we are supposing his judgment and conception to be, he might discover it all without pen, ink, and paper, and in a dark room. But we cannot discover a single one of the fundamental properties of matter without observing what goes on around us, and trying experiments upon the nature and motion of bodies. Thus, the man whom we have supposed shut up, could not possibly find out beyond one or two of the very first properties of matter, and those only in a very few cases; so that he could not tell if these were general properties of all matter or not. He could tell that the objects he touched in the dark were hard and resisted his touch ; that they were extended and were solid : that is, that they had three dimensions, length, breadth, and thick
He might guess that other things existed besides those he felt, and that those other things resembled what he felt in these properties; but he could know nothing for certain, and could not even conjecture much beyond this very limited
number of qualities. He must remain utterly ignorant of what really exists in nature, and of what properties matter in general has. These properties, therefore, we learn by experience; they are such as we know bodies to have; they happen to have them—they are so formed by Divine Providence as to have them—but they might have been otherwise formed; the great Author of Nature might have thought fit to make all bodies different in every respect. We see that a stone dropped from our hand falls to the ground; this is a fact which we can only know by experience; before observing it, we could not have guessed it, and it is quite conceivable that it should be otherwise : for instance, that when we remove our hand from the body it should stand still in the air; or fly upward, or go forward, or backward, or sideways : there is nothing at all absurd, contradictory, or inconceivable in any of these suppositions; there is nothing impossible in any of them, as there would be in supposing the stone equal to half of itself, or double of itself; or both falling down and rising upwards at once ; or going to the right and to the left at one and the same time. Our only reason for not at once thinking it quite conceivable that the stone should stand still in the air, or fly upwards, is that we have never seen it do so, and have become accustomed to see it do otherwise. But for that, we should at once think it as natural that the stone should fly upwards or stand still, as that it should fall down. But no degree of reflection for any length of time could accustom us to think two and two equal to anything but four, or to believe the whole of anything equal to a part of itself.
After we have once, by observation or experiment, ascertained certain things to exist in fact, we may then reason upon them by means of the mathematics ; that is, we may apply mathematics to our experimental philosophy, and then such reasoning becomes absolutely certain, taking the fundamental facts for granted. Thus, if we find that a stone falls in one direction when dropped, and we further observe the peculiar way in which it falls, that is, quicker and quicker every instant till it reaches the ground, we learn the rule or the proportion by which the quickness goes on increasing ; and we further find, that if the same stone is pushed forward on a table, it moves in the direction of the push, till it is either stopped by something, or comes to a pause by rubbing against the table, and being hindered by the air. These are
facts which we learn by observing and trying, and they might all have been different if matter and motion had been otherwise constituted ; but, supposing them to be as they are, and as we find them, we can, by reasoning mathematically from them, find out many most curious and important truths depending upon those facts, and depending upon them not accidentally, but of necessity. For example, we can find in what course the stone will move, if, instead of being dropped to the ground, it is thrown forward : it will go in the curve already mentioned, the parabola, somewhat altered by the resistance of the air, and it will run through that curve in a peculiar way, so that there will always be a certain proportion between the time it takes and the space it moves through, and the time it would have taken, and the space it would have moved through, had it dropped from the hand in a straight line to the ground. So we can prove, in like manner, what we before stated of the relation between the distance at which it will come to the ground, and the direction it is thrown in; the distance being greatest of all when the direction is half way between the level or horizontal and the upright or perpendicular. These are mathematical truths, derived by mathematical reasoning upon physical grounds; that is, upon matter of fact found to exist by actual observation and experiment. The result, therefore, is necessarily true, and proved to be so by reasoning only, provided we have once ascertained the facts; but, taken altogether, the result depends partly on the facts learned by experiment or experience, partly on the reasoning from these facts. Thus it is found to be true by reasoning, and necessarily true, that if the stone falls in a certain way when unsupported, it must, when thrown forward, go in the curve called a parabola, provided there be no air to resist : this is a necessary or mathematical truth, and it cannot possibly be otherwise. But when we state the matter without any supposition,without
any if,”—and say, a stone thrown forward goes in a curve called a parabola, we state a truth, partly fact, and partly drawn from reasoning on the fact; and it might be otherwise if the nature of things were different. It is called a proposition or truth in Natural Philosophy; and as it is discovered and proved by mathematical reasoning upon facts in nature, it is sometimes called a proposition or truth in the Mixed Mathematics, so named in contradistinction to the Pure Mathematics, which are employed in reasoning upon
figures and numbers. The man in the dark room could never discover this truth unless he had been first informed, by those who had observed the fact, in what way the stone falls when unsupported, and moves along the table when pushed. These things he never could have found out by reasoning: they are facts, and he could only reason from them after learning them by his own experience, or taking them on the credit of other people's experience. But having once so learned them, he could discover by reasoning merely, and with as much certainty as if he lived in daylight, and saw and felt the moving body, that the motion is a parabola, and governed by certain rules. As experiment and observation are the great sources of our knowledge of Nature, and as the judicious and careful making of experiments is the only way by which her secrets can be known, Natural and Experimental Philosophy mean one and the same thing; mathematical reasoning being applied to certain branches of it, particularly those which relate to motion and pressure.
Natural Philosophy, in its most extensive sense, has for its province the investigation of the laws of matter—that is, the properties and the motions of matter; and it may be divided into two great branches. The first and most important (which is sometimes, on that account, called Natural Philosophy by way of distinction, but more properly Mechanical Philosophy) investigates the sensible motions of bodies. The second investigates the constitution and qualities of all bodies, and has various names, according to its different objects. It is called Chemistry, if it teaches the properties of bodies with respect to heat, mixture with one another, weight, taste, appearance, and so forth ; Anatomy and Animal Physiology, (from the Greek word signifying to speak of the nature of anything,) if it teaches the structure and functions of living bodies, especially the human ; for when it shows those of other animals, we term it Comparative Anatomy; Medicine, if it teaches the nature of diseases, and the means of preventing them and of restoring health ; Zoology, (from the Greek words signifying to speak of animals,) if it teaches the arrangement or classification and the habits of the different lower animals ; Botany, (from the Greek word for herbage,) including Vegetable Physiology, if it teaches the arrangement or classification, the structure and habits of plants; Mineralogy, including Geology, (from the Greek words meaning to speak of the earth,) if it teaches the arrangement of minerals,