out sand. If the seams of coal had been formed by drifted wood, the current or flood that drifted the wood would have drifted also some gravel or sand. But of this there is not a vestige in mineral coal. 5. TREES STANDING ERECT IN THE COAL MEASURES.-The instances are very numerous, in which the workings of the coal measures expose the stems, trunks and roots of trees, which seem to have grown on the identical banks of sand or mud where we now discover them, and whose decomposed leaves and associated plants formed the coal. Imagine that you had a garden of about a quarter of an acre of ground. You remove the soil, several feet deep,-say for brick-making. As the earth is wheeled away, you find treetrunk after tree-trunk exposed to view, standing some feet high, and with their roots fixed. Would you doubt that those trees grew there? would you infer that some flood placed them there all in an upright position? The evidence would be demonstrative that the trees grew on the spot. Precisely such a quarter of an acre is found at Parkfield, near Wolverhamp ton. The workmen cleared away all the rock that covered the coal, and then they found throughout that area seventy-two upright trees with their roots attached to the bottom soil. Some of these trees were more than eight feet in circumference. Some of the trunks were lying prostrate in different directions, for they had been broken off close to the root by some powerful agent. This was undoubtedly the remains of a submerged forest. But below this bed, there was another forest of the same character, and five feet below that there was a third forest with large stumps of trees. These seams of coal, therefore, are the vegetable matter of decomposed plants and trees that grew on the spot. The spot was liable to be inundated from time to time, and was consequently raised higher and higher by the accumulation of sediments, as is now the case in jungles and swamps near large rivers like the Ganges or the Mississippi. As one growth of trees perished, and as the soil rose higher, other trees grew up from the new soil, now several feet higher above the level of the first morass, as is represented in our engraving of the coal measures at St. Etienne, fig. 20. in the Silurian beds; but they bear no proportion, either in extent or in thickness, to the coralline limestones of the coal period. The bottom rock, then, of the coal strata consists, in most countries, of solid compact limestone, the whole of which, in some places, is the production of the coral insect. This bed exists everywhere as a cover over the old red sandstone, except in Ireland, where it is either covered up by other rocks, ot, most likely, replaced by the millstone grit. The existence of this mountain limestone indicates that in our latitudes, at the time of its formation, there was a shallow sea, the bottom of which formed a fit foundation for coral reefs, such as we have now in the Pacific. On banks in this bottom the coral insects began to work, and as such banks belonged to a land that was gradually sinking, the insects continued to work upwards until they produced those ent. mous masses of limestone, which now form high mountains in both the Old and the New Worlds. 2. During the formation of this limestone in the seas that then c ered England, there was, in what is now called the Atlanti a large tract of land, extending from the north and south of England for some hundreds of miles westward to the ocean. In the meantime, the building up of such extensive coral reefs, and of such great thickness, would necessarily raise the level of the sea bottom. Nevertheless, the land is still supposed to be sinking. 3. After the land continued to sink gradually for some time, a change took place, when it began to rise again. In the course of its elevation, the limestone work of the corals became covered with a very extensive and thick bed of sandstone and grit, now called the Millstone Grit, consisting of the detritus, probably, of the large tract of land which we have supposed to be extending to the Atlantic. 4. The deposition of this grit was succeeded by the forms tion of muddy and sandy beds, on which a most luxuriant vegetation began to grow. These extensive beds appear to have been first formed, especially in South Wales, in water of a moderate depth, during a slow and perhaps intermittent subsidence of the ground, in a region to which rivers, from the supposed Atlantic land, would be bringing down a constant supply of sand and muddy sediment. I might quote instances of a similar character from the coal works of Capel Coelbren, near Swansea, of Balgray, near Glasgow, and from a railway cutting, near Salford, on the As these muddy beds rose above the waves, the whole ares Manchester and Bolton line; but one other, from Cape Breton, became covered with forests, such as we see now in the delias in Nova Scotia, will be sufficient. In the Sydney coal field of of large American rivers in warm climates-deltas which are that country, Sir CHARLES LYELL saw erect trees occurring at liable to be submerged beneath the sea, or covered by inunda different levels successively. In that section there are forty-tions of fresh water, should the district sink but a very one different beds of clay, with roots of Stigmaria in their few feet. natural position, and eighteen layers having upright trees at 5. The peculiar character of this coal forest has been repre levels one above the other. The whole section, he says, fur-sented in one of our late engravings, fig. 17. This forest is nishes clear evidence that at least FIFTY-ONE forests, now fossil, had grown and decayed on that spot, one after another. III. THE PROGRESSIVE FORMATION OF THE COAL STRATA. 1. At the commencement of the coal epoch, or rather at the close of the age of the old red sandstone, much of the northern part of the globe appears to have been covered with the ocean. But now, in that ocean, a very great change took place as to its elementary constituents. Carbonate of lime seems to have predominated, and to have extended itself over much of its area from the arctic regions to the equator. The gradual diminution of the size of the pebbles, in the upper portions of the old red sandstone, implies that the alternation with fine submarine gravel was not very sudden. There are, indeed, limestones, and those produced by corals, depicted as growing in a broad sheet of water, or in a shallow lagoon, which received at intervals deposits of mud and silt, the detritus of neighbouring lands. Such lakes of profusion of plants and trees, until, by the accumulation of sheets of water would be speedily filled up by a growth of muddy sediment and the mixture of decayed vegetables, it would be converted into a swamp or morass. On the surface of this morass or boggy ground, a fresh growth of plants and trees would now take place of plants and trees somewhat different from the preceding, and consist ing of reed-like plants, called Equiseta and Calamites, with here and there a large tree. As these plants in their turndecayed, the decomposed matter furnished beds of peat, etc. 6. The succession of beds of coals, clays, sandstones, shales and limestones, implies that our lagoon or morass forest may, by a repetition of subsidences and elevations, have sunk beneath the level of the sea, and have rendered its basin the Fig. 21. The North-east Portion of the Coal Measures in the Plauen Grund, near Dresden. Rothliegendes receptacle of deposits of sands and clays, which produced the strata of sandstone and shale, and occasionally limestone, between the seams of coal. The alternation of the coal measures with marine deposits abounding in sea shells is explained by supposing that the area of the vegetation must have subsided beneath the level of a neighbouring or adjacent sea, in consequence of which depression, the submerged soil would become covered with marine sediments embedding the remains of sea animals. In time, either by the deposition of sand, or mud or clay drifted from land, or by the elevation of the bed or bottom of the sea, the swamp or morass would be again and again filled, and become the area of a fresh growth of plants and trees, while the repetition of depressions and elevations accounts for the alternations of sandstone and shales. IV. DISTURBANCES OF THE COAL BEDS. After the completion of the coal strata, and before the formation of the Permian or New Red Sandstone beds, very great disturbances were produced, by volcanic agency, in the stratification. 1. In some cases the earthquake agency would curve the greatest portion of the beds, and tilt them upward at one of their extremities, as represented in fig 21. In this illustration, the perpendicular black lines represent shafts sunk into the coal measures; the curved lines, the contorting influence of volcanic agency on the overlying beds; and the inclined lines on the extreme right, the dislocations of the coal seams by the upward pressure of porphyry and greenstone. 2. Such dislocations in the strata are called Faults, probably because when a miner is working in one of these beds, and comes to a fissure or crack, he finds himself at fault. In some cases the volcanic agency has dislocated a seam of coal in so many directions, that the mining engineer becomes greatly puzzled where and how to find the continuation of the bed. The engraving, fig. 22, will show how this occurs in coal fields. The letters a, b, c, d represent shafts sunk in search of coal. At a the miner has reached the seam, which he may work right and left till he loses it. At b he is misled to think that he has reached a thicker seam of coal. At c he may think that he has found two beds. At d his shaft fails of the coal altogether. A very remarkable instance of such dislocation is represented Instances of these zigzag flexures are found at Mons, in in fig. 23. Fig. 23. Various Dislocations of a Coal Bed at Vieille-Pompe, France. Belgium, and at Charleroi, in France. In these cases, the shaft sunk in the coal measures cuts through the same bed of coal several times, in the manner represented in fig. 24. 4. Instead of bending the seams in an angular direction, as in the last illustration, sometimes the disturbing agency seemed as if in a freak, for it curves and twists them in the wildest manner. The next diagram, fig. 25, represents these dislocations and contortions of the coal seams. The vertical and the horizontal lines represent the shafts and the adits by which the miner seeks to find the coal. 5. The flexures, curvatures and contortions of the coal seams, represented in the preceding diagrams, are confined to comparatively narrow limits; but they are developed on an enormous scale in the Alleghanies, or Appalachian [Ap-pal atch-yan] Mountains, in the United States of America, of which you have an outline in fig. 26. In this diagram, A to B is part of the Atlantic plain; в to c the Atlantic slope; c to D the Appalachian Mountains; D to E part of the Appalachian coal field. 1. Chalk group. 2. Gneiss. 3. New Red Sandstone. 4. Silurian Rocks. 5. Old Red Sandstone. 6. The Coal Measures. 6. Anthracite or Stone Coal. 7, 8, and 9. The parallel folds of the Appalachians becoming successively more open and flat in going from east to west-7 and 8 representing portions of the curved rocks removed by denudation. The illustration shows, that on the eastern side the dips predominate to the south-east, in consequence of the beds haring been folded back upon themselves, as under 7, while those the north-west side of the arch have been inverted. The al strata are horizontal to the westward of p, and become pare and more curved as we come eastward towards c invariably found that the coal is more pitchy towards the west where it is horizontal. It becomes gradually less pitchy we come to the south-eastward of D, from 9 to 6, where the beds are most disturbed. At length we come to a completely insulated coal field, 6', associated with the boldest flexure The Appalachian strata consist of Silurian, Devonian and Carboniferous rocks, extend from Vermont to Alabama, and are about 1,000 miles long, from 50 to 100 miles broad, and from 2,000 to 6,000 feet thick. These strata are all folded and bent into a succession of curves, convex and concave, parts of which, as at 7, 8, 9, have been subsequently exposed by denudation. The bendings and the breakings of the beds are greatest on the south-eastern side of the Atlantic districts; and as we go westward the strata become less and less distorted, until at length they regain at E their original horizontality. where the strata are actually turned over, and where the ca has brome pure anthracite." This section teaches three lessons:-First, the flexure of the beds has been produced by the intrusion of igneous rocks represented by 2. Secondly, the disturbance must have t place before the bed 3, or New Red Sandstone, was depos for otherwise it also would have been tilted up. Thirdly, peak in the New Red Sandstone, and the dotted curves and 8, show that enormous quantities of rock have bee removed by denudation. Fig. 26. The Geological Structure of the American Districts between the Atlantic and the Mississippi, as described by Str system into the subject, and by spreading over it the soft attractive light of a correct and elegant style, they converted the Chronicle into History, and carried History so far forward to perfection as to recall the ancient models offered in Tacitus, Thucydides and Xenophon, thereby forming a school te pupils in which may never surpass their masters, but must eve remain very largely in their debt. ROBERTSON forms one of the trio-Hume, Robertson and Gibbon-who together constitute the pedestal of English William Robertson was born in the year 1721, at af Borthwick, Historical Writing. Before them there was, strictly speaking, County of Mid-Lothian, Scotland, where his father no history in the vernacular tongue of Great Britain. By parish minister. His first educational discipline he rece profound research, by minute scrutiny, by accurate investiga- from Leslie, a then celebrated teacher at Dalkeith. We tion, by careful comparison and exact representation, as well his fall er in 1733 was promoted to a church in Edinbur as by tracing events to their causes and exhibiting facts in took his son with him, and sent him to the Metropolitan terminating his studies, the young Robertson was in 1743 appointed minister at Gladsmuir, from which place he received only £100 a year. On this sum, however, he contrived to bring up seven brothers and sisters, thrown resourceless on his hands by the death of his parents. Necessity is said to be the mother of invention; she is certainly the parent of industry. Robertson was impelled by duty to turn his talents to account, and happily applied himself to historical studies. As the reward of some years' labour, he found his circumstances improve while his name grew into repute.. While his "History of Scotland" (which appeared in 1751) was passing through the press, he received a call to a ministerial charge in the capital of his native land; in 1761 he was named Royal Chaplain of Scotland; in 1762 he became Principal of the University of Edinburgh; and two years after he received, with a salary of £200 a year, the title of Historiographer for the northern portion of Great Britain. The course of his life was little diversified, and certainly was unmarked and undisturbed by any of those signal events which in retrospect give interest to biography. Dr. Robertson died on the 11th of June, 1793, at his country-seat, Grange House, near Edinburgh. Luther was saved, by a reasonable death, from feeling or beholding its destructive rage. Having gore, though in a declining state of health, and during a rigorous season, to his native city of Eisenach, in order to compose, by his authority, a dissension among the counts of Mansfield, he was seized with a violent inflammation in his stomach, which in a few days put an end to his life, in the sixty-third year of his age. As he was raised up by Providence to be the author of one of the greatest and most interesting revolutions recorded in history, there is not any person, perhaps, whose character has been drawn with such opposite colours. In his own age, one party, struck with horror and inflamed with rage, when they saw with what a daring hand he overturned everything which they held to be sacred, or valued as beneficial, imputed to him not only all the defects and vices of a man, but the qualities of a demon. The other, warmed with the admiration and gratitude which they thought he merited as the restorer of light and liberty to the Christian church, ascribed to him perfections above the condition of humanity, and viewed all his actions with a veneration hordering on that which should be paid only to those who are guided by the immediate inspiration of A sermon which Robertson in 1755 preached before "The heaven. It is his own conduct, not the undistinguishing censure Scottish Society for the Propagation of the Gospel," is his or the exaggerated praise of his contemporaries, that ought to only theological publication of a superior character. The regulate the opinions of the present age concerning him. theme of the discourse is, that God bestowed Christianity on Zeal for what he regarded as truth, undaunted intrepidity the world at the exact time when it was most needed. As was to maintain his own system, abilities, both natural and natural in handling such a subject, he refers to the world as acquired, to defend his principles, and unwearied industry it was at the advent of the Saviour, and draws a vivid picture in propagating them, are virtues which shine so conspicuof its then political, social, moral and domestic condition. To ously in every part of his behaviour, that even his enemies his historical works, however, he owes his undying reputation. must allow him to have possessed them in an eminent degree. The first that appeared was the "History of Scotland during To these may be added, with equal justice, such purity and the Reigns of Queen Mary and King James VI. till his acces- even austerity of manners as became one who assumed the chasion to the Crown of England." The catastrophe of the racter of a reformer; such sanctity of life as suited the doctrine unfortunate (wicked is the right word) Mary Stuart and the which he delivered; and such perfect disinterestedness as history of the Reformation in Scotland which he narrates, affords no slight presumption of his sincerity. Superior to all procured for the work great attention. In a few weeks the selfish considerations, a stranger to the elegancies of life, and general voice assigned him one of the first places among despising its pleasures, he left the honours and emoluments of historical writers, an honour earned as well by his correct and the church to his disciples, remaining satisfied himself in his nervous style, as by his well-grounded and judicious views. original state of professor in the university, and pastor of the In foreign countries, too, the history was honourably received. town of Wittemberg, with the moderate appointments annexed Robertson had the satisfaction of seeing the fourteenth edition to these offices. His extraordinary qualities were alloyed with of this history before he left the world. The "History of no inconsiderable mixture of human frailty and human pasScotland" was followed by the instructive and attractive sions. These, however, were of such a nature, that they canHistory of the Reign of the Emperor Charles V. with a view not be imputed to malevolence or corruption of heart, but seem of the progress of society in Europe, from the subversion to have taken their rise from the same source with many of his of the Roman Empire to the beginning of the Sixteenth Cen- virtues. His mind, forcible and vehement in all its operations, tury" (London 1769, 3 vols. 4to). Such was the earnest desire roused by great objects, or agitated by violent passions, broke for the appearance of this work, that it brought its author the out, on many occasions, with an impetuosity which astonishes sum of £4,500. Of inferior worth is his "History of America," men of feebler spirits, or such as are placed in a more tranthough the fourth book, which contains a picture of the physical quil situation. By carrying some praiseworthy dispositions to condition of America, together with a disquisition on the man-excess, he bordered sometimes on what was culpable, and was ners and institutions of its inhabitants, is accounted Robert- often betrayed into actions which exposed him to censure. His son's masterpiece; and certainly his skill in writing, his confidence that his own opinions were well founded, approached penetrating spirit of observation, and the beauty of his diction, to arrogance; his courage in asserting them, to rashness; his never appeared in a more advantageous light than here. firmness in adhering to them, to obstinacy; and his zeal in Robertson's last production was an Historical Disquisition confuting his adversaries to rage and scurrility. Accustomed concerning the Knowledge which the Ancients had of India," himself to consider everything as subordinate to truth, he (London, 1790). After his death there appeared (1798) a con- expected the same deference for it from other men; and tinuation of his "History of America," under the title, "The without making any allowances for their timidity or prejuHistory of America, Book ix. and x., containing the History dices, he poured forth against such as disappointed him, in of Virginia to the year 1652." The manuscript was found by this particular, a torrent of invective mingled with contempt. the author's son in a state apparently prepared for the press. Regardless of any distinction of rank or character when his Taken as a whole this fragment in no respect falls below the doctrines were attacked, he chastised all his adversaries indisother works, an on every page the critical reader recognises criminately with the same rough hand; neither the royal Robertson's characteristic excellencies, the same power of com- dignity of Henry VIII., nor the eminent learning and abilities bination, the same depth of reflection, the same charming flow of Erasmus, screened them from the same gross abuse with of narration. A full" Account of the Life and Writings" of which he treated Tetzel or Eccius. this distinguished historian was published by Dugald Stewart (London, 1801), forming one of three memoirs of Smith, Robertson, and Reid, read by that elegant writer before the Royal Society of Edinburgh. The following extracts may serve as specimens of Robertson's style of writing. MARTIN LUTHER. "While appearances of danger daily increased, and the tempest which had been so long a gathering was ready to break forth in all its violence against the Protestant church, "But these indecencies, of which Luther was guilty, must not be imputed wholly to the violence of his temper. They ought to be charged in part on the manners of the age. Among a rude people, unacquainted with these maxims which by putting continual restraint on the passions of individuals, have polished society and rendered it agreeable, disputes of every kind were managed with heat, and strong emotions were uttered in their natural language without reserve or delicacy. At the same time the works of learned men were all compos d in Latin, and they were not only authorised, by the example of eminent writers in that language, to use their antagonists with the most illiberal scurrility, but in a dead tongue indecancies of every kind appear less shocking than in a living language, whose idioms and phrases seem gross, because they aze familiar. the use of her limbs. No man,' says Brantome, 'ever be held her person without admiration and love, or will read her history without sorrow.'" LESSONS IN ALGEBRA.-No. XXIX. (Continued from page 627.) PROBLEMS IN GEOMETRICAL PROGRESSION. PROB. 1. Divide the number 49 into two such parts, that the greater increased by 6 may be to the less diminished by 11 as 9 to 2. Let the greater, and 49 — the less. By the conditions proposed, Adding terms, "In passing judgment upon the characters of men, we ought to try them by the principles and maxims of their own age, not by those of another; for although virtue and vice are at all times the same, manners and customs vary continually. Some parts of Luther's behaviour, which appear to us most culpable, gave no disgust to his contemporaries. It was even by some of those qualities which we are now apt to blame that he was fitted for accomplishing the great work which he undertook. To rouse mankind, when sunk in ignorance or superstition, and to encounter the rage of bigotry armed with power, required the utmost vehemence of zeal, as well as a temper daring to excess. A gentle call would neither have reached nor have excited those to whom it was addressed. A spirit more amiable, but less vigorous than Luther's, would have shrunk back from the dangers which he braved and sur-Multiplying the extremes and means, x+6=36. Andz=30. Prob. 2. What number is that, to which if 1, 5, and 16 be severally added, the first sum shall be to the second as the second to the third? mounted." MARY QUEEN, OF SCOTTS. "To all the charms of beauty, and the utmost elegance of external form, Mary, adding those accomplishments which render their impression irresistible, was polite, affable, insinuating, sprightly, and capable of speaking and writing with equal ease and dignity; sudden, however, and violent in all her attachments, because her heart was warm and unsus picious; impatient of contradiction, because she had been accustomed from her infancy to be treated as a queen; no stranger, on some occasions, to dissimulation, which, in that perfidious court where she received her education, was reckoned among the necessary arts of government; not insensible to flattery, or unconscious of that pleasure with which almost every woman beholds the influence of her own beauty. Formed with the qualities we love, not with the talents that we admire, she was an agreeable woman rather than an illustrious queen. The vivacity of her spirit, not sufficiently tempered with sound judgment, and the warmth of her heart, which was not at all times under the restraint of discretion, betrayed her both into errors and crimes. To say that she was most unfortunate, will not account for that long and almost uninterrupted succession of calamities which befell her; we must likewise add, that she was often imprudent. Her passion for Darnley was rash, youthful and excessive. And though the sudden transition to the opposite extreme was the natural effect of her ill-requited love, and of his ingratitude, insolence and brutality; yet neither these, nor Bothwell's artful address and important services, can justify her attachment to that nobleman. Even the manners of the age, licentious as they were, are no apology for this unhappy passion; nor can they induce us to look on that tragical and infamous scene which followed upon it with less abhorrence. Humanity will draw a veil over this part of her character, which it cannot approve, and may, perhaps, prompt some to impute her actions to her situation more than to her disposition; and to lament the unhappiness of the former rather than accuse the perverseness of the latter. Mary's sufferings exceed, both in degree and duration, those tragical distresses which fancy has feigned to excite sorrow and commiseration; and while we survey them, we are apt altogether to forget her frailties; we think of her faults with less indignation, and approve of our tears, as if they were shed for a person who had attained much nearer to pure virtue. Dividing the consequents, - I 6:38::9:2 I +6:44::9:11 I +6:4::9:1 the less as their sum to 42, and as their difference to 6. the difference of their cubes is to the cube of their difference Prob. 8. There are two numbers in the proportion of 5:6; the first being increased by 4 and the last by 6, the proportion will be as 4: 5: what are the numbers? Prob. 9. A farmer has a quantity of corn in his granary, and sells a certain number of bushels, which is to the number of bushels remaining as 4: 5. He then feeds out 10 bushels, which is to the number sold as 1:2. How many bushels had he at first, and how many did he sell? Prob. 10. There are two numbers whose product is 135, and the difference of their squares is to the square of their difference as 4 to 1: what are the numbers? Prob. 11. What two numbers are those, whose difference, sum and product, are as the numbers 2, 3 and 5, respectively Prob. 12. Divide the number 24 into two such parts, that their product shall be to the sum of their squares as 3 to 10. between the quantities of each is to the quantity of brandy as Prob. 13. In a mixture of rum and brandy, the difference 100 is to the number of gallons of rum; and the same difference is to the quantity of rum as 4 to the number of gallons of brandy: how many gallons are there of each? Prob. 14. There are two numbers which are to each other less, the sum and remainder will be to each other as 3 to as 3 to 2; if 6 be added to the greater and subtracted from the 1: what are the numbers ? Prob. 15. There are two numbers whose product is 320; and the difference of their cubes is to the cube of their dif ference as 61 to 1: what are the numbers? Prob. 16. There are two numbers, which are to each other in the duplicate ratio of 4 to 3, and 24 is a mean proportional between them: what are the numbers? CONTINUED GEOMETRICAL PROPORTION OR PROGRESSION. When all the ratios of a series of proportionals are equal, the quantities are said to be in continued proportion or progression. As arithmetical proportion continued is arithmetical pro "With regard to the queen's person, a circumstance not to be omitted in writing the history of a female's reign, all contemporary authors agree in ascribing to Mary the utmost beauty of countenance and elegance of shape of which the human form is capable. Her hair was black; though, according to the fashion of the age, she frequently wore borrowed locks and of different colours. Her eyes were of dark gray, her com-gression, so geometrical proportion continued is geometrical plexion was exquisitely fine, and her hands and arms remark-progression. It is sometimes called progression by quotient. ably delicate, both as to shape and colour. Her stature was of a height that rose to the majestic. She danced, walked and rode with equal grace. Her taste for music was just, and she sang and played upon the lute with uncommon skill. Towards the end of her life she began to grow fat; and her long continement, and the coldness of the house in which she was The numbers 64, 32, 16, 8, 4, are in continued geometrical proportion. the common ratio, the quotient will be the following term. Thus, In this series, if each preceding term be divided by 32, and 16, and 4o 8, and § = 4. = imprisoned, brought on a rehumatism, which deprived her of If the order of the series be inverted, the proportion will still |