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This problem has no limitation. The ratio which
B the rectangles 10 x OE, JA XOA are to bear to each other is thus determined. Let ABC be an iso. sceles triangle having the vertical angle ABC = the
EL given, demit BD therefrom perpendicular to, the base AC, and bife & BD in E ; then the required ratio of 10 X OE IA X OA is that of AC : DE.
A Elegant Conftrudions suere received from Mr. Sanderson, Mr. Merrit, and Mr. Robbins.
QUESTION III. Answered by Mr. Todd. If x = ac, y=de, and aG = a, the given line
» then j:*::y:
j = bd; and bd
be x a = ac x dc by quer. ay
art that is, V *+ y2 = xy; which will re.
P duce to y =
and thence y = a x hyp.
a-x log, where y = 0, when x = 0; and when a b c
G a? -*2 x=a, y will be infinite, or an assymptote to the curve.
223% To find the area. A =xy
- 2ax +
= flux. of adp, whose a? -*
a+* Auent A=- 2ax + a’ x hyp. log. correct, (for when x = 0, A=0):. the required area ade = xy, less by the preceding area. To find the length of the curve ad = 2.
2.a?* Here 3 = x +
therefore % =*+ 22-*219
a2-x-X x hyp. log. =ad. It may be observed, that A and z = 0, and inã. mite, when x = a.
Mr. Bonnycastle, Mr. Ogie, and others, favoured us witbo folwions to this gueftion.
Mr. Lawson bas defired us to insert his reduction of the four caso of Venion 17 in his Synopsis (uther folutions of which have been given in our two last Magazines and Appendix) to determinate section as restored by Mr, Wales. As they will take up but little rooin, and serve to shew the use of that most excellent treatise, we willingly comply with his defire.
I u cale 1. of book 2. fig. 44.
1. II. V. S+s, B on P.Pri Il. ep. 2. case 1. of bock 2. fig. 50.
I IL III. V. S -S.B+P. Pr. II.
0 ep. 1. cafe 1. of book 2. fig. 46.
IT IV. V.S-S. Bis P. two cases
0 ift. when S-sis less than Bu P.
А E Pr. Ill. ep. 3. cafe 7, of book 2.
E Tu 2d. When S-s is greater than
0 Bos P. Pr. III.'ep. 3. of book 2.
In all these figures AE and EU are put for S+s, or Ss, and EO always fupposed = B. The required ratio is determined from V when sms is cong cerned, but from the su; piement of V wken S+s is concerned.
NEW MATHEMATICAL QUESTIONS.
QUESTION I. By T. P. GIVEN one of the diameters of an ellipsis, and the periphery, to find the Lide of an equilateral triangle inscribed therein.
QUESTION IL. By Mr. Robbins. IN a plane triangle there is given the base, the difference of the sides, and the nearest distance from one of the angles at the base to the circumference of the inscribed circle ; to construct the triangle.
Question III. By Caput Mortuum. TWO lesser circles being given on the plane of the stereographic projection, to describe a given arc of a great circle within one of them, so that when continued it mall touch the other.
An Impartial Review of New Publications.
wine, which had been fined down with OBSERVATIONS Hißorical, Critical, and arsenic. Two of them died in the country
Medical, on ibe Wines of ihe Ancienis ; in a few days: the other, who came to and tbe Analogy between ibom and modern town, either from the strength of his con. Writers. Wird general Observations on the Ritution, or having drank a less quantity, Principles and Qualities of Water, particular. survived: but the effects of it appeared foon by obese of Baib. By Sir Edward Barry, in bloody spots over the whole surface of his Bart. 153. Cadell.
body; his urine, saliva, and whatever ha The learned author's observations have hawked up, or expectorated, was deeply great meritwall wine mercbants and wine tinged with blood : these appearances cealed drinkers, may be much benefited by perufiag in some time, and he became cedematous, them. The general properties of the wines However he recovered; but though his state of the ancients, are here explained from ob- of health was from that time very imperfect, fervation, facts, and the established princi- yet he married two years after, and died in ples of fermentation and philofophy. 'Rules about four of a dropsy, owing to a total diftsare given also for the preparation and manager lution and acrimony of his humours, from this ment of vinous liquors. We are told that mineral poison--Mineral poisons of this the ancients in depurating or fining their kind are generally fo violent as immediately wines, used plain and burnt salt, bitter al. to thew their effects in the stomach and monds, the whites of eggs, and particularly bowels; and, unless soon discharged and ilinglais.
corrected by emetics, lenient purgatives, and But our author observes, " that when the soft plentiful diluents, excite a fatal inflamwines continued more obstinately foul than mation and mortification ; but how far in a usual, they added sand, or marble finely less quantity they may more Nowiy affect the powdered. They were much better acquaintblood and nervous system, can only be de. ed with these arts than our modern wine termined by future obiervacions." coopers, who pretend to conccal, as valuable To prelerve wines in the bings, he prefecrets, some of these common forms; but I fers dry sand to saw duft, as its density is do not find that they ever made use of ar much greater; and Sir Edward gives a refenic, or any noxious mineral bodies, in markable instance within his own knowledge fining down their wines, which certainly, of the benefit arising from a defence of his by its very fuperior gravity, will powerfully kind : “ A hogshead of claret, which had aitenuate them, and force down any lees, been lately bottled, was heaped up in a corwhich will in some time entirely subfide, ner of a merchant's common large cellar, perhaps without communicating any noxious with a view of removing it soon to the wine quality to the wine; but the too early use of cellar. In the mean time a load of salt, luch wines has been often succeeded with from the want of a more convenient place, fatal consequences. I fall mention a re was thrown on the bottles, and remained markable instance of this kind, which came there several months before it was removed, within my observation. Three gentlemen of This wine was afterwards found to be dihination had dian's pretty freely of whits much superior to the wine of the same
growth, which had been imported and bot. bufiness of farming, but that the whole tled about the same time, and had been im- country is divided into much smaller pormediately placed in the wine cellar. The tions than land is with us, and occupied by a large quantity of salt formed a compa&t vault set of laborious people, who in general over the bottles, which entirely defended the work for themselves, and live very much upwine from the influence of the air, though on a footing of equality. greatly exposed to it; and probably the cold This seems a presumptive proof, that agriness of the salt contributed to this improve culture, when it is thrown into a number of
hands, becomes the life of industry, the The ancients certainly more effcctually source of plenty, and the fountain of riches preserved their wine in larger earthen vessels to a country; but that monopolized, and pitched externally than we can in our bottles, grasped into few hands, it must dishearten the as they are niore capable, from their superior bulk of mankind, who are reduced to ladensity and capacity, of refifting the frequent bour for others instead of themselves ; muft changes in the air; and it is a common ob- Jeffen the produce, and greatly tend to geneservation, that the wine received into bottles ral poverty. which contain two quarts, proves better than I shall not attempt wholly to account for that which had been kept in single quarts. the amazing increased price of provisions
It appears very probable, that our best with us. There are, undoubtedly, many modern wines, especially those of a de causes which contribute to it; but it is very licate texture and Aavour, may be more ef. evident that no single cause affects it, lo fe&tually, preserved in earthen vessels, of a much as the destructive practice which has Jarger fize than our bottles, well glazed ex- prevailed, for near half a century back, of ternally and internally. The vessels of this demolishing small farms. This absurd cufkind, which were formerly used for that tom, which is not without its advocates, draws purpose, were pitched externally, and lined its birth from ill-digested calculations ; is atinternally, on account of their being porous, tended with great cruelty to individuals ; and imperfectly vitrified; but our artists are and ends in considerable private loss, and arrived to such a perfection in this article of public calamity. manufactory, that their glazed vessels are im The specious inducements are, to avoid pervious to the air, and incapable of com- trouble, to save expences in repairs, and to municating any bad taste to any liquors con secure the rent by having more capital tctained in them; however pitching them ex nants, ternally would be a greater defence, elpecially Granting these arguments their utmost when the glazing is not equally firm." weight, they may be easily confuted.
We cannot conclude this article without Those who contribute towards the destruc. observing, that claffical scholars will find tion of small farms, can have very little reLeveral passages in Horace, &c. agreeably il flection. If they have, their feelings are not Justrated, and new light thrown upon them, to be envied. Where this has been the prace in this work.
tice, we see a vaft number of families redu. II. Hints to Gentlemen of landed Property ced to poverty and misery, the poor rates by Naib. Kerit. .55. Dodsley.
much increased, the small amicles of pro. Gentlemen and farmers will find in this vision greatly diminished in quantity and volume, many valuable hints on the follow. number, and consequently augmented in ing particula's. Of the application of soil price. to its right use; draining; natural and arti. The increase of farms has a general bad ficial graffts ; improving meadow and paf- tendency, for as soon as the little schools of ture land ; a suitable ftock of caitle ; ma industry are grasped into the hands of an nures; turneps ; cole and rape seed ; hops; over-groun, rapacious farmer, the former building and repairs ; limber and planting; occupicrs are, as once, all reduced to the advantages of small farms ; importance of fate of day-labourers; and when their health cottages ; difrels of the poor, and increase or Arength fails, there is but one resource ; of rates.
they, and their children, are thrown upon the Of the advantages resulting from small parish. This has undoubtedly swelled the farms, and those of the most profitable size rates to their present enormous height, more described, Mr. Kent thus speaks, “ Every than any cause whatever. speculative Englishman who travels through The mechanic and manufacturer next feel the Auftrian Nerberlards, is aftonished at the blow. The market wears a different the great population of that country, and at face. The vast number of poultry, the the light of the markets, which are plenti. quantity of pork, and a variety of other ful beyond description. Upon erquiring in small articles of provifion, are no longer sup. to the internal Atate, and regulation of the plied in their former abundance. The great country, he finds that there are no large farmer raises no more of these, than are ne. farms, no class of men who pass under the cessary for his own confumption ; because character of gentlemen-farmers, acquiring his wife and children will not take the Targe fortunes inerely by superintending the trouble and care of them, or condescend to
attend the market, like the wives and chil IV, The Law of Liberty, a Sermor et dren of little farmers. His views are form- American Affairs, preached at the opening of ed upon a large scale, and everything flows the Provincial Congress of Georgia, addrefed from him in a wholesale channel. And as to ibe Right Honourable the Earl of Dario no man can execute any very extensive bufi. mouth, with an Appendix, giving a concise Dess, so well as that which lies in a more niccount ibe Struggles of Switzerland to contracted space, he must, when he has a recover their Liberty, by 7. J. Zubly, D. D. great deal upon his hands, neglect many Is. 60. Almon. Imall objects, partly for want of time, and By the address already inserted p. 35, the partly because they appear trivial in their na reverend writer's file and sentiments must ture: and many trifles added together, make be sufficiently known to our readers. His a large deficiency upon the whole.
text was James ii. 12. “ So speak ye and The case is different upon the small farm. so do as they that shall be judged by the law Here the tenant's great dependance rests up of liberty," Which is treated with judgon trifles merely ; and therefore it behoves ment and perspicuity. bim to make the most of every thing. As he V. The Speech of bis Grace the Duke of has no great space to superintend, it lies un Mancbefter, against the Bill to probibit all In. der his eye at all times, and seasons ; he tercourse with ebé Colonies. is. Kearlly. Seizes all minute advantage ; cultivates This noble Duke shines as a patriot, and every obscure corner ; generally accumulates brings a variety of arguments to prove that more manure in proportion to his land ; and the late bill which he opposed was directly confidering his animal as well as vegetable opposite to that great palladium of our liberproduce, bas likewise in that a greater pro- ty, tbe bill of rights. portion.
VI.On Illicit Love, written among the Ruins He does great part of his work with his of Godftow Nunnery, near Oxford, by Joba own hands; and every man works more Brand, A. B. IS. 68. Wilkie, chearfully, zealously, and diligently for Godftow is at present a ruin on the mare himself, than for another. His wife and gin of the llis, at a small distance from Oxchildren are likewise of great service to him, ford. It was formerly a house of nuns, faespecially if his gains depend much upon a mous perhaps on no account so much as for dairy. And, in general, the children of having been the burial place of Rosamond, these little farmers prove the most useful daughter of Lord Clifford, the beautiful papeople the country produces. The girls ramour of Henry the second. This monarch make the best dairy-maids ; the boys the best is said to have built a labyrinth at Woodstock gentiemen's bailiffs ; the best head-men in to conceal her from his jealous queen, who, larger farms; the best persons to superintend, during his absence, when he was called away and manage cattle; and, in a word, the by an unnatural rebellion of his sons, at the most regular servants, in most capacities. supposed instigagion of their mother, found
Upon an eftate of one thousand pounds a means to get access to her, and compelled her year, I wish to see something like the follow to swallow poison. Frequent walks in this ing proportion: one farm of 1601. one of delightful recess, sacred to the moments of 1201. one of 1001, two of 8cl. two of 6ol. contemplation, suggested the following two of 50'. three of 401, and four of 301. thoughts, for the publication of which, each. This would be fixteen farms upon a the alarming progrets of lewdness, and conthousand pounds a year, and would be a pro- fequently of licentiousness of manners, fitable, division to an owner, and to the pub. which indeed threatens the diffolution of lic. But, instead of this, the generality of cur ftate, should be accepted as an apology. Jarge eftates do not support above a third part The following extract is selected from this of The e families. And I will venture to ase agreeable poem for our fair readers. sert, that the poor rates will be much higher Ah haple's maid! th'atherial power began, in the latter, than in the former mode of al. (While pensive sadoels thro' my bosom ran!) lotment; because a great many families, which What mou'd the first thy father to disgrace? would get a decent livelyhood upon the farms The boast and brand of Clifford's noble race ! of 30l. 401. and 501. a year, come to the pa- Cou'd icy age thy youthful breast inspire, rith, as I have before observed, when they Or e'er grey hairs enkindle green defire ? are deprived of this method of supporting Love's living smile ambition's frowns devour, themselves.
And pleasure flies the rude embrace of pow's. III. Tbe Evidence of ibe Common and Sta. Could Henry's crown a charm so pow'rful tate Laws of the Realm, Usage, Records,
prove, Hiftory, witb obe greatest and best Ausborities To blanch the negro front of lawless love? down so ebe 3d of George III. in Proof of tbe Too juftly blam'd! to blast wbole fame con. Rigbts of Britons tbrougbout tbe British Em. spire pire. 25. Williams.
A lover old, wrong'd Queen, and injur’d Great authorities and a number of good evi. fire! dences are here produced in favour of the I see the father tear his hoary hairs, American cluims,
And beat a bolom, rack'd with hopeless cares;
Invoke high Hear's on Henry's head to VII. Adventures of Alonso, containing fome show's
Ariking Anecdotes of the projent prime Minister The vengeful light’nings of incensed pow'r : of Poringa!, 2 vols. 58. Bew. Bare the red arm against th' adult'rous flame, The most striking anecdotes we shall select And hide in doft a darling daughter's theme ! next month : the adventures contain some The pray!r's preferr'd-Nor ever move in pleasing particulars, and extraordinary events;
some of them too extrao dinary to be true ; The holy lips of age, incens'd hy pain. however, at last, Alunfo is reconciled to his War's Aern alarms their infant loves annoy, father, Survives him, and inherits great And black remorse fucceeds the blaze of joy. wealth. His crime was an intrigue with a
vain has Woodilock rear' her haughty narried lady, and running away with her, tow'rs,
which involved both in numerous evils. In vain immur'd thee in meand'ring bowr's: Warned by their errors and sufferings, may Eludes no lab'rinth guilt's intrusive eyes, others avoid their evil footsteps. And conscience follows whereroc'er she flies ! VIII. A Letter to Lord Carbcart, concerts How chang'd by absence ev'ry haunt re ing tbe Recovery of Persons drowned and maine !
seemingly desd, by Dr. William Cullen, 16, 6d. The scene of pleasures past, of present pains! Murray. There mourn, fair maid! till o'er the nurky The Author hath displayed great judge gloom,
ment and humanity: he oblerves, that lite Repentance shine to mitigate thy doom : doth not ccale immediately upon the ceftijon By man unhcard, unwept; and unforgiven, of the action of the lungs and heart, and the The mercy earth deris; draw down from
confequent ccaging of the circulation of the heav'n!
blood, baton a certain condition in the nerves The dark retreats stern jealousy explores, and muscular fibres, by which they are fenfible Faze's clue conducting toro che mazy doors ! and irriiabie, and on which the action of the See guilt at once, and injur'd love arraign, heart iifeif depends. As long as this subsists White piry pleads, and mercy moves in vain! it is preluined, that the action of the heart Nor fighs, nor pray’rs, nor icars in torrents and lungs, the circulation of the blood, and fhed,
therefore all the functions of life may also, Avert the doom from her devoted head, though ihoy have many of the long cealed,
be again entirely relored. The directions." Till poison's fpumy bowl avenge the spot. for the recovery of perfons drowned, are juHere paus's the pow's ! and having glean'd dicious, and very similar to those already reher store
commended by ihe London suciety for the lame From ages patt, to future fram'd her lore. purpose. Be warn’d je luir ! (the cried) by Clifford's IX. An Heroic Epistle to Lord Craven, falc,
Is. Wheble, What vengeful uocs on lawless love await? If his Lordship faid at the county meeting I ne phantoms, fanty pleasure rais'd, thall at Abingdon, « i will have it known there is fail,
[gall! respect due to a Lord,” for which he is here And fucn her luscious sweets be dah'd with Satyrized, we think he justiy, deserved some Sila picalure ties from guilt on fitting of che lines here bestuwed upon him, but wings,
our poct is not a Juvenal. And 'mid her fiow'rs the respent sorrow X. El-giac Verjes 10 a young Lady ox Transcribe the tale that on ihis wall is ibe Dealb of ber Braber, by M. Robinfor, wroughi,
15. Johnson. The tablit hangs a toilett for your thought ! For, “ The first essay of an early muse," Here look-norio chole tilt'ring mirrors fly cominendable. Where couls are poilon'd ny the pleasur'd eye; X1. In Ejly on Polirerefs, r9 which is Nor vainly wish, to future lortunes blind, prefxed an allegorical Description of ibe Orio Lucretia's face, wi bowi ber fairer mind!
gin of Politeness, by a young Gearleman. Think then! and from the case let Law. thought restrain,
This young grntieman hould have much Fortransient joys, wiat lafting ille remain ! longer villet she two chief places of instrucThe tail in vain from honour's height you tion, “The academy of Science, and the mourn ;
univerlity of the world,"
before he veng In vain with ears to ruthless man you turn; turid tu write on politeness. AS Mon the streams that down the valleys xli. d folemn Deciaration of Mr. Datray,
miel Perreau, addressed in tbe Public. Shall backwards to their fountains force a Evans.
In this publication, the writer solemnly Sooner ihall frost its freezing pow'r& forego, declares boin himself and his brother to be and Afric's foot be chang'd in Europe s inow, free and innocent from every degree of crimi.
Than blaffed beauty shut its bloom rega n, nalkowicdge in the fougeries tor which they Orlemale bonvur fusi'd, remove the tain ! lullcand cath, and chai they fell innocent