distant from the angular point than the point assigned within | the angle; in either of these cases the assumption made above will have been allowed" (p. 28). To which the answer seems to be, that to know by what necessity attendant on the constitution of the straight line, the several results here taken for granted will take place, is precisely the object which it was in question to attain. The apparent application of the proposed principle in the 20th Proposition of Euclid's Eleventh Book, is a mere error of Euclid's, and corrected by the Arabs, and subsequently by Legendre and probably others, through a very simple alteration in the construction. Euclid's straight lines will fail to meet, whenever his greatest angle exceeds half the angle cut off, by not less than a right angle, Thus if the angles composing the solid angle were 70°, 80°, and 130o, neither by cutting off one of the smaller angles nor the other, could Euclid's intended construction take place. 20. Professor Thomson. of Glasgow, proposes to take as an Axiom, that "if a triangle be moved along a plane, so that its base may always be on the same straight line, its vertex describes 2 straight line equal to that which is described by either extremity of the base."* In which there are two things demanded, where either would be enough. For if it could be established that the locus of the vertex is a straight line, every thing else might be demonstrated without premising that the lines described are equal; as has been done in kindred cases by Clavius and others. Or if it could be established that the distances between the first and last situations of the travelling points respectively are equal, this would suffice for the author's own demonstration, without asking whether the vertex had been always in the joining straight line. But how the equality of these distances is to be established, does not appear. One way of trying to proceed, would be to show, that if the line on which the base of the triangle travels (and of part of which the base is composed), instead of a straight line were a circular arc, the vertex would travel farther than the point in which the straight line from the vertex to the centre cuts the base, if on the convex side, and less far if on the concave; which is easily done, by proving that if not, the straight lines that ought to be the radii of the circle would not meet. And this would throw the responsibility on establishing, that the radius of a circle may be increased till a portion of the circumference approaches within any assignable difference to a straight line of given length; in other words, that there cannot be three points not in a straight line, through which a circle may not be described. Which involves Euclid's Axiom. 21. The demonstration presented by M. Legendre in the earlier editions of his "Eléments de Géométrie," consisted in first establishing that the three angles of a rectilinear triangle cannot be greater than two right angles (which may be passed over as irrefragable and liable to no remark), and afterwards proceeding to show cause why they should not be less. But the evidence offered on this latter point, depended on taking for granted that two straight lines (D E and B E in fig. 35 a in the Fourth Edition, and probably in the subsequent editions as far as the Eighth inclusive) meet when they make with a third straight line (D B) angles of which one (as ED B) is, or may be made to be, less than a right angle, and the other looks less than a right angle, but without further proof. 22. In the Seventh Edition another attempt was made to show that the lines must meet; but what is advanced as the proof involves the same fallacy as that of the Bolognese Professor.† 23. This was withdrawn in the Ninth Edition, and a new demonstration offered in the Twelfth. The new one depended upon taking in any triangle an angle that is not less than any other in the triangle, and a second that is not greater (See 12ème édition, p. 20, and Plate); bisecting the side opposite to the second angle, and drawing a straight line from the angular point to the point of bisection; cutting off in this straight line and its prolongation a part from the angular point equal to the side opposite to the first-mentioned angle (viz. that angle which is not less than any other in the triangle), and in this side and its prolongation towards the same hand a part equal to double the straight line between the angular point and the point of bisection formerly mentioned, and joining the extremities of the two parts thus cut off. It is not difficult to show, that in the new triangle thus last * «The first Six and the Eleventh and Twelfth Books of Euclid's Elements; with Notes and Illustrations. By James Thomsom, LL.D. Professor of Mathematics in the University, Glasgow, 1834. Notes, p. 358," + Elém. de Géom. Par A. M. Legendre, 7ème édit. p. 280. Note II. ‡ Not less and not greater are substituted for the greatest and least of the original. The demonstration is plainly intended to be applicable to any triangle; but the terms in the original would not apply to an equilateral triangle, nor to any kind of isosceles. | constructed, the sum of the three angles is the same as in the original triangle; and moreover that of the angles of these two triangles which are at a common point, that belonging to the new triangle is not greater than half that of the old, while another of the angles of the new triangle is equal to their difference. And if these operations be applied in like manner to the last constructed triangle, a third triangle will be constructed having the same relations to the second; and so on. Whence it follows, that the described process may be continued, till two of the angles of the last-resulting triangle are together less than any magnitude that shall have been assigned; and consequently the third or remaining angle may be made to approach, within any magnitude however small it may be chosen to assign, to the sum of the three angles of the original or any of the intervening triangles. All this is irrefragable; but not so the inference next taken for established, which is that the third angle last mentioned approaches within any magnitude however small it may be chosen to assign, to the sum of two right angles. That it approaches it (that is, that the angle continually grows larger) is certain; but that it approaches to it within any magnitude however small, is the point which, as in so many parallel instances, is taken for granted without sufficing proof. The weakness in the actual case, is in the fact that the base or side opposite to the continually increasing angle, becomes itself of unlimited length. If the resulting triangles had been all on the same base, the inference might perhaps have been conceded to be good. But it is precisely because by the extension of the base to an unlimited magnitude the progress of the operation is removed from human eyes, that the force of the inference is diluted and done away. Just as fast as the diminution of the two acute angles appears to induce a necessity for the obtuse angle's approximating to the sum of two right angles, does the increase of the length of the sides hold forth an augmented probability that the angle may after all evade increasing by the quantity required to make it attain to two right angles in the end. To argue that when the acute angles are nothing, or the lines coincide, the third angle will make a straight line, is substituting for,what really happens, what by the construction is not to happen. The demonstration is therefore finally of the same strength as Franceschini's and others that have been mentioned. There is evidence of a perpetual approach towards a given magnitude; but there is not evidence of the degree and rapidity of approach which are necessary to insure arriving at it. 24. Another demonstration, or step towards a demonstration, presented by the same author (See Note II. p. 279, 12ème édition), consists in representing, that if any angle less than two right angles is bisected, all perpendiculars to the bisecting straight line must meet the sides, because otherwise there would be a straight line shut up between the lines that make an angle, which is repugnant to the nature of the straight line." On which it is sufficient to observe, that the existence, cause, and origin of this repugnance, are precisely what it was demanded to demonstrate. 25. The next paragraph in the same page is directed to establishing the sort of postulate assumed in the last, viz. that a straight line cannot be shut up within an angle. The argument appears to be, that either of the straight lines which make an angle, being prolonged both ways, will divide the infinite plane in which it exists into equal parts, and any other straight line must do the same; but a straight line that should be shut up [renfermée] the sides in any direction however prolonged, would cut off more within the angle, without being able to escape from it by cutting on one side and less on the other; therefore a straight line caunot be shut up within an angle. Whoever examines this closely, will see that it would equally prove that two straight lines cannot be parallel to one another; for in that case it might equally he urged, that if the one divides the infinite plane into two equal parts, the other must cut off more on one side and less on the other. The whole is consequently a mal-reasoning, arising from overlooking Plato's observation (See Note to Prop. IV. of Book I), that quality of magnitude can only be predicated of things finite. 26. The nex. in order is the so-called analytical proof, which professes to demonstrate that if two angles in one rectilinear triangle are respectively equal to two in another, the remaining angles are necessarily equal. If two angles of a triangle and the that individual triangle are determined; that is to say, they can side between them are given, the rest of the sides and angles of severally be oni" of one certain magnitude and no other. Hence, said the advaucers of this demonstration, the angle opposite to the given side is a function of the two angles and the given side; their meaning by this term being, that a quantity is a function of other quantities, when on those other quantities being fixed and determined in magnitude, the first quantity is necessarily fixed and determined in magnitude,* or is what Euclid in his Book of Data would call given. "Let the right angle be represented by unity or 1, and then the angles will all be numbers somewhere between 0 and 2; and since the third angle is a function of the two other angles and the side between them, it will follow that the side cannot enter as an element into the determination of the magnitude of the angle." And this, they said, because the side is heterogeneous with the other quantities which are numbers, and no equality can be compounded or made to exist between them.† LESSONS IN GEOLOGY.-No. L. BY THOS. W. JENKYN, D.D., F.R.G.S., F.G.S., &c. CHAPTER V. ON THE CLASSIFICATION OF ROCKS. SECTION IV. ON THE TERTIARIES. THE term "Tertiaries," as applied to certain beds, has a reference to the three grand divisions into which the fossiliferous rocks have been distributed by geologists. If you will consult the tabular view given in the commencement of this chapter, you will find that, taken in an upward direction, all the rocks from the Silurian to the Permian are called PRIMARY; that all the rocks from the Trias to the Chalk are called SECONDARY; and that all the beds between the Chalk and the Recent, or what I have called Post Pleistocene are called TERTIARY. The tertiary rocks are generally divided into three, or rather four distinct groups, called, as viewed downward, the Pleistocene, the These terms were Pleiocene, the Meiocene, and the Eocene. introduced and invented by Sir CHARLES LYELL. The reasons of this distribution are founded on the proportion which the fossil shells of each group bear to the species now living. All the recent rocks, called in our last lesson Post Pleistocene, might have been called Anthropozoic, that is, human-life rocks, but for the fact that their lower division contains fossils of all the existing species of shells, without any remains or traces of the human race. Sir Charles Lyell takes the fossils of this division of recent rocks as his standard in grouping the other beds downward to the chalk. All the different beds downward to the chalk, contain different proportions of the shells called present, modern, or recent. The Greek word for recent or new is kaivos, kainos, and the feminine kain kainee. It has been the arbitrary custom of English scholars to write the Greek at as a diphthong, thus æ, and Hence the uncouth word cane, now generally written cene and pronounced seen. Hence, the above names are pronounced as if written Ply'-sto-seen, Ply'-o-seen, My'-o-seen, the x as c. E-o-scen. καινη The beds which contain the greatest abundance of living or recent shells., i.e. from 90 to 95 per cent., are called Pleistocene, from πλeloros, pleistos, most. The beds which contained some smaller proportion than this, but more than the inferior beds, are called Pléiocene, from Tλstwv, pleiôn, more. The next underlying beds, as they contain only from 35 to 50 per cent., are called Méiocene, from μetov, meion, fewer or less. The lowest of these "toute quantité formée d'une manière quelconque d'une autre quantité."-Lagrange, Théorie des Fonctions Analytiques. "Il faut donc que l'angle a soit entièrement déterminé, lorsqu'on connait les angles A et B, avec le côté p; car, si plusieurs angles c pouvaient correspondre aux trois données A, B, p, il y aurait autant de triangles différents qui auraient un côté égal adjacent à deux angles égaux, ce qui est impossible: donc l'angle c doit être une fonction déterminée des trois quantités A, B, p; ce que j'exprime ainsi, 0=& : (A, B, p).” beds in which are only about 33 per cent. of species identical with the present, are called Eocene, from nws, eeos, dawn, as if in this group we find the first indication or dawn of the existing species. since no recent or present species have been discovered in any of the secondary or the primary formations. As the geological designations of these rocks are founded on their respective proportions of fossils identical with the recent fauna, you will perhaps find that the following summary explanation of them will answer every purpose in your efforts to learn the science. 1. The Pleistocene 2. The Pléiocene 3. The Méiocene 4. The E'ocene { { most recent, or containing most of recent shells. very recent, or having a large number of recent shells. middling recent, or having a small proportion of recent shells. somewhat recent, having some few indications of the present race of shells. These groups are ascertained partly by their lithological character, and partly by their paleontology, or their fossil contents. ? 1. THE LITHOLOGICAL CHARACTER OF THE TERTIARIES. The lithological character of a bed means the kind of material, sandy, clayey, flinty, or limy ingredients of which the rock is composed. The upper group of the Tertiaries are called Pleistocene, and are thus divided into minor formations. I. THE PLEISTOCENE. 1. The Boulder Formation, or Drift. 3. Cavern Deposits and Osseous Breccia. I. THE BOULDER FORMATION, OR DRIFT. The drift, or boulder formation, Las been described in a preceding lesson as being found associated with freshwater strata and marine beds, and as having been formed about the close of the pleistocene period. The mineral ingredients of this formation exhibit every where a confused mixture of the ruins of adjacent lands, and an immense number of stones, some angular and rugged, others rounded and smoothed, and brought to their present position from very remote districts, by the agency of icebergs. In the Eastern counties of England, this formation supplies specimens of almost every known rock. It extends from Scotland as far south as to Muswell Hill, near London, and no trace of it is found farther south. The best place to study it in England, is in the cliffs of the Norfolk coast, where it presents a section from 50 to 70 feet high, and about 20 miles in length. In that section it consists of clay, loam, and sand, partly stratified and partly unstratified. It contains pebbles and boulders; of porphyry, greenstone, lias and chalk. These are found everywhere interspersed, but especially in the Till. Your attention has already been directed to the vast extent of this formation in North America, and in the northern parts of Russia and Germany, and also to the Alps as another centre from which these erratic blocks have been carried by icebergs. You find the same to be the case in your own country, as instanced in the mountains of Galloway, Cumberland and North Wales. Though the drift is, comparatively, a most recent formation, you are not to expect to find it always resting on some other tertiary strata. In many places, and especially in Scotland, it is found to rest immediately on some of the older rocks, and is covered by stratified beds of sand and clay which are usually Such a position is represented by the without any fossils. diagram, fig. 1, page 263, where a represents the ancient rock, and 11. THE NORWICH CRAG. "Soit l'angle droit égal à l'unité, alors les angles A, B, C, seront des nom- On each side of the river Yare, within five miles of the city of Norwich, are seen beds of sand, loam and gravel, which are called by the country people CRAG, or gravel. These beds abound with the shells of animals, marine, freshwater, and land. The strata have every appearance of having accumulated at the bottom of the sea near the mouth of a large river. This formation is found in patches of different thickness, and covered with a dense mass of stratified flinty gravel, and resting on the chalk. In the sea cliffe, near Thorpe and Southwold, Suffolk, this sea and river formation is exposed in good and clear sections, where it consists of sand, shingle, loam, and laminated clay. Some of the strata appear to have been deposited in tranquil waters. bones there. The preservation of such bones is due to the slow but constant supply of stalactite matter brought into the caverns by water infiltrating from the roof. Cavern breccias are found in every part of the world, but at San Ciro, in Sicily, there is one of great interest. It is about 20 feet high, 10 wide, and 180 above the sea. Within it there is an ancient sea-beach formed of pebbles of different rocks brought thither from very distant places. Broken corals and shells mingle with the pebbles. Under a mass of breccia were found an immense quantity of bones of the mammoth, &c., in a dark brown calcareous marl, and many of the bones were worn as if rounded by the action of the waves. This bed of breccia is about 20 feet thick, and under it is a bed of sand filled with sea shells of recent species. III. CAVERN DEPOSITS AND OSSEOUS OR BONY When rounded pebbles and gravel are cemented together into a hard stone, the mass is called a conglomerate, and sometimes, plum-pudding stone; but when such a cemented mass is composed of angular and unworn fragments of rock and other materials, it is called, from the Italian, Breccia. In mountainous districts, many fissures are found, into which animals seem to have fallen from time to time, or into which they have been washed by floods. These animal remains are frequently found covered with alluvial matter and with fragments of rocks which have been detached by frost. The whole mass is then formed, by stalactite infiltration, into what is called a bony or osseous breccia. Limestone hills often abound with a series of caverns with low and narrow passages from one suite to another, which hold a tortuous course through the interior of the mountain. These caverns and passages seem to have served, at some early period, the subterranean channels of springs and rivers. In the ter 3 tiary period, these channels had become and remained open for the homes and shelters of animals which perished and left their IV. SICILIAN LIMESTONE. In Sicily the Pleistocene tertiaries enter largely into the structure of rocks, covering nearly one half of the island, and in the centre forming hills which rise 2,000 feet above the level of the The structure and arrangement of these beds are best developed at Girgenti, Syracuse, and Castrogiovanni. sea. The Sicilian beds consist of two divisions. The upper division is calcareous or limy, and consists of a yellowish white stone in some places, and in others of a rock nearly as compact as marble. The beds are usually regular and horizontal, and their thickness are from 700 to 800 feet. The lower division is clayey, or argillaceous, and pass downwards into a sandstone, and conglomerates: below which there are again clay and blue marls, abounding in perfect shells and corals. In the south plains of Catania these pleistocene beds are intermixed with volcanic matter, which must have been thrown up while the rock was forming at the bottom of the sea, and while the clay, sand, and yellow limestone were in the course of being deposited. All these Sicilian rocks belong probably to the same period as the Norwich crag. II. THE PLEIOCENE. 1. The Suffolk Crag. 2. The Subapennine Beds. I. THE SUFFOLK CRAG. The Pleiocene rocks are confined chiefly to the eastern parts of the county of Suffolk, where these beds like those of a later class in Norfolk, are called crag. This rock is a mass of shelly sand, which is much used in agriculture. The shells imbedded in it, indicate that the bed was formed in a sea of moderate depth, in most places from 15 to 25 fathoms, but in some parts deeper, and at the distance of about 40 or 50 miles from any land. The natural group of the Suffolk Crag series is divided by Mr. Charlesworth into three subdivisions, which, in the downward order, are thus designated. 1. THE MAMMALIFEROUS CRAG; which is a sandy loam and clay formed by sea and river water, and charged with shelly detritus. It occurs about Southwold in Suffolk, and Cromer in Norfolk. It contains the teeth and bones of several extinct mammalia, or animals that suckle their young. 2. THE RED CRAG; which is so called from its deep ferruginous or irony colour. It consists principally of quartzose sand and comminuted shells and corals, and is about 40 feet thick. 3. THE CÓRALLINE CRAG; which is a series of calcareous and marly strata of loose white sands, layers of shells and corals, and concretionary bands of stone. It is of very limited extent, about 20 miles in length, and three or four in breadth, covering a district in Suffolk between the rivers Alde and Stour. At Sudbourn, near Orford, in this county, there is a large quarry in this formation furnishing a soft building stone. In some places, the softer mass is divided into thin flags of hard limestone, presenting fossil corals in the upright position which they assumed in their growth. Where the red and the coralline crags are met together in the same district, the red always lies uppermost, and both lie on the London clay. In some sections, the coralline bed seems to have suffered denudation before the red crag had been deposited on it. The red crng is distinguished by its deep ochreous or yellow tho moralline by its white-coloured sands. II. THE SUBAPENNINE BEDS. The A'pennines, composed chiefly of secondary limestone, are a chain of hills which commence at the base of the Ligurian Alps and extend through the whole length of Italy. At the foot of these mountains and on each side of them, is found a series of tertiary strata which forms a line of low hills between the central ridge of mountains and the Adriátic on the east side, and the Mediterranean on the west. The strata of these low subapennine hills consist generally of light-brown or blue marl, covered by a yellow calcareous sand and gravel, imbedding fossil shells. The marl is very aluminous, containing much calcareous matter and scales of mica. Near Parma it attains a height of about 2,000 feet, abounding in marine shells. Near Sienna, the yellow sand conglomerate rests immediately on the Apennine limestone, and at St. Vignone (pronounced Vinion) it passes into a calcareous sandstone. As this yellow sand formation is superimposed upon the marl, it represents the deltas of rivers and torrents which gained upon the bed of the sea where the blue marl had been previously deposited. Geologists now acknowledge that all the subapennine tertiaries do not belong to the same period. The beds indicate three distinct geological eras. 1. The beds of Piedmont, e.g. at Superga, are Meiocene. 2. The beds of North Italy, Tuscany, and the Seven Hills of Rome, are Pleiocene. 3. The Tufaceous formations about Naples, Ischia, &c., are Pleistocene, and Post Pleistocene. III. THE MEIOCENE. 1. The Faluns of Touraine. 2. Part of Bourdeaux. 3. Part of the Molasse of Switzerland. I. THE FALUNS OF TOURAINE. III. THE LOWER EOCENE. 1. Lower sands with marine shelly beds. I. THE UPPER EOCENE is represented in the upper marine 1. The freshwater marls and limestones of Paris seem to have been formed in marshes and shallow lakes. Some of the siliceous rocks of this formation are used for millstones. 2. The upper marine sands consist of marls, micaceous and quartzose sand, with beds of sandstone abounding in marine shells. The Upper Eocene is not found in England. II. THE MIDDLE EOCENE is represented by the Paris gypsum, the beds of Headon Hill in the Isle of Wight, the Barton beds, and the Bagshot and Bracklesham sands. Near Paris we find, below the upper marine sands, a series of white and green marls, with bedst gypsum lying under them, which are best developed at Montmartre, where its fossils were first discovered by CUVIER The gypsum is quarried for the manufacture of the plaster of Paris. In England, the Middle Eocene is developed in various instances. In French Brittany, near Dinan and Rennes, and also in the provinces bordering on the river Loire, there is a tertiary formation called by the peasantry Faluns (faloons). It consists of shelly sand and marl, and is used for agricultural purposes. Some of the shells and corals are entire, some are rolled, and others are intain a few marine and estuary shella. comminuted fragments. In some places, as at Doué, near Saumur, these sands and marls form a soft building stone, which is composed of broken shells united by a calcareous cement, and which looks much like a mass of the coralline crag in Suffolk. clay, sand, and a friable limestone containing freshwater shells. 1. In Headon Hill, in the Isle of Wight, we find beds of marl, These beds are seen in the sea cliffs, where some of the strata con This formation exists in scattered patches of slight thickness, and very rarely exceeding 50 feet in depth. They are frequently found to rest on a great variety of older rocks, such as gneiss and clay slate. In other districts, as between the Seine and the Loire, they repose upon the upper freshwater limestone of the Parisian tertiaries. At some points south of Tours, the shells are stained a ferruginous colour, like those of the red crag in Suffolk. The fossil shells indicate that these Faluns were formed partly on the shore itself at the level of low water, and partly at very moderate depths, not exceeding ten fathoms below that level. II. PART OF THE BOURDEAUX BEDS. Immense deposits of tertiary rocks are found in the country which lies between the Pyrenees and the Gironde river. Seven hundred species of shells have been found in these beds, and they all indicate that this division of the Meiocene strata is older than the Faluns of Touraine. III. THE MOLASSE OF SWITZERLAND. In Savoy we find, at the northern base of the great chain of the Alps, and throughout the lower country of Switzerland, a soft green sandstone, which is probably one of the oldest Meiocene groups hitherto discovered. It is associated with marls and conglomerates and is called "molasse," derived from "mol," soft, as the stone is easily cut in the quarry. It is of very great thickness, and might perhaps be divided into several formations. No rocks of the Meiocene period are found in England. IV. THE EOCENE. The Eocene group of rocks is divided by Sir Charles Lyell into three subdivisions, which he calls the Upper, the Middle, and the Lower Eocene. 2. In the cliffs of Barton, the pure white sand without fossile, on which the freshwater series of Headon Hill rested, is found to repose on a marine deposit, in which 209 species of shells have been found. This is the newest purely marine bed of the Eocene series known in England. about Bagshot and in the New Forest. They may be divided into 3. The Bagshot sands consist chiefly of silice s sand found three beds, the upper and lower being of light yelle w sands, and the middle of dark green sands and brown clays, al' reposing on the London clay. 4. At Bracklesham near Chichester, there is a bay, bounded by teeth. a low cliff of blue clay and green sand, full of fossil shells and The lower Bagshot sands have supplied the boulders of sandstones which are frequently found in some of the chalk valleys, and which are called Sarsden stones, and Druid sandstone, as may be seen at Stonehenge in Wiltshire, and Kitt Kotty near Maidstone in Kent. Sablés (sab-lé) of the Paris basin, the mottled and plastic clays III. THE LOWER EOCENE consists of the London clay, the of Hampshire and London, and the nummulites of the Alps. In the Paris basin, just below the Calcaire grossier, are extensive deposits of sand, having in the upper portion some marine beds called "lits coquilliers," in which 200 species of shells have been found. At the very base of the tertiary system in France, are beds of sands and plaetic clay abounding with fossil oysters. In the lower clays and sands layers of lignite are found. 1. The London Clay consists of a tenacious brown and bluishgray clay, with layers of concretions called Septaria, which are employed in manufacturing Roman cement. The best places to study this bed are Highgate near London, the Isle of Sheppey in Kent, and Bognor in Sussex. 2. Mottled or Plastic Clays are accumulations of sand, pebbles, and mottled clays. They are well developed in some of the railway cuttings about Reading, in Berkshire; in different parts of Hampshire; and especially about Blackheath and Woolwich. In many places it appears to be a mixture accumulated by the combined action of river and ses-water. At Poole, in Dorsetshire, this clay is used for pottery, and hence the term "plastic clay." 3. The Nummulite of the Alps and Pyrenees. This is a cal- NOTES AND REFERENCES-a. Faire entendre raison au petit careous rock, consisting often of a compact crystalline limestone, B., induce little B. to listen to reason; L. S. 96, R. 4.-6. il full of nummulites or shells of the class Foraminifera, or ex- s'engagea une disputc, an altercation commenced; the verb is unitremely diminutive forms of shelly animals. As these fossils are personal.-c. from se mettre ; L. S. 68, R. 3, also part ii., p. 96. very much like pieces of coin, and as nummus is the Latin ford. remit, delivered; from remettre; L. part ii., p. 102.-e. L. coin, and nummulus, is little coin, this rock is called Nummulite. S. 43, R. 6.-f. fit coudre, had it sewed; L. S. 31, R. 3.—g. In the Alps this rock is of great thickness. In many parts of causa, talked, spoke.—h from falloir; L. part ii., p. 92.-i. on Europe, Asia, and Africa, this group forms a very large part of se remit en marche, the march was resumed; L. S. 34, R. 1, 2.the Tertiary formations. It is found in Algeria and Morocco; inj. the verb is unipersonal.-k. from atteindre; L. part ii., p. 78. the Carpathian Mountains; in the districts between Egypt and. qu'il, let it.-m. from suffire; L. part ii., p. 106. Asia Minor; and between Persia and India. sac.s 2 FRENCH READING S.-No. III. b k i 4 3 -n. s'il restait, if there remained; the verb is unipersonal; L. S. 84, R. 4.-0. L. S. 77, R. 2.-p. L. S. 25, R. 2.-4. faire sauter, blow up.-r. from produire; L. part ii., p. 100.—s. la retenait, supported it. ANSWERS TO CORRESPONDENTS. n Le pauvre marchand voulut faire entendre raison1 au petit Bilboquet, mais il était entêté comme un cheval aveugle, et il s'engagea une dispute qui attira bientôt quelques soldats. Ils entrèrent pour s'informer du motif de la querelle, et ils trouvèrent l'idée du tambour si drôle, qu'ils obligèrent le pauvre Juif à lui céder sa barbe, et l'un d'eux, Gascon et perruquier du régiment, tira des rasoirs de sa poche, se mit à raser le malheureux marchands et a remit solennellement la toute à Bilboquet qui l'emporta en triomphe. En arrivant au régiment, il la fit coudre par le tailleur sur un morceau de peau d'un tambour crevé, et sans rien dire de son dessein, il la mit au fond de son On en causas pendant quelques jours, mais il fallut bientôt penser à autre chose. On se remit en marche, et on ne pensait plus au petit Bilboquet, quand on arriva à Moscou. Alors il arriva d'affreux malheurs, le froid et la dévas-that the subject will be duly considered. tation privèrent l'armée française de toutes ses ressources,1 la famine l'atteignit, et bientôt il fallut se retirer à travers un pays désert et des neiges sans fin. Je ne veux pas vous faire un tableau de cet horrible désastre; c'est une chose trop vaste et trop épouvantable 12 à la fois, pour que je vous en parle dans cette histoire: qu'il vous suffise de savoir que chacun s'en retournait comme il pouvait,13 et que c'est à peine s'il restait quelques régiments réunis en corps d'armée et obéissant aux généraux. Celui de Bilboquet était de ce nombrc. Il était de l'arrière-garde,11 qui empêchait des milliers de Cosaques, qui suivaient la retraite de l'armée,15 de massacrer les malheureux soldats isolés. Un jour, ils venaient de P franchir une petite rivière, et, pour retarder la poursuite des ennemis, on avait essayé de faire sauter deux arches d'un pont de bois qu'on venait de traverser ; 16 mais les tonneaux de poudre avaient été posés si precipitamment,1 que l'explosion ne produisit que peu d'effet les arches furent cependant démantibulées, mais toute la charpente appuyait encore sur une grosse poutre qui las retenait,18 et qui, si les ennemis fussent arrivés, bientôt permis de reconstruire le pont.19 GEORGE ISAAC E. (Nottingham): The Italian language has no nasal sounds, and each vowel keeps its alphabetical sound irrespective of any consonant that may follow; e. g. in the words tempo, time; sento, I feel; mento, chin, the consonants m and have no influence whatever on the tion of each vowel preceding them. The combination gn, pronounced as in French, is the only exception, and approaches a nasal sound. This constitutes an important difference between the two languages, French being to great extent a nasal language, and Italian a language spoken from the chest. A great many examples in the first ten lessons, exclusively devoted. have clearly illustrated this. The best Italian translation of the Bible, for to the explanation of the principles and mechanism of Italian pronunciation, Protestant readers, is by Giovanni Diodati. The "Society for Promoting Christian Knowledge," 67, Lincoln's-inn-fields, and the " British and Foreign Bible Society," Earl-street, New Bridge-street, Blackfriars, have both published this translation. The price varies from 3s. 8d., 4s. 8d., &c., according to the binding, and it may be had at the above-stated premises in Lincoln's-innFields, or at Bagster's, Paternoster-row. With regard to the Italian Dictionary, we must refer you to former remarks, and only beg to repeat pronunciation of the vowel e, such as they have in French on the pronuncià ANNA PRINGLE (Ferry Hill): She must try and beat the boys in the Four Ball question; neither they nor she have mastered it yet. She is very right about fractional questions and solutions; we are proud of her correspondence.-E. PHILLIPS (Machen): We are sorry that we can't give our correspondent the information he requires. COLLOQUIAL EXERCISE. 1 T. G. L: The result will be most conveniently illustrated by regarding the solution as hydrochlorate of protoxide of tin: to which solution nitric protoxide of tin, and converts it into peroxide. One portion of this peroxide acid being added, the latter becomes decomposed,-yields oxygen to the is precipitated, leaving an excess of hydrochloric acid to combine with the rest. Thus the hydrochlorate of peroxide of tin results. A. C. HILLARY: Probably the inetal was not in the state of fine powder, or the acid employed was not sufficiently strong. E. WILLIAMS: The result of such distillation would not be simply one chemical product, but many very complex products, whose investigation would belong to the higher departments of organic chemistry. D. B. C. (Hartlepool): We do not answer some questions for fear of giving offence to some readers, especially when they refer to religious worship. -J. D. (Newcastle): High Dutch is German.-G. W. R. (Walnut-tree walk): The ch in archbishop is pronounced like ch in church.-MATHETES The Greek upsilon is generally replaced by y in English; as in cuv, with; astronomical day begins at the noon of one day, and terminates at the noon and in σkuens, scythes, a Scythian.-H. WATKINS (Wolverhampton): The of the next day. The civil day varies in different nations; with ourselves it begins at midnight of one day, and terminates at midnight of the next day. -G. H. H. (Haslingden): See our answer to R. S. S. (Glasgow).—A POOR STUDENT will get solutions of his questions in any treatise on Trigonometry. eût-DON QUIJOTE (Grahamston): We don't know any Spanish Dictionary about 8s. or 10s. that we can recommend.-B. H. (Bristol): See page 79, vol. iii. P. E., where the rule is that things without life are neuter. Now heart and hand apart from the body are without life, and therefore strictly neuter. But by poetic gender, as it is called, sex may be attributed to these nouns in that case, we should call the heart feminine, and the hand masculine, that is, if we were writing poetry.-HOPEFUL: Very well, go on.SOCIUS (Liverpool) should have had an answer if his address had been 1. Le marchand chercha-t-il à | 11. Que fut-elle bientôt obligée 2. Pourquoi ne put-il lui faire entendre raison ? 3. Comment les soldats trouvèrent-ils l'idée du tambour? 4. Que firent-ils ? 5. Que fit le perruquier du régiment ? 6. Le tambour parut-il content de sa prise? 7. Que fit-il de cette barbe en 8. Où la plaça-t-il ensuite ? 10. Qu'arriva-t-il à l'armée fran- 12. Pourquoi l'auteur ne veut-il 13. Que suffit-il de savoir ? 15. Que faisaient les Cosaques? 18. Pourquoi la charpente du given. YOUNG WHITEBREAD wishes to know the proportion in which liquor potassæ must be added to sugar of lead in order to produce the potash solution of oxide of lead so useful as a test for sulphur, A slight amount of consideration will prove to our correspondent that the proportion will altogether depend on the strength of the liquor potasse and of the lead solution. The best plan of procedure consists in disregarding solution until the desired result is accomplished. Thus, having taken some weighed or measured proportions, and adding liquor potassæ to the lead solution of acetate of lead (sugar of lead), or still better,solution of trisacetate of lead (Goulard's extract), add to it by small quantities at a time liquor more until nearly, but not quite, all this precipitate is redissolved. By thus potasse until all the oxide of lead is precipitated. Then continue to add leaving a little oxide of lead, the operator is assured that liquor potassæ has not been added in excess. G. H. BALDING (Hastings) wishes to know how to make crucibles for chemical experiments. He is not sufficiently precise. What sort or crucibles? and what kind of experiments? The crucible adapted for one use is totally unfitted for others. The chemist employs crucibles of clayware, German porcelain, blacklead-ware, iron, silver, platinum, and, occasionally, gold; but he does not prepare those crucibles himself; they ars the manufacture of various trades. |