drawn through the points A and o, is the principal axis of the Foci of Spherical Concave Mirrors. In curved mirrors, the points where the reflected rays or their prolongations meet, are called foci. According to the distance from the luminous object, or the illuminated object, which transmits light to a spherical mirror, there are three kinds of foci; the principal focus, the conjugate focus, and the virtual focus. The Principal Focus.-This focus, which is formed by the incident rays parallel to the principal axis, is situated on that axis, at an equal distance from the centres of curvature and of the mirror. Thus, let a ray GD be parallel to the principal axis A L. According to the hypothesis that curved mirrors are composed of an infinity of plane elements infinitely small, the ray G D is reflected from the element at the point D, according to the laws of the reflection of plane mirrors; that is, CD being the normal at the point of incidence D, the angle of reflection CDF is equal to the angle of incidence G DC, and in the same principal section. Hence, it is plain that the point F, where the reflected ray meets the principal axis, very nearly divides the radius of curvature A c into two equal parts. For, in the triangle DFC, the sides CF DF are equal, being opposite to equal angles; because the angles DCF and FDC are both equal to the angle CDG, the former by Euclid, Book I. Prop. 29, and the latter by the laws of reflection. Also FD approximates to FA in magnitude, in proportion as the arc AD diminishes. We may therefore consider, when this arc is only a small number of degrees, that the straight lines A F and FC are sensibly equal, and that the point F is the middle point of A C. So long as the aperture мON of the mirror does not exceed 8 or 10 degrees, every other ray parallel to the axis Fig. 260. passes, approximately after reflection, through the point F This point, where all the parallel incident rays meet after reflection, is called the principal focus, and the distance FA the principal focal distance; and we have seen that it is equal to half the radius of curvature. As all the rays parallel to the axis sensibly meet in the same point F, it is important to observe that reciprocally, if a luminous body be placed at F, the rays emitted from this body take, after reflection, the directions D G, BR, etc., parallel to the principal axis; for it is evident that then the angles of reflection are changed into the angles of incidence, and the angles of incidence into those of reflection. Conjugate Focus.-Let the rays which issue from a luminous body L be now divergent instead of parallel, the body being situated at a point on the principal axis at a sufficient distance from the focus to produce the divergency of the rays, fig. 259. The incident ray LK makes with the normal cк an angle of Fig. 259. incidence LKC, smaller than the angle of incidence 8 K c, which the incident ray s K parallel to the axis makes with the same normal; consequently, the angle of reflection corresponding to the ray LK will be smaller than the angle of reflection corresponding to the ray s K. The ray L K will, after reflection, therefore, meet the axis in a point 7, situated between the centre of curvature c and the principal focus F. So long as the aperture of the mirror does not exceed a small number of degrees, all the rays emitted from the point L will, after reflection, sensibly meet in the same point. This point is called the conjugate focus, in order to indicate the connection which exists between the points L and 7, a connection such that these are reciprocals of each other; that is, if the luminous point be transferred to 1, its conjugate focus will be L, Kl becoming the incident ray, and KL the reflected ray. On examining the figure, it will be seen that when the luminous body L comes nearer to the centre c, its conjugate focus will be nearer the same point, and when it is removed farther from the centre c, its conjugate focus will be removed farther from the same point; for the angles of incidence and reflection increase and decrease together. If the luminous body L coincides with the centre c, the angle of incidence is nothing, and so is the angle of reflection; hence, the reflected ray returns upon itself, and the focus coincides with the luminous body. When this body passes beyond the centre c, that is, between this point and the principal focus, the conjugate focus in its turn passes to the other side of the centre, and recedes from it in proportion as the luminous body approaches the principal focus. Lastly, when the luminous body coincides with the principal focus, the reflected. rays being parallel to the axis, do not meet, and consequently there is no focus. The Virtual Focus.-When the luminous body is placed between the principal focus and the mirror, any ray LM, fig 260, emitted from the point L, then makes with the norma. Fig. 261. CM, an angle of incidence LMC greater than the angle FMC; the angle of reflection must therefore be greater than the angle CMS. Hence, it follows that the reflected ray ME is divergen in reference to the axis A K. The same thing taking place with all the rays emitted from the point L, these rays will not meet, and, consequently, will not form a conjugate focus; but if they be produced on the other side of the mirror, their prolongations will sensibly meet in the same point of the principal axis, so that the eye which receives them will have the impression as if they proceeded from the point 7. In this point, therefore, is produced a virtual focus exactly analogous to that presented by plane mirrors. It may be remarked that in the various cases brought under consideration, the position of the principal focus is constant, whilst those of the conjugate and virtual foci are variable. Lastly, the principal and the conjugate foci are always situated on the same side of the mirror as the luminous body, whilst the virtual focus is always situated on the other side of the mirror. Hitherto we have supposed the luminous point to be situated on the principal axis, and then the focus is formed on that axis; in the case where the luminous point is situated on a secondary axis LB, fig. 261, by applying to this axis the same reasoning as to the principal axis, we find that the focus of the point L will be situated in a point on the secondary axis, and that according to the distance of the point this focus will be a principal focus, a conjugate focus, or a virtual focus. Further, the secondary axis, as well as the principal axis, mirror is concave, we place it in the rays of the sun so that its principal axis shall be parallel to them; then with a small screen of ground glass, we seek for the place where the image presents the greatest intensity; this is the principal focus, and measuring its distance from the mirror and doubling that distance, we have the radius of the mirror. If the mirror be convex, we cover it with paper, but make in the paper two circular apertures at H and 1, at equal distances from the centre of figure A, and in the same meridian plane, fig. 263. Then placing before the mirror a screen, MN, having in its centre a circular aperture wider than the distance H1, and receiving on the mirror a pencil of solar rays, s H and s'i parallel to the axis, the light is reflected at н and I Fig. 262. always represent a luminous ray; but a ray which coincides with the normal and consequently with the reflected ray. Convex Mirrors.-In convex mirrors, the foci are only virtual. Thus, let the rays s I, TK, etc. fig. 262, parallel to the principal axis A B of a convex mirror, take after reflection the directions IM, K H, etc. These directions are divergent, and when produced will meet in a point r, which is the principal virtual focus of the mirror. By means of the triangle cK F, it may be proved, in the same manner as in concave mirrors, that the point F is sensibly in the middle of the radius of curvature CA. If the luminous rays, instead of being parallel to the axis, proceed from a point L, situated on the axis at a finite distance, we readily perceive that the focus is still virtual, but that it is formed at 1, between the principal focus and the mirror. The Principal Focus.-In the application of concave or convex mirrors, it is often necessary to know the radius of curvature. Now this radius depends on the place of the principal focus; for this focus being situated in the middle of the radius, it is sufficient to double the focal distance in order to obtain the radius of curvature. In order to find the focus when the on the parts where the mirror is uncovered, and forms on the screen two brilliant images at h and i. By drawing the screen MN backwards and forwards, we find a position where the interval hi is double that of H I. The distance A D of the screen from the mirror then represents the principal focal distance. For, the triangles FHI and rhi being similar, we have hi: HI: FD:: FA; but HI is the half of hi, therefore FA is the half of FD. Consequently AD is equal to FA; but FA is the principal focal distance, because the rays s H and s'I are parallel to the axis; the double of A D therefore represents the radius of curvature of the mirror. Formation of Images.-Hitherto we have supposed that the luminous body or the illuminated one, placed before a mirror, was merely a point; but if this body has a certain extent, we can imagine for each of its points a secondary axis, and thus determine a series of foci real or virtual, of which the assemblage will form a real or virtual image of the object. We can now determine the position and magnitude of those images in concave and convex mirrors by employing the constructions resorted to in finding the foci. Fig. 264. The Real Image.-Let us first take the case where the mirror D H I E K In reviewing our preceding observations, we see that concave mirrors give rise to two kinds of images, or to none at all, according to the distance of the object, which is proved by placing one's self before a concave mirror; at a certain distance we see its image inverted and smaller, which is its real image; nearer than this distance the image becomes confused, and it disappears at the focus; nearer still, the image becomes erect and greater, which is the virtual image. ON THE TRIAS, OR NEW RED SANDSTONE.! BELOW the lias beds is a series of rocks, the whole of which has been generally called the new red sandstone, but which has also been sometimes called, as by Conybeare and Buckland, the Poikilitic series. These beds were called poikilitic from TOLKIλos, poikilos, variegated, because some of the most remarkable seams in it exhibited spots and streaks of various colours, such as green, light blue, and buff in a base of red rock, and therefore called variegated by WERNER. The term new red sandstone was given to this series, partly on account of the colour of the loams, the shales, and the sandstones which, in the midland and the western counties of England, were found to interpose between the lias and the coal formation, and partly to distinguish it from the shales and sandstones which lie under the mountain limestone, and was called the old red sandstone, a rock of precisely the same lithological character, but long anterior in geological time. The term New Red Sandstone comprehended the whole series of beds that lie between the lias and the coral, and comshales and its quartzy conglomerates, and also the magnesian limestone and the various-coloured shales and freestones that lie below it. Geologists have lately discovered that the fossil contents of the upper and the lower new red sandstone are sufficiently distinct to divide them into two separate groups, the upper of which is now called the Trias, and the lower the Permian. The name Trias has been given to the upper new red sandstone by the German geologists; and as this group is better developed in the north-west of Germany than it is in England, the English geologists have adopted the name as appropriate. This division has been called the Trias, because that in Germany it consists of three distinct beds, called the Keuper (pronounced Koyper), the Muschelkalk, and the Bunter Sandstein. The following table represents the Trias in England and Germany: globules are larger, and are more like peas than the roe of a fish. In England similar impressions have been found in the trias of Cheshire, Lancashire, and Dumfriesshire. The footprints discovered at Storton Hill, near Liverpool, are the most celebrated as having the most distinct and the best defined outlines. These footsteps used to be ascribed to a reptile whi h geologists called the Cheirotherium, from xepog, cheiros, the Fig. 10. The relation of the Trizs to the Lias and the Old Red Sandstone. These three beds constitute strata of about 1000 feet in thickness, and their relation to the lias above and to the old red sandstone below is represented in the following illustration, fig. 10. A, the Lias. B, the Trias. c, the Permian. D, the Coal Beds. E, the Mountain Limestone. F, the Old Red Sandstone or Devonian. In Germany, the triassic beds follow, in the descending order, immediately after the lias; but in England the lowest beds of the lias rest upon strata of red or green marl or clay. Also in the Westbury cliffs, near the new passage of the Severn, and at Exmouth in Devonshire, there is under the lias a dark-coloured stratum called the "bone bed," which abounds in fossil remains of saurians and fish. The red and green marls which underlie this bone bed have no fossils-which is the case with nearly all the equivalent beds in different parts of England. There are some exceptions in Warwickshire and Worcestershire, where a few fossils have been found, accompanied by bivalves called posidonia minuta. In parts of Cheshire and Lancashire, the red shales and marls of the trias contain gypsum and salt. The shales and loams lie in beds of from 1,000 to 1,500 feet in depth, and the rock-salt lies in wedge-like masses between the clays. Two of these salt-beds at Northwich, in Cheshire, are from 90 to 100 feet in thickness, and the area of these saliferous clays and sandstones is supposed to be about 150 miles in diameter, while the total thickness of the triassic beds in the same district is more than 1,700 feet thick. II. THE ORGANIC REMAINS OF THE TRIAS. 1. The plants of the Keuper strata are, as to their genera, very analogous to those which we have already observed in the overlying formations of the lias and the oolite. They consist of ferns, cone-bearing trees, etc. The remains of rays and fish, and especially of reptiles of the lizard and crocodile tribes, have been found in this division of the trias. The most remarkable reptiles are the saurians called Nothosaurus and Phytosaurus, and a creature of the Batrachian or frog tribe, called from his tooth the Labyrinthodon. 2. The very name of Muschelkalk, or mussel limestone, implies that it abounds in fossil shells of that species. Among the bivalve shells, two species, called Avicula socialis and Posidonia minuta, abound, and range throughout the three divisions of the Trias, the Keuper, the Muschelkalk, and the Bunter Sandstein. There are, however, no Belemnites, and no Ammonites, except one genus of a shell like the ammonite, and called Ceratite. 3. The Bunter Sandstein, in the neighbourhood of Subzbod, near Strasburg, has afforded many plants, especially a conebearing tree called Voltzia, of which even the fruit has been found fossil. It is remarkable that out of thirty species of plants, ferns, and cone-bearing trees, not one is common to the Keuper. 4. In several parts of England, and at Hildburghausen in Saxony, the clays of the Keuper have exhibited the footprints of a reptile called the Labyrinthodon. The impressions are those of the fore and hind feet of an animal, and much resemble traces of the human hand, as you will see by the annexed engraving, fig. 11. hand, from the circumstance that the impressions of the fore and hind feet resembled a man's hand. The cheirotherium was at first supposed to be allied to the species of animals called Marsupialia, or the Kangaroo tribe, since the first toe of the fore foot of the kangaroo is, in this manner, set obliquely to the others, so as to form a kind of a thumb; and his hind and fore feet have just the disproportions exhibited in the woodcut. The character, however, of the animals that left their footprints could not be well ascertained until the teeth were discovered; and when these were found, naturalists decided at once that the animal was a gigantic batrachian, that is, a prodigious frog or toad. The surface of his teeth are very remarkable for having a series of irregular foldings and windings, something like the labyrinthian curved lines of animal brain, which occasioned the name Labyrinthodon, the labyrinthtooth, to be given to the animal. The varieties observed in the complicated structure of the teeth have enabled naturalists to distinguish and determine three species of this reptile. From the structure of the cavity of the nose of the labyrinthodon, it is inferred that the reptile was an air-breathing animal, like the saurians. When the animal came to breathe the air, he walked on the clear shore, and upon the sand when it was moist and yielding; for the impressions could not have been produced by an animal whose feet were under water. The footprints of the labyrinthodon are of two kinds, some of them indented in the upper surface of one bed of sandstone and others in relief, or sticking out from the lower surface of the bed that rested on that sandstone. Those which stick out are, in fact, only casts formed in the depressions of the real footprints as in a mould. The footprints are very disproportioned to each other-the larger impressions being those of the hind foot, which are generally eight inches in length and five inches broad. One, indeed, has been found twelve inches long, which shows that the animal must have been of prodigious size. About an inch and a half from each of the larger footprints, and always before it, is a smaller impression of a fore foot, and which is generally four inches long and three inches broad. The footsteps are always in pairs, and follow in the same line, at intervals of fourteen inches from pair to pair. Each step, the large as well as the small, makes the print of five toes, the first, or great toe, in each bending inwards like a thumb. 5. Professor HITCHCOCK, in his account of the Trias in the valley of the Connecticut river, in the United States, says that the footprints of no less than thirty-two species of twofooted creatures and twelve of quadrupeds have been discovered in those rocks. Out of those thirty-two bipeds, thirty are supposed to be the impressions of the feet of birds, four o saurians or lizards, two of chelonians or tortoises, and six of batrachians or frogs. These tracks are found distributed through an area of nearly 80 miles from north to south. They Fig. 11. Footprints of an Animal on the surface of the Sandstone. are also repeated in a succession of beds, which attain at some points more than 1,000 feet in thickness, showing that they must have been thousands of years in formation. III. SOME GEOLOGICAL PHENOMENA INDICATED BY THE 1. The beds of the trias formation abound with the heads and stems of the Lily Encrinites, like No. 15 in fig. 7, of Lesson LIV.-a fact which proves that these beds of limestone were formed in a slow manner at the bottom of a clear sea. 2. The "bone bed," found in the Westbury cliffs at the New Passage, on the Severn, used to be regarded as the lowest bed of the lias; but its fossil remains have lately demonstrated that it belongs to the upper beds of the trias, for it contains a species of fish peculiar to this division, or belonging to a species well known in the muschelkalk of Germany. 3. In examining the phenomena of the trias, the questions naturally arise, where did all this red mud and red sand come from? and why are they of a red colour? The disintegration of crystalline and slate rocks, by the influence of the weather and by the action of running water, will account for the matter of the trias rocks; for in Scotland, mountains of gneiss, mica slate, and clay slate, are overspread with diluvium derived from the disintegration of the neighbouring and underlying rocks. And this mass of detritus is coloured by the oxide of iron, of precisely the same tinge as the more ancient beds of the Old Red Sandstone. Suppose that this kind of alluvium were washed down to a sea or a large lake, a new stratum, of course, of red marl and sandstone would be formed that would be, literally, a "new red sandstone," whose colour would be quite undistinguishable from that of the "Old Red." The red colouring matter is, in both rocks, probably furnished by the decomposition of horneblende or mica, which contain the oxide of iron in large quantity. It is a remarkable fact, and not yet satisfactorily accounted for, that scarcely any fossil remains have been preserved in those stratified rocks in which the oxide of iron is very plentiful; for the fossils which have been discovered have been found in the grey beds, usually calcareous, and not in the strata that are of a red colour. 4. The footprints, to which we have already referred, are found at Storton Hill to have been impressed upon five thin❘ beds of clay, one lying above the other, and each separated from another by a bed of sandstone. The character of those impressions of the feet, the toes, and the claws of the animal, prove clearly that the reptile trod on that rock when its clay was moist and yielding. Both the footprints and the ripple marks found on the upper surface of these sandstone beds, are made at so many different levels that there can be no doubt that the whole area has undergone a slow and gradual subsidence during the formation of the triassic rocks. For since each seam of clay has the casts of the feet moulded in salient relief upon its lower surface, and the indented impressions were made upon the upper surface when the sand was above water and not under water, it is evident that each of these seams formed, in succession, a surface above water, and over which the Cheirotherium and Labyrinthodon walked when they came to breathe the open air. After the animal had walked over the sand, a time came when the whole shore subsided and was submerged under the sea, until eventually a new beach or shore was made at low water, on which other tracks would continue to be made. 5. One of the most remarkable and mysterious phenomena in the structure of the trias is the formation of ROCK SALT. Both the gypsum and the salt have been thought by many geologists to be the results of volcanic influences. It is well known that volcanic exhalations take place under the waters of the ocean as well as in the open air. These exhalations take place not at the craters of eruption, but at a considerable distance from such localities; and as they are generally charged with sulphur, sulphuric salts, and with muriate of soda, or common salt, they have been deemed sufficient to account for the origin of rock-salt. There are other naturalists who think that rock-salt originates in a precipitation of salt from salt water by evaporation, either in inland lakes or in lagoons communicating with the waters of the ocean. Sir CHARLES LYELL thinks that the circumstances of the Runn of Cutch will help us to understand the formation of rock-salt. The Runn of Cutch is a flat region, near the delta of the river Indus, and forming an area of about 7,000 square miles. This district is not land, nor is it sea; but during a part of every year it is perfectly dry, and again it is covered by salt water from the ocean: but at times, also, it is liable to be overflowed by the waters of the river. Its surface has no grass, but is crusted over, here and there, by pure salt about Here successive layers of pure an inch in depth. This crust of salt is evidently caused by the evaporation of sea water. salt might, if we grant time enough, be easily thrown down, one upon the other, for thousands of square miles; for the supply of brine from the ocean to cause the deposit, and the supply of heat from the sun to cause evaporation, are inexhaustible. To a length of geological time for such a formation of salt layers, we must also add the provision of a continuance of the subsidence of the district, so as to allow the waters of the ocean to deposit brine at higher and higher levels. If this sinking of the shore would be very rapid, so as to deepen the water much, then there would be no precipitation of salt, and probably the previous layer of salt would be covered with a thin layer of silt or sand from the river. If, again, instead of subsiding, the shore would be rising, the area would then dry up, and ripple marks of the waves and footprints of animals would be formed on surfaces underneath where salt had formerly been accumulated, LITERARY COMPOSITION. Ir is a singular truth that the most striking and universal facts in philosophy have been the latest in discovery; and that while the most learned philosophers have often been the slowest in recognising these facts, accident, as it is called, has often brought their existence under the notice of the most ordinary observer. The reason for this may be traced to the following causes: First, those who accustom themselves to difficult speculations in their research after truth, naturally conceive that the principles which have escaped their own observation are more than usually difficult; and they imagine, according to the old maxim, that truth lies at the bottom of a well, whereas, in most cases, it lies upon the very surface of their researches, and is covered only by a mass of learned rubbish. Secondly, men of genius are guided by a variety of considerations arising from their extensive knowledge, and are frequently directed in their investigations by rules of which they have long felt the truth, although they have never precisely defined them in words; and they are therefore slow to acknowledge such rules as the discoveries of others. Moreover, when the rules are for the first time, perhaps, clearly stated and properly illustrated, they feel a reluctance to confess that they constitute any discovery at all, seeing that they have been led by the same views in their own researches, although they never embodied them in a set of definite expressions. A curious instance of the truth of the preceding observations occurred at the beginning of the present century. The editor of a Journal of Science, which made high pretensions to learning, and which really possessed some title to this distinction, announced in the first number, which now lies before us, that he had discovered a universal rule for Literary Composition, applicable to all possible cases, and essential in the construction of every sentence either in written or in spoken language; and although he acknowledged that the truth of this rule must have been often felt by men of genius in their writings, yet he claimed the merit of generalizing the ideas which it involves, of clearly enunciating it as a rule, and of presenting it to the student, the writer, and the orator, as one universally applicable to all kinds of composition. He relates also that having submitted the rule to the consideration of Sir James Mackintosh, that eminent statesman and accomplished writer could scarcely be convinced that every good writer had not always acted in his composition according to its dictates. He then proceeds to state the rule, and to illus |