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The formation of the beds or strata, by a successive deposition from water, would lead us to expect that the separate layers should be disposed horizontally, or that they should, in their whole extent, be arranged at right angles to the force of gravity; that they should be continuous or without fissures; and that they should have no elevations or depressions. The reverse of this, however, is the fact. Instead of universal horizontality, we frequently find them almost in a vertical position; instead of a continuous surface, hke the coats of an onion, we see wide irregular sents and fissures; and, instead of a uniformly revel appearance, we find mountains and alpine chains shooting up many thousand feet above their surrounding regions. In a system that lays claim to consistency, some explanation must be provided for reconciling these apparent anomalies with its general principles, and many suppositions may obviously be resorted to. The greatest inequalities of the earth's surface must have originated in the manner in which the primitive strata assumed the crystalline appearance, and the circumstances under which chemical affinities acted upon the materials of the chaotic fluid. The irregularities of the subsequent depositions may be partly owing to the kind of surface or bed on which they were arranged, and partly to an unequal subsidence in the contiguous parts deposited at the same time. Many rents, fissures, and dislocations, must have originated in the different degrees of solidity in the contiguous strata, in the unequal weight which crystallisation imposed upon them, in the withdrawing of the water sooner or later from different portions, and in several other causes, which it is unnecessary, in this short sketch, to enumerate. Many of these rents and fissures were made while the strata were still immersed in the waters, and, being filled up with precipitates of a more crystalline kind, constitute what are demominated veins, those repositories of mineral wealth. The structure of veins, narrowing in diameter as we descend, and the more regular disposition of their contents, according to laws of chemical attraction, are offered as decided proofs, both of their being filled by infiltration from above, and of their consolidation taking place in circumstances where the mass suffered no disturbance. After this statement of the Wernerian theory, it might be proper to adduce some of the arguments that tend to confirm it, and some of the objections to which it has been thought liable; but both these will be more duly appreciated, after we have drawn a similar outline of the rival system to which it is opposed. Dr. Hutton does not go back to chaos to lay the foundation of his habitable world, nor does he borrow much assistance in constructing his fabric from chemical attractions. He rests upon a pre-existing continent, out of the ruins of which our present dry land was formed and arranged principally by mechanical means. The portion of the globe which we now possess was, according to his hypothesis, the bottom of the sea when the older continent was decaying to form it; this older continent was then, of course, immersed; and, lest we should be alarmed at the recurrence of a similar catastrophe to this scene of our inte

rests, we are told that it will be followed by a similar renovation. Thus, as one continent descends another rises, like the opposite scales of a balance; and, in the resources of the system, that order of organic nature is supposed to be traced by which the continued existence of the different races is secured, not by the perpetuity of the individual, but by the successive re-production of the kind. Our present world is thus one in an indefinite series of worlds which have existed in times past, and which are destined in future to appear; and all the less obvious or more striking changes which we witness are steps in the progress of mighty revolutions, to which the imagination can set no limits, either with regard to duration or magnitude. He lays down as a certain position, that the solid parts of our earth are suffering decay from the action of the elements; that the portions detached from the more elevated ground are carried by the operation of water to the lower levels, and ultimately deposited in the basin of the ocean. He conceives, that tides and currents there arrange what is carried within their influence in layers along the bottom of the sea. This operation must proceed very slowly, but Dr. Hutton is not limited with respect to time, and can make as large a use of it as his system demands. Every river, every brook, every stream of water that we see, descends towards the ocean, charged with some portions of the surface over which it flows. All the soil and softer parts on which our plants are produced, have been confessedly loosened by water, and may be ultimately transported by it to the lowest levels of the same element. The strata of our dry land have all been thus carried from a pre-existing one, and arranged by the ocean which then covered it. For their consolidation and other appearances, a new principle is assumed by the Huttonian geologists, which forms the chief characteristic of their system. They conceive that there perpetually exists in the heart of the mineral kingdom an immense force of heat that has been sufficient to fuse or to soften the various strata of which its crust is composed. The greater or less degree of liquidity which it thus produced, allowed the substances on which it acted to be consolidated upon cooling, either into crystalline fossils, or into less regular masses. The strata that were arranged at the bottom of the ocean, from the debris of a former world, were thus brought from their soft state of simple mechanical aggregation, to assume the compact structure of mountain rocks. To this powerful agent of internal heat, is not only assigned the office of first softening and finally indurating the strata, but that likewise of elevating them from the bottom of the sea, and converting them into dry land. The strata at the bottom of the ocean, being arranged by water, must, it is conceived, have been arranged in a horizontal direction, though now their appearance is extremely different. Their present fragmented and shattered surface, their deep chasms, their apparently ruinous contortions and dislocations, the vertical position of some of them, and the considerable declination of almost all, are also accounted for by the operation of internal fire. The volatile ingredients of many bodies are easily dissipated by caloric, and some compounds are discovered in the mineral kingdom, which must have been exposed, upon this hypothesis, to such an intensity of heat as would have effected a dissolution among their parts. To obviate objections of this kind, the modification of the effects of heat from the pressure under which it acts, is illustrated and applied with great ingenuity. This modification of heat, by pressure, is a very important fact to the Plutonian theory. With regard to the order of time, or the succession in which the different rocks were formed that compose the crust of our earth, the Huttonian differs as much from the Wernerian as in the agent he principally employs. It will be remembered that Werner calls granite the earliest of the primitive rocks, from the supposition that it was separated from the chaos by crystalline precipitation, prior to the existence of any other mineral. Dr. Hutton, on the contrary, in his chronology of the fossil kingdom, *: granite among its last formed products, and brings forward its appearance as a triumphant proof of the truth of his system. He conceives it in a state of fusion to have burst the superior strata with which it was enveloped, aided by the expansive power of his central fire, and to have issued forth from its confined furnace somewhat in the manner of a stream of lava from a volcano. The greatest heights of our globe, and the most extensive mountain ranges, are thus nothing else but the consolidated torrents of mighty eruptions, the matter of which had been rendered liquid by a subterranean fire, which still exists for the future accomplishment of similar effects, and gives proofs of present activity in the phenomena of the volcano. To its complete fusion is ascribed its perfect crystalline texture, its want of stratification, and its perfect freedom from organic remains. A similar account is given by this system of the formation of veins, and of the fossils which enerally fill them. They are rents caused by a #. acting from beneath, and filled with matters injected into them from the same quarter in a state of fusion. Their contents are thus different from the materials of the strata which they traverse, and almost always present a highly crystalline structure. Such is the outline of the Huttonian theory of the earth, as far as regards the manner in which its crust was stratified in the bottom of the ocean, consolidated into a compact mass, elevated into islands and continents, separated into distinct H. by veins and beds, and deranged in its orizontal appearances by an eruptive force. It is needless to mention the account which the supporters of this geological system give of volcanoes. They accord with their opinions, or rhaps suggested them; and the Wernerian eaves them in full possession of such ground without reluctance, satisfied that the central heat, which raised continents, is not necessary to explain their phenomena. After giving a very imperfect account of these two theories, it may be necessary to say a few words with regard to their merits, the consistency of their parts, and their agreement with the phenomena which they profess to explain. The Huttonian geologist commences with the

history of the formation of the strata, as in his system the strata were deposited and arranged prior to the operation of fire upon them, and prior likewise to the existence of the more crystallised masses formed by fusion. With the mode of forming the stratified structure he therefore begins his system ; and here likewise begin the objections to which it has been thought liable. . . He supposes that the materials of all the strata are the debris of a pre-existing world; that they have been detached from it by the operation of the elements; carried, by the agency of water, to the ocean; and there spread in regular order over its bottom by the same power. Thus all the rocks that exhibit the stratified structure, are nothing but mechanical deposits, and rivers have been the great agents in conveying them to their present situation. Now it cannot fail to strike every one, that effects are here attributed to those streams that mark the surface of our globe, which they seem inadequate to produce. It is true that most rivers flow towards the ocean, charged with a part of the soil or softer rock which border their channels; but it is not so true that they carry this burden to their ultimate destination. A great part of it is deposited on their banks, or in the hollows of their courses, and much of what reaches the sea goes to form bars, or, being driven back to the shore, makes an addition to the sea-coast. It is evident that a small portion only can reach the ocean, and ‘if the disintegration be so slow as is admitted,' observes Mr. Murray; “if, as Dr. Hutton himself observes, the description which Polybius has given of the Pontus Euxinus, with the two opposite Bosphori, the Maeotis, the Propontis, and the port | Byzantium, is as applicable to the present state of things as it was at the writing of that histo if the Isthmus of Corinth is apparently {: same at present as it was 2000 or 3000 years ago; if Scylla and Charybdis remain now as they were in ancient times, rocks hazardous for coasting vessels; if the port of Syracuse, with the island which forms the greater and less, and the fountain of Arethusa, the water of which the ancients divided from the sea with a wall, do not seem to be altered; and if, on the coast of Egypt, we find the rock on which was . formerly built the famous tower of Pharos; and, at the eastern extremity of the port Eunoste, the sea-bath cut in the solid rock on the shore, to all appearance the same at this day as they were in ancient times: if such be the extreme slowness of the disintegration, the reflection is obvious, that, admitting it, a duration will be allowed to the world infinitely beyond our conception, and adequate to any purpose which we can conceive it designed to serve; and there is at least no necessity pointed out for supposing an arrangement by which it is to be perpetuated or restored. “Neither are the facts conclusive which are stated by Dr. Hutton and Mr. Playfair, to prove that all our strata have originated from the waste

of a former world, for they are equally well ac

counted for by the Wernerian system. . It is stated, that many rocks are found which contain fragments of others, or which are connected with collections of gravel loose or consolidated. Such fragments and gravel necessarily suppose the existence of former strata, from the waste of which

they had originated. It is also observed, that, in many of the most extensive strata of the earth, remains or impressions of organic substances are found, both animal and vegetable, and of course these must have existed prior to the formation of such strata. “These facts are considered by the Huttonian geologist as sufficient proof of the existence of a habitable world, from the decay of which ours has been formed. They are, however, equally well accounted for by the Neptunist, without admitting such a supposition. It is supposed that the existence of marine animals commenced after the crystallisation of the great primary strata; and that after that period, too, the waters of the ocean began to diminish in height, so as to leave elevated land, on which vegetation commenced. The retreat of the ocean continued to be gradual for many ages, and during this time the secondary strata were formed. It is obvious, therefore, that the fragments of rock, the sand and gravel which these often contain, or with which they are associated, or which even in many cases compose the greatest part of their mass, might originate from the disintegration of the primary strata above the level of the sea; a disintegration to which, in this early period of their consolidation, they might even be more liable than they are now. And the origin of the remains of marine animals, and even of vegetables, found in the secondary rocks, it is obvious, are equally well accounted for on this theory, since the existence of these may have begun previous to the existence of these strata. The facts, therefore, do not prove the hypothesis of Dr. Hutton, since, on a different hypothesis, they are explained with equal facility. ‘It has been affirmed, however, that the same appearances of sand and gravel, and of marine impressions, are occasionally to be met with in the primitive strata, and that of course the Wernerian explanation is defective; for marine animals are not supposed to have existed at their formation; and it is obvious that the presence of sand and gravel are true indications of strata having existed before them. “But it is asserted, on the other hand, by Neptunian geologists, that such appearances are not to be met with in strata truly primitive; but that when they do occur in strata, not of the secondary class, it is in those of the intermediate kind, or what Werner terms the rocks of transition. These, it will be recollected, are supposed to be posterior in their formation to the primary, but prior to their secondary strata, and to have been formed at that period when the existence of marine animals, or at least of some species of them, had commenced; and of course they may occasionally be found with impressions or remains of these beings. This supposition is liable to no difficulties, and seems to follow justly from the facts. Since certain rocks, having peculiar characters, and composing the most elevated parts of the globe, are found destitute of organic remains, while in others they are in abundance, doth not this afford a presumption, that the former had been produced prior to the period when these beings began to exist? and if rocks are found intermedia’e in their character between

these, connected, principally with the primary, but in general less elevated, and sometimes, though rarely, containing vestiges of sea animals, is it not reasonable to believe that these have been intermediate in their formation, and that at least the few species of those animals, whose remains are found in them, had begun to exist at the time they were formed.” The Huttonian theory gives a solution of these phenomena, according to its own peculiar principles, which is pressed with greater difficulties than any which its adherents have been able to raise against its rival system. As all strata, according to it, are arrangements from the wrecks of a former world, they ought all to have their Fo of animal remains and fragmented ossils assigned them. No reason can be given for their existence in one situation which would not lead us likewise to expect their occurrence in another., Gneiss, mica-slate, and clay-slate are stratified rocks, and should have these proofs of their prior history inscribed upon them as legibly as slate-clay, sandstone, and the calcareous fossils. In the former class, however, they are seldom or never found; in the latter they are met with in abundance. The Huttonians endeavour to remove this inconsistency, by answering, that the gneiss and mica-slate are in a higher degree of crystallisation than the other kinds of rock in which petrifactions occur, and that, in the fusion which enabled them to assume that state, the traces of animal exuviae may have been destroyed. This statement would obviate the objection, if it accorded with the fact; but unfortunately it has not that recommendation. We need only refer to that species of marble in which organic remains occur in abundance, to show that a higher perfection of the crystalline structure than is by this hypothesis consistent with their appearance in gneiss, actually admits of their existence in the carbonate of lime. Without allowing, with the Wernerian, a priority in the arrangement of these different kinds of rocks how shall we account for such phenomena? and by allowing such successive formations, how easily are they explained 1 Nor does the Huttonian theory labor with greater success, to reconcile the occurrence of fragments in some peculiar situations with its general principle of stratification. There frequently occurs between the strata, or what Werner calls the primitive and floetz formations, a bed of conglomerated fragments of rolled pieces. This appearance, for instance, occurs placed upon a basis of clay-slate, and covered with a stratum of sandstone, and is easily accounted for on the Wernerian doctrine of the prior existence of granite, from the rocks of which such debris might be detached as formed these beds, while the waters of the chaos still covered the gneiss and the somewhat lower levels of the globe. Let us hear the Huttonian explanation of this fact, as detailed by Mr. Murray. “The explanation, according to the Huttonian hypothesis, involves a supposition so extraordinary as to furnish a singular contrast with that of the Neptunian. It is supposed that the schistus had been formed in beds nearly horizontal, and that, by an expansive power exerted from beneath, these had been elevated to the surface, and placed in a vertical position. In this situation, the bed of gravel, from which the breccia is formed, had been deposited on the summit of the vertical schistus. To admit of the formation of the horizontal strata of sandstone, it is further supposed, that the schistus, with this superincumbent breccia, had again sunk in the ocean, and remained depressed for ages, till the materials of the sandstone were deposited on it. These materials are supposed to have been then consolidated by the central fire operating on them, even with the intervention of the deep strata of schistus on which they are incumbent; and, lastly, we are told that the whole, when thus prepared, were again elevated by a new exertion of heat. It may surely be affirmed, without far, ther reasoning, that suppositions so extravagant and improbable can never be real interpretations of the operations of nature.' The second class of operations in the order of succession, according to the Huttonian theory, is the process of consolidating, deranging, and elevating the earth's crust, formed, as above described, at the bottom of the sea; and the second great principle it assumes is the agency of internal heat for accomplishing these purposes. By employing this agent, and assigning it so important functions, the Huttonians have exposed their system to objections evident to those least acquainted with geological speculations, and which the most able Huttonian cannot satisfactorily obviate. The first thing that strikes us as a difficulty, in the conception of this theory, is the immense volume and intense force of that heat which could melt or soften masses so gigantic in their bulk, and so infusible in their nature, as those that compose the habitable world. This, however, is an objection founded rather upon a comparison of the great operations of nature, with the limited scale on which we conduct our own, than upon any natural inconsistency in the theory against which it was alleged. There are objections to the principle of the Huttonian theory of a different kind, and not so easily answered. What is the nature and source of this central heat? and what are the laws by which it is regulated ? These are questions, in the answers to which the supporters of the Plutonic system are certain to involve themselves in difficulties, if not in contradictions. Does this heat arise from combustion ? No; for combustion requires conditions for its existence which are not to be found in the circumstances under which this central heat is supposed to act. Where could such a quantity of combustible matter be found, as could fuse and eject those mighty chains of mountains which extend so far and rise so high If combustible substances should be found in the magazines of nature, whence could come that gas which is necessary for this operation ? The circumstances of compression under which the central heat is supposed to act, and the consequent exclusion from oxygen or atmospheric air, are sufficient to destroy every idea of combustion. But even though we should admit the possibility of ordinary burning, in the instance before us, are the stores, both of the combustible materials and the supporters of combustion, inex

haustible 2 and will there always be sufficient quantities of them available for the purposes of making worlds when the old are worn out? or, in other words, for answering the ends of the theory in the renovation of hature ? We all know that a substance which has undergone combustion, forms products which are not capable of undergoing a second time the same process. It should be observed, however, that the ablest adherents of the Huttonian hypothesis have entirely renounced the use of fuel in the production of the central heat, and have resorted to other means of exciting and supporting it. Most of them also have given up the solar rays, friction, and condensation : indeed the sup sition on which Mr. Playfair, the ablest supporter of the system, finally rests, seems little else than the old doctrine of occult qualities. If his hypothesis has any meaning, it implies, that an immense heat was originally stored in the lower parts of the earth, and that it is there preserved by the mutual action and reaction of the bodies in which it resides upon each other. But its preservation in the same volume and intensity, without any fresh supply, is contrary to all the laws by which the action of heat is regulated. The only condition on which the hypothesis of its accumulation would be conceivable, would be a state in the bodies that contained it, so completely insulated that they could diffuse no more of it than what they received; or, in other words, a state in which no new distribution could take place, because the most perfect equilibrium of temperature was established among all the bodies which could, by their vicinity, partake of it, either by radiation or through the medium of conducting substances. Now it will not surely be pretended that there is, in the bowels of the earth, any region so insulated. Indeed the simple idea, that the central fire has softened the strata which were formerly cold mechanical deposits, presupposes a new distribution of its influence, with a consequent decrease of intensity in its original repository; and thus the very purpose for which its operation is assumed cannot be accomplished, without destroying the necessary conditions of its existence. The other phenomena exhibited by veins, beds, and individual fossils, are more hostile to the hypothesis that employs fire in producing them, than even those which we have stated. But we cannot at present enter farther into the subject. We need only add that Dr. Boué seems to have adopted from the Huttonian theory some valuable suggestions, and that the commendation of M. Necker, with respect to the habits of Saussure as a geologist, seems well worthy the attention of all students of this science. “In proportion to the avidity with which he sought for facts, was the care with which he avoided vain speculations. If he sometimes advances a hypothesis, it is with a reserve justly admired, although rarely imitated, and only when the facts seem imperiously to command it. When new facts come in opposition to his former opinions, he abandons or modifies them without regret.”

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Although there be a certain truth, geometricians would not receive satisfaction without demonstration thereof. Browne. Must men take the measure of God just by the saine geometrical proportions that he did that gathered the height and bigness of Hercules by his foot? Stillingfleet. Him also for my censor I disdain, Who thinks all science, as all virtue, vain; Who counts geometry and numbers toys, And with his foot the sacred dust destroys. Dryden. All the bones, muscles, and vessels of the body are contrived most geometrically, according to the strictest rules of mechanicks. Ray. Does not this wise philosopher assert, That the vast orb, which casts so fair his beams, Is such, or not much bigger than he seems? That the dimensions of his glorious face Two geometrick feet do scarce surpass? Blackmore.

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GeoMANcy, GeoMANT1A, is performed by ineans of a number of little points, or dots, made on paper at random : and by fortning from the various lines and figures which those points present, a pretended judgment of futurity, upon any question proposed. The word is derived from the Greek Yu and Havreia, divination; it being the ancien' custom to cast little pebbles on the earth, and thence to form their conjectures, instead of the points afterwards made use of Polydore Virgil defines geomancy a kind of divination performed by means of clefts or chinks made in the ground; and supposes the Persian Magi to have been the inventors of it.

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GeoMETRY, Gr. Yewpierpia, Fr. geometrie, originally signified the art of measuring the earth, or any distances or dimensions on or within it; but it is now used for the science of quantity, extension, or magnitude, abstractedly considered, without any regard to matter. Geometry is usually divided into speculative and practical ; the former of which contemplates and treats of the properties of continued quantity abstracted§: and the latter applies these speculations and

eorems to use and practice.

The word geometry literally signifies measuring of the earth, as it was the necessity of measuring the land that first gave occasion to study the principles and rules of this science, which has since been extended to numberless other speculations. Some define it the science of enquiring, inventing, and demonstrating all the asfections of magnitude. Proclus styles, it the knowledge of magnitudes and figures, with their limitations; as also of their ratios, affections, positions, and motions of every kind. -

In a word, geometry, together with arithmetic, now forms the chief foundation of all the mathematics.

History of GeoMETRY.

The invention of geometry is generally ascribed to the Egyptians. Herodotus, Diodorus, Strabo, and Procius, all agree that the annual inundations of the Nile gave rise to it, by carrying away the land-marks and boundaries of estates and farms; and covering the surface of the ground with mud, which effaced every trace of their for: mer limits. Hence the o were oblige' every year to distinguish and lay out their lands by the consideration of their figure and quantity, that every person might have his own property: and thus, by repeated experience and practice, in drawing figures, lines, and schemes, for this purpose, they gradually formed an art which, from its origin, in measuring of lands, the Greeks at last named yewporpia, geometry. . By farther contemplation on the draughts of o their

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