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of many of the present inhabitants of the country, the falls have receded several yards. The Commodore of the King's vessels on Lake Erie, who had been employed on that lake for upwards of thirty years, informed me, that when he first came into the country it was a common practice for young men to go to the island in the middle of the falls; that after dining there, they used frequently to dare each other to walk into the river towards certain large rocks in the midst of the rapids, not far from the edge of the falls; and some. times to proceed through the water, even beyond these rocks. No such rocks are to be seen at present; and were a man to advance two yards into the river from the island, he would be inevitably swept away by the torrent. It has been conjectured, as I before mentioned, that the Falls of Niagara were originally sicuated at Queenstowu ; and indeed the more pains yon take to examine the course of the river from the present falls downward, the more reason is there to imagine that such a conjecture is well founded. From the precipice nearly down to Queenstown, the bed of the river is strewed with large rocks, and the banks are broken and rugged ; circumstances which plainly denote that some great disruption has taken place along this part of the river; and we need be at no loss to account for it, as there are evident marks of the action of water upon the sides of the banks, and considerably above their present bases. Now the river has never been known to rise near these marks during the greatest floods: it is plain, therefore, that its bed must have been once much more elevated than it is at present. Below Queenstown, however, there are no traces on the banks to lead us to imagine that the level of the water was erer much higher there than it is now. The sudden increase of the depth of the river just below the hills at Queenstown, and its sudden expansion there at the same time, seem to indicate that the waters must for a great length of time have fallen from the top of the hills, and thus have formed that extensive deep. basin below the village. In the river, a mile or two above Queenstown, there is a tremendous whirlpool, owing to a deep hole in the bed: this hole was probably also formed by the waters falling for a great length of time on the same spot, in consequence of the rocks which composed the then precipice having remained firmer than those at any other place. did. Tradition tells us, that the great fall, in. stead of having been in the form of a horse shoe, once projected in the middle. For a century past, however, it has remained nearly in the present form; and as the ebullition of the water at the bottom of the cataract is so much greater at the centre of this fall than in any other part, and as the water consequently acts with more force there in undermining the precipice than at any other part, it is not unlikely that it may remain nearly in the same form for ages to come.'

How will the philanthropist, even while contemplating the progress of civilization, lament the wretched and reduced state, to whic! nations once happy, powerful, and populous, have been reduced by the introduction of European knowlege and European manners! Of all the tribes of that once virtuous and happy people, by whom the whole of that extensive territory

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was inhabited, which lies between the Mississippi and the AtJantic, a few wretched and wandering families are now alone to be found. The people of the United States, instead of treating with humanity and kindness the miserable Indian, whose natural possessions they have wrested from him, consider him as a wild beast, whom they ought to exterminate from the face of the earth. -As so much has already been written with respect to the persons, manners, character, and mental and corporeal qualifications of the Indian of America, we shall not enlarge on this subject, but refer the reader to the work before us; concluding our extracts with the following anecdotes of Captain Joseph Brandt, a war chief of the Mohawk nation :

• Brandt, at a very early age, was sent to a college in New England, where, being possessed of a good capacity, he soon made very considerable progress in the Greek and Latin languages. Un common pains were taken to instil into his mind the truths of the gospel. He professed himself to be a warm admirer of the principles of christianity, and in hopes of being able to convert his nation on returning to them, he absolutely translated the gospel of St. Mat. thew into the Mohawk language ; he also translated the established form of prayer of the church of England. Before Brandt, however, dad finished his course of studies, the American war broke out, and fired with that spirit of glory which seems to have been implanted by nature in the breast of the Indian, he immediately quitted the col lege, repaired to his native village, and shortly afterwards, with a considerable body of his nation, joined some British troops under the command of Sir John Johnston. Here he distinguished himself by his valour in many different engagements, and was soon raised, not only to the rank of a war chief, but also to that of a captain in his Majesty's service.

• It was not long, however, before Brandt sullied his reputation in the British army. A skirmish took place with a body of American troops; the action was warm, and Brandt was shot by a musket-ball in the heel; but the Americans in the end were defeated, and an officer with about sixty men taken prisoners. The officer, after having delivered up his sword, had entered into conversation with. Colonel Johnston, who commanded the British troops, and they were talking together in the most friendly manner, when Brandt, having stolen slily behind them, laid the American officer lifeless on the ground with a blow of his toinakawk. The indignation of Sir John Johnston, as may readily to supposed, was voused by, such an act of treachery, and he resented it in the warmest language. Brandt listened to him unconcernedly, and when he had finished, told him, that he was sorry what he had done had caused his displeasure, but that indeed his heel was extremely painful at the moment, and he could not help revenging hinıself on the only chief of the party that he saw taken. "Since he had killed the officer, his heel, he added, was much less painful to him than it had been before.

• When the war broke out, the Mohawks resided on the Mohawk River, in the state of New York, but on peace being made, they,


emigrated emigrated into Upper Canada, and their principal village is now si. tuated on the Grand River, which falls into Lake Erie on the north side, about sixty miles from the town of Newark or Niagara ; there Brandt at present resides. He has built a comfortable habitation for himself, and any stranger that visits him may rest assured of being well received, and of finding a plentiful table well served every day. He has no less than thirty or forty negroes, who attend to his horses, cultivate his grounds, &c. These poor creatures are kept in the greatest subjection, and they dare not attempt to make their escape, for he has assured them, that if they did so he would follow them him. self, though it were to the confines of Georgia, and would tomahawk them wherever he met them. They know his disposition too well not to think that he would adhere strictly to his word.

• Brandr receives from Government half pay as a captain, besides annual presents, &c. which in all amount, it is said, to £ 500 per annum. We had no small curiosity, as you may well imagine, to see this Brandt, and we procured letters of introduction to him from the governor's secretary, and from different officers and gentlemen of his acquaintance, with an intention of proceeding from Newark to his village. Most unluckily, however, on the day before that of our reaching the town of Newark or Niagara, he had embarked on board a vessel for Kingston, at the opposite end of the lake. You may judge of Brandt's consequence, when I tell you, that a lawyer of Niagara, who crossed lake Ontario in the same vessel with us, from Kingston, where he had been detained for some time by contrary winds, informed us, the day after our arrival at Niagara, that by his not having reached that place in time to transact some law business for Brandt, and which had consequently been given to another person, he should be a loser of one hundred pounds at least.

• Brandt's sagacity led him, early in life, to discover that the Indians had been made the dupe of every foreign power that had got footing in America ; and, indeed, could he have had any doubts on the subject, they would have been removed when he saw the British, af. ter having demanded and received the assistance of the Indians in the American war, sp ungenerously and unjustly yield up the whole of the Indian territories, east of the Mississippi, and south of the lakes, to the people of the United States ; to the very eneinies, in short, they had made to themselves at the request of the British. He perceived with regret that the Indians, by espousing the quarrels of the whites, and by espousing different interests, were weakening them. selves; whereas, if they remained aloof, and were guided by the one policy, they would soon become formidable, and be treated with more respect ş he formed the bold scheme, therefore, of uniting the Iridians together in one grand confederacy, and for this purpose sent messengers to different chiefs, proposing that a general meeting should be held of the heads of cvery tribe, to take the subject into consideration ; but certain of the tribes, suspicious of Brandt's designs, and fearful that he was bent upon acquiring power for himself by this measure, opposed it with all their might, Brandt has in consequence become extremely obnoxious to many of the most warlike, and with such a jealous eye do they now regard him, that it would not be perfectly safe for him to venture to the upper country.

• He

• He has managed the affairs of his own people with great ability, and leased out their superfluous lands for them, for long terms of years, by which measure a certain annual revenue is ensured to the nation, probably as long as it will remain a nation. He wisely judged, that it was much better to do so than to suffer the Mohawks, as many other tribes had done, to sell their possessions by piecemeal, the sums of money they received for which, however great, would soon be dissipated if paid to them at once.

« Whenever the affairs of his nation shall permit him to do so, Brandt declares it to be his intention to sit down to the further study of the Greek language, of which he professes himself to be a great admirer, and to translate from the original, into the Mohawk language, more of the New Testament ; yet this same man, shortly before we arrived at Niagara, killed his only son with his own hand. The son, it seems, was a drunken good for nothing fellow, who had often avowed his intention of destroying his father. One evening he absolutely entered the apartment of his father, and had begun to grapple with him, perhaps with a view to put his unnatural threats : into execution, when Brandt drew a short sword, and felled him to : the ground. Brandt speaks of this affair with regret, but at the same time without any of that emotion which another person than an Indian might be supposed to feel. He consoles himself for the act, by. thinking that he has benefited the nation, by ridding them of a rascal.

• Brandt wears his hair in the Indian style, and also the Indian dress ; instead of the wrapper, or blanket, he wears a short coat, similar to a hunting frock.

A great variety of interesting and amusing particulars, concerning the manners, customs, present state, and internal po-. licy of the American colonies, are to be found in this work: but, unable as we obviously are to follow the author through all these minute details, we have rather chosen to submit to the reader Mr. Weld's account of a few prominent objects; and we shall conclude by observing that Mr. W.'s summary and decided opinion of America may be perceived from the few following words, with which he terminates his book: 'I shall speedily take my departure from this continent, well pleased at having seen as much of it as I have done ; but I shall leave it without a sigh, and without entertaining the slightest wish to re-visit it.'

The composition of Mr. Weld is frequently inelegant and in., correct ; but his work affords considerable entertainment and information. It is ornamented by a map of part of the United States of North America, and of Upper and Lower Canada; a plan of the city of Washington, and the city of Quebec, and twelve neat descriptive engravings.

'Gell.....d. P4



For OCTOBER, 1799.

MATHEMATICS. Art. 17. The Elements of Mathematical Analysis, abridged for the

Use of Students. With Notes, demonstrative and explanatory; and a Synopsis of Book V. of Euclid. By Nicholas Vilant, A.M. F. R. S. Edinb. ; and Regius Professor of Mathematics in the University of St. Andrew's. 8vo. Pp. 160. 45. se wed.

Wingrave. 1798. W intend not to enter into any particular examination of the ar,

ticles contained in this treatise, because, as we are informed in the preface, it is only an abridgment of part of a comprehensive system of the Elements of Mathematical Analysis, common and Auxionary, and now almost finished:'-but, although we do not minutely criticise the accuracy and excellence of the methods here to be found, the work itself must be considered.

With the learned, this abridgment will be superseded by the more comprehensive one which, according to the author, is soon to be offered to the world. To young students, then, as the title sets forth, the use of this essay is apparently destined. It is desirable to know the object of an author, in order that we may estimate the success of his endeavours to attain it :-Now, if the object of this work be to afford to beginners an introduction to the easy parts and common propositions of algebra, the author may be said to have attained his object : yet we cannot avoid remarking an obvious defect, an unsystematic arrangement, and a want of coherence in the several parts. The work is not distributed into chapters ; nor does it follow the order proper to a scientific treatise. The proofs of some rules are not given ; of others, the proofs are disjoined from the rules, and placed separately in the notes. These defects might easily have been remedied; and it is to be regretted that a work should labour under the want of essential advantages, which are to be procured at a very moderate expence of thought and labour. The typographical errors also are not few; and the sign of greater and less is injudiciously altered ; there is no necessity for placing an r and s after the symbols > and <; every mathematician immediately understands that a>b means a greater than b.

In regard to the matter of the work, it is very good ; the principles of the propositions are clearly laid down, and the proofs are logically conducted. Some of the rules, however, might be changed for others which are more commodious : but we do not recollect to have elsewhere seen the method which the author has given for the resolution of commensurate cubic equations; the resolution is founded on this

and if x=n, 2n, 3n, 40, 5n, &c. then

у y=m, 2m, 3m, 4m, 5m, &c.




i principle: if


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