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which being that which reduced the waters to their present level. Patrin formed the opinion, that in the beginning all the matters which now compose the exterior part of the globe were held in solution, or suspension in a fluid; and that of these, some were deposited in a crytallized state, as the granite, &c. whilst those that were not in a state of actual solution formed the different schists, and other earthy, saline, and metallic strata, regularly and concentrically disposed. Whilst thus existing in a soft and yielding state, the different substances, by acting on each other, he supposes to have passed into a state of fermentation, necessarily productive of a swelling or raising up, which taking place first of all in the granitic and saline pasty masses, these were elevated, carrying with them, or bursting through the other strata, thus forming the rocks and mountains now existing on the face of the earth. That respectable and excellent mineralogist, Mr. Kirwan, has zealously endeavoured to form a system which may accord with the Mosaic account of the creation. He supposes the superficial parts of the globe to have been in a fluid state, being held in solution by water considerably heated. From the coalescing and crystallization of the contents of this solution, the various metallic substances, the different earths, &c. were deposited in various combinations, sorming, according to the predominant proportion of the ingredients, granite, gneiss, phorphyry, and the other primeval rocks. By the crystallization of these immense masses,a prodigious quantity of heat was generated, even to incandescence, and the oxygen uniting with inflammable air occasioned a stupendous conflagration; by this the solid basis on which the chaotic fluid rested was rent to a great extent. From the extrication, by this heat, of the oxygen and nitrogen gases, the atmosphere was formed: and from the union of the oxygen with ignited carbon, carbonic acid proceeded, which, being absorbed by calcareous earth, was precipitated in combination with it, forming |. primitive lime stones. The level of the ancient ocean becoming then lowered to the depth of 9000 feet, fish were created; and the various stratified secondary mountains were formed within it during its retreat, and after the creation of fish. Soon after, the higher tracts of land being left uncovered by the retreat of the sea to its bed, the land became supplied with vegetables and animals. The deluge he considers as a miraculous effusion of water, both

from the clouds and from the great abyss which originated in, and proceeded from, the great southern ocean below the equator, and which, rushing into the northern hemisphere, descended southwards, and at length spread over the face of the whole earth. M. de la Metherie, who has investigated the subject with much attention, is of opinion, that all the mountains, vallies, and plains, composing the crust of the earth, were formed nearly in the state in which they now exist, by crystallization of the mass of water which surrounded the earth. The matters composing the highest mountains, he shows, have evidently been held in solution: the water, therefore, must have reached above their summits, and of course have stood 18,000 feet, at least, above its present level. But this being admitted, it becomes necessary to determine what has become of the immense quantity of water which has disappeared since that period. Of this he imagines that some part has ... by eva[..." and passed into other planets, ut that by far the greatest part is buried in the immense caverns which exist in the interior part of the globe. On reviewing the systems which have been just enumerated, it is obvious that some are so abundant in fanciful conjecture, and so deficient of probability, as not to require any further remark; whilst in others of a more specious appearance, there are some points which cannot be allowed to their ingenious authors. On these particular doubtful points, it is thought best to offer a few remarks, rather than separately examine each system. With respect to crystallization from an aqueous solution, a supposition which has not yet been generally adopted, it may be remarked, that the primitive mountains and vallies give exactly that irregularity of appearance, from lofty needle-like forms shooting up in some parts, and extensive plains existing in others, which are observable in cases of crystallization on the small scale. It has been objected, that the secondary mountains do not every where cover the primary on which they rest; this circumstance must, in all robability, have depended on particular ocal circumstances, and especially on such as would, as in ordinary cases of crystallization, direct the formation of crystals more numerously on one spot than on another. Particular currents may perhaps be considered among the causes which assisted in producing these effects, as well as in forming particular chains: whilst to the action of contrary currents may be attributed the formation of separate mountains. The formation of secondary mountains seem also to concur with what is generally observed in the ordinary progress of crystallization, where it is observed, that after one series of crystals are formed of the least soluble matters, others are then formed of those substances which the fluid was able to hold still longer in solution. It has been objected against the system of crystallization of rocks, &c. that nature seems to perform nothing of that kind at the present period; but were this the fact, the objection would not possess much force, since a most satisfactory answer might be jo. by asserting that the operation as ceased, in consequence of the task being accomplished; and, speaking with respect to the granitic and phorphyry rocks, all the materials being employed. The formation of stone by crystallization is, however, carrying on in various situations at the present moment; the incrustations formed in certain springs, and the various stalactitic formations which take place daily, are instances of this kind. The unfitness of water to hold the substances forming the primitive rocks in solution has been considered as a powerful objection; but it is to be considered, that the menstruum cannot be supposed to have been simple water, but, as Mr. Kirwan observes, this primitive fluid must have contained all the various simple saline substances, and indeed every simple substance, variously distributed,

“forming, upon the whole, a more com

plex menstruum than any that has since existed, and ...no, endued with properties very different from any with which we have been since acquainted.” Geological Essays, P. II. Considerable difficulty must, however, continue, in adapting any system which confines the production of the various geological phenomena, which present themselves to our observation, to too few and to too limited causes; since, however necessary it may be to refer the general phenomena to the operation of one particularly powerful agent, it still must be necessary to take into the reckoning the sinking and the raising of particular spots from subterraneous submarine fires; as well as the changes produced by the subversion of lofty mountains, rapid and violent currents of water, and various other powerful causes. By the preceding sketch of the numerous systems which have been advanced, and by these cursory remarks on some of

the objections which have been made against those which appear to posses; the greatest share of probability, the mind becomes better prepared to attend to the system of the celebrated Werner, to whom, in the opinion of his learned and zealous annotator, we owe almost every thing that is truly valuable in this important branch of knowledge. For the purpose of conveying some notion of this ingenious system, the following sketch is taken from the view of it, given in the “ Elements of Geognosy,” by Professor Jameson.

Agreeable to this system, the earth is supposed to have existed originally in a state of aqueous fluidity, which is inferred from its spheroidal form, and from the highest mountains being composed of rocks, possessing a structure exactly resembling that of those fossils, which have as it were, under the eye, been formed by water. From this circumstance it also

follows, that the ocean must have former

ly stood very high over these mountains; and as these appear to have been formed during the same period of time, it follows, that the ocean must have formerly covered the whole earth at the same timeContemplating the formations of the mountains themselves, Werner discovered the strongest proofs of the diminution of the original waters of the globe. He ascertained, 1st, that the outgoings (the upper extremities as they appear at the surface of the earth) of the newer strata are generally lower than the outgoings of the older, from granite downwards to the alluvial depositions, and this, not in particular spots, but around the whole globe. 2d. That the primitive part of the earth is entirely composed of chemical precipitations, and that mechanical depositions only appear in those of a later period, that is, in the transition class, and thence they continue increasing, through all the succeeding classes of rocks. This evidence of the vast diminution of the volume of water which stood so high over the whole earth is assumed to be perfectly satisfactory, although we can form no correct idea of what has become of it. By the earliest separations from the chaotic mass, which are discoverable in the crust of the globe, was formed a class of rocks, which are therefore termed primitive rocks, being chiefly composed of silex, alumina, and magnesia, constituting, by their various intermixtures, 1, granite; 2, gneiss; 3, mica-slate; 4, clayslate; 5, primitive lime-stone; 6, primitive-trap; 7, serpentine; 8, porphyry; 9, sienite; 10, topaz rock ; 11, quartz rock; 12, primitive flinty slate; 13, primitive gypsum ; 14, white stone. The circumstances which chiefly mark the high antiquity of these rocks are, that they form the fundamental rock of the other classes; and that the outgoings of their strata are generally higher than those of the other classes. Having been formed in the uninhabitable state of the globe, they contain no petrifactions; and, excepting the small portions which sometimes accompany those which will be next mentioned, they contain no mechanical deposits, but are throughout pure chemical productions. Small portions of carbonaceous matter occur only in the newer members of the class.

Before the summits of the mountains appeared above the level of the ocean, and before the creation of vegetables and animals, a rising of the waters is supposed to have taken place, during which that class of rocks which are said to be of the second porphyry and sienite formation was deposited. The rocks of this formation are of clay-porphyry, pearl-stone porphyry, obsidian porphyry, sienite, and pitch-stone. . They contain very little mechanical depositions, are of complete chemical formation, and contain little or no carbonaceous matter, and never any petrifactions.

On the appearance of land, or during the transition of the earth from its chaotic to its habitable state, rocks, which, from this circumstance, are denominated transition rocks, were formed. In these rocks the first slight, traces of petrifactions, and of mechanical depositions, are to be found. The species of rocks which come under this class are, the transition lime-stone, transition-trap, gray-wacke, and flinty slate. . The petrifactions are, corallites, encrimites, pentacrinites, entrochites, and trochites. The lime-stone of Derbyshire is said to be of this kind. As the former class of rocks were purely of chemical formation, so the contents of these are chiefly chemical productions, mingled with a small proportion of mechanical depositions. To explain the cause of this mixture we are referred to the period of their formation, that at which the summits of the primitive mountains just appeared above the waters, when, by the attrition excited by the motion of the waves, and which we are reminded extends to no great depth, particles of the original mountains were worn off and deposited.

As the height of the level of the ocean diminished, so would the surface on which

its waves acted increase, and of course

the quantity of the mechanical depositions. Hence these are much more abundant in the rocks of the next formation, which are denominated floetz rocks, on account of their being generally disposed in horizontal or flat strata. In these, petrifactions are very abundantly found, having been formed whilst vegetables and animals existed in great numbers. These. rocks are generally of very wide extent, and commonly placed at the feet of primitive mountains. They are seldom of very great height, from whence it may be inferred, that the water had considerably subsided at the time of their formation, and did not then cover the whole face of the earth. Countries composed of these rocks are not so rugged in their appearance, nor so marked by rapid inequalities, as those in which the primitive and transition rocks prevail. The formations of this class are supposed to be, 1, first or old red sand-stone; 2, first or oldest floetz lime-stone; 3, first or oldest floetz gypsum ; 4, second or variegated sand-stone ; 5, second floetz gypsum ; 6, second floetz or shell lime-stone; 7, third floetz sandstone; 8, rock-salt formation; 9, chalk formation ; 10, floetz-trap formation; 11, independent coal formation; 12, newest floetz-trap formation. Most of the rocks which have been just enumerated are covered by a great formation, which is named the newest floetztrap. This formation also covers many of the high primitive mountains: it has but little continuity, but is very widely distributed. It contains considerable quantities of mechanical deposits, such as clay, sand, and gravel. The remains both of vegetables and animals also occur very abundantly in these deposits. Heaps of trees and of parts of plants, and an abundance of shells and other marine productions, with the horns of stags, and great beds of bituminous fossils, point out the lateness of the period when this formation was deposited. In this formation several rocks occur, which are also met with in other floetz formations; but the following are supposed to be peculiar to this class, basalt, wacke, gray-stone, porphyry, slate, and trap tuff. These rocks are said to have been formed during the settling of the water consequent to a vast deluge, which is supposed to have taken place when the surface of the earth was covered with animals and vegetables, and when much dry land existed. From various appearances observed in these rocks it is concluded, that the waters in which they were formed had risen with great rapidity, and had afterwards settled into a state of considerable calmness. The collections and deposits derived from the materials of pre-existing masses, worn down by the powerful agency of air and water, and afterwards deposited on the land or on the sea coasts, are termed alluvial, and are, of course, of much later for ination than any of the preceding classes. These deposits may be divided into, 1. Those which are formed in mountainous countries, and are found in vallies, being composed of rolled masses, gravel, sand, and sometimes loam, fragments of ores, and different kinds of precious stones. 2 Those which occur in low and flat countries, being peat, sand, loam, bog iron oar, nagelflech, calc-tuff, and calcsinter: the three latter being better known by the names breccia, tufa, and stalactite. In this ingenious system, in which so much knowledge of the subject prevails, and in which the marks of long and patient investigation are evident, a very close accordance with geological facts is generally observable. Some few difficulties however occur, particularly it seems with respect to the new trap formation; since, although the appearances which this is intended to explain do not better agree with any other supposition, still the rising of the waters, whilst they yet covered the summits of primitive mountains, has much the appearance of a supposition made | for this particular purpose ; and as, at the same time, it appears to be warranted by no other phenomena, it seems to require some further consideration, before it is fully admitted. For more particular observations on the various characters, and on the different classes of rocks, see Rocks. GEOMETRA, in natural history, one of the families of the Phalaena genus of insects. See PHALENA. GEOMETRY, in its original sense, related simply to the measurement of the earth, and was invented by the Egyptians, whose lands being annually inundated, required to be frequently measured out to the respective owners, so that each might repossess his property. It seems probable, that in the operations attendant on that act of justice, many discoveries were made relating to the properties of figures, which gradually led on to an extension of the science, and to

the cultivation of the arts of navigation and astronomy, which, indeed, first flourished in that quarter. We are rather in the dark as to many improvements made in the infancy of geometry, and its attendant speculations; many tracts of supposed value having been entirely lost, though some faint traces and fragments of their subjects, if not of their convents, have from time to time been discovered. The Grecians appear to have been enthusiasts in their reception of the new science; accordingly we find that Thales, Pythagoras, Archimedes, Euclid, &c. exerted themselves to instruct their countrymen, and thus to prepare the way for the philosophy of Ptolemy, Copernicus, and others of the ancient school ; and of Des Cartes, Leibnitz, and the immortal Newton, in our more enlightened times. At present, geometry is justly considered to be the basis of many liberal sciences, and to be an indispensable part of the education of those who purpose exer. cising even the more mechanical arts to advantage.

We shall submit to our readers a general view of this most useful and fascinating attainment, and, by a gradual display of its rudiments, open the field to further advancement, which may be easily insur. ed, by consulting those authors who have become eminent for the display of whatever relates to the superior branches of geometry. In the first instance, we shall submit the following definitions, as laid down by Euclid in his Elements, recommending them to the serious attention of the student; they being absolutely necessary towards his competent appreciation and understanding of the succeeding propositions.

DEFINITIoxs.

1. A point hath neither parts normag. nitude; 2. A line has length, without breadth. 3. The ends, or bounds, of a line are points. 4. A right line lies evenly Petween two points. , 5. A superficies or plane has only length and breadth. 6. Planes are bounded by lines. 7. A plain superficies lies evenly and level between its lines. 8. A plain angle is formed by the meeting of two right lines. 9. When an angle measures 90 degrees, it is called a right angle. 10. When less than 90 degrees, it is said to be an acute angle. , 11. When more than 90 degrees, it is called an obtuse angle. 12. A term, or bound, implies the extreme of any

thing. 13. A figure is contained under one or more bounds. 14. A circle is a plain figure, contained in one line, called the circumference, every where equally distant from a certain point within it. 15. That equi-distant point within the circle is called its centre. 16. A line passing from one side to the other of a circle, and through its centre, is the eatest line it can contain, and is called its diameter. 17. The diameter divides the circle into two equal and similar parts, called semi-circles. 18. When a line shorter than the diameter is drawn from one point to another on the circumference of a circle, it is called a chord. 19. The part of the circle, so cut off or divided by such line or chord, is called an arc or segment. 20. Figures contained under right lines are called rightlined figures. 21. A figure having three sides is called a triangle. 22. If all the sides of a triangle are of the same length, it is called an equilateral triangle. 23. If all the sides and angles are unequal, it is called a scalene triangle. 24. If two of the sides are of equal length, it is called an isosceles, or equi-crural triangle. 25. If containing a right angle, it is called a right-angled triangle. 26. The long side subtending, and opposite to, the right angle, is called the hypothenuse. 27. When the two shortest sides of a triangle stand at a greater angle than 90 degrees, the figure is said to be “obtuse;” j when all the angles are acute, it is called an so triangle. 28. When two lines preserve an equal distance from each other in every part, they are said to be parallel. , 29. Parallel lines may be either straight or curved, but can never meet. 30. A figure having four equal sides, and all the angles equal, is a square. 31. But if its opposite angles only be equal respectively, the figure will then be a rhombus, or lozenge. 32. When all the sides of a figure are right lines, and that the opposite sides are parallel and equal, it is called a parallelogram. 33. If the opposite sides are equal, the others being unequal, the figure is called a rhomboides. 34. Foursided figures unequal in all respects, are called trapesia. 35. Figures having more than four sides are called polygons, and are thus distinguished: with five sides, it is called a pentagon; with six, an hexagon; with seven, an heptagon; with eight, an octagon ; with nine, an enneagon; with ten, a decagon; with eleven, an endecagon; with twelve, a dodecaVOL. V.

gon. 36. A solid has length, breadth, and thickness. 37. A pyramid is a solid standing on a base, of any number of sides, all of which converge from the base to the same point or summit. 38. When standing on a triangular base, it is called a triangular pyramid; on four, a square pyramid; on five, a pentagonal; and thus in conformity with the figure of its base. 39. Every side of a pyramid is a triangle. 40. A cone is found by the revolution of a triangle on its apex, or summit, and a point situated in the centre of its base; therefore a come (like a sugar-loaf) has a base, but no sides. 41. A prism is a figure contained under planes, whereof the two opposite are equal, similar, and parallel; and all the sides parallelograms. 42. A sphere is a solid figure, generated by the revolution of a circle on its diameter, which is then called the axis. 43. A cube is a solid formed of six equal and mutually parallel sides, all of which are squares. 44. A tetrahedron is a solid contained under four equal, equilateral triangles. 45. A dodecahedron is a solid contained under twelve equal, equilateral, and equiangular pentagons. 46. An icosahedron is a solid contained under twenty equal, equilateral triangles. 47. A parallelopipedon is a figure considered under six quadrilateral figures or planes, whereof those opposite are respectively parallel. 48. Figures, or bodies, are said to be equal, when their bulks are the same; and similar, when they are alike in form, though not equal. 49. Therefore simi. lar figures or bodies are to each other in proportion to their respective areas or bulks. 50. The line or space on which a figure stands is called its base; its altitude is determined by a line drawn parallel to its base, and touching its vertex, or highest part. 51. A rightlined figure is said to be inscribed within another, when all its projecting angles are touched thereby, 52 The figure sur. rounding or enveloping another is said to be described around, or on it. 53. When a line touches a circle, and proceeds without cutting it, such line is called a tangent. 54. Any portion less than a semicircle, taken out from a circle by two lines, or radii, proceeding from the centre, is called a sector. Certain Axioms are likewise proper to be carried in mind; viz. 1. That things equal to one and the same thing are equal to one another. , 2. If to equal things (or **) we add equal things, (or num, s

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