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42

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This problem has no limitation. The ratio which

B the rectangles 10 * o£, JA XOA are to bear to each other is thus determined. Let ABC be an ifo. sceles triangle having the vertical angle ABC = the

EL given, demit BD therefrom perpendicular to , the bare AC, and biftet BD in E ; then the required ratio of 10 X OE :IA XOA is that of AC: DE.

Elegant Conftruétions were received from Mr. Sanderson, Mr. Merrit, and Mr. Robbins.

QUESTION III. Answered by Mr. Todd. If x = ac, y=ds, and aG = a, the given line

♡ then j :* :::

+ j2)
ў
bd; and bd bc x a = ac x dc by qued.

ау
that is,
?
= xy; which will re.

P duce to y =

and thence y = a x hyp.
a-x?
a2

G log.

where y = 0, when x = 0; and when a b c a_X2 x=a, y will be infinite, or an assymptote to the curve.

2237 To find the area.

=- 2ax +

= flux. of adp, whore a' -**

a+* Auent AE-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.?* Here is x? +

therefore z = -x + 42-4219

a2-x4* a x hyp. log. =ad. It may be observed, that A and z= , and insi. nite, when x = a.

Mr. Bonnycastle, Mr. Ogle, and others, favoured us witbo folwions to this guefion.

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Mr. LAWSON bas defired us to insert his reduction of the four caras of Question 17 in his Synopfis (ut her folutions of which have been given in our two last Magazines and Appendix) to determinate sectio« 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.

Reduced to
I. V. Sts.B+P.Pr. I, ep. 3.

A

E

T
case 1, of book 2. fig. 44.

I.
II. V. Sts. BP. Pr. 11. ep.
2. case 1. of bock 2. fig. 50.

II.
III. V. S-5. B+P Pr. II.
ep. 1. cafe 1. of book 2. fig. 46.

A

E
IV. V.S-S. Bus P. two cales
Ift. when S-sis less than BWP.

A E

Ա Ա
Pr. lll. ep. 3• cafe 7. of book 2. I.

E su
2d. When S-s is greater than

I

0 Bus P. Pr. III. ep. 3. of book 2.

In all these figures AE and EU are put for Sts, or S-s, and E0 always fupposed = B. The required ratio is determined from V uhen S-; is cone cerned, but from the su; piement of V wken S+s is concerned.

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1776.

Review of New Publications.

43 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 lefler circles being given on the plane of the ftereographic projection, to describe a given arc of a great circle within one of them, so that when continued it all touch the other.

An Impartial Review of New Publications.

ARTICLE I.

wine, which had been fined down with OBSERVATIONS Historical, Critical, and arsenic Two of them died in the country

Medical, on ibe Wines of rbe Ancients ; in a few days : the other, who came to and tbe Analogy between ibem and modern town, either from the strength of his con. Writers. Wird general Observations on the fitution, or having drank a less quantity, Principles and Qualities of Water, particular. survived: but the effects of it appeared loon by obese of Baib. By Sir Edward Barry, in bloody spots over the whole surface of his Bart. 158. Cadell.

body; his urine, saliva, and whatever he The learned author's observations have hawked up, or expectorated, was deeply great meritiwall wine merebanes and wine tinged with blood : These appearances cealed drinkers, may be much benefited by perusing in some time, and he became cedematous, them. The general properties of the wines However recovered; but though his ftate 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 philosophy. 'Rules about four of a dropsy, owing to a total diffiare given also for the preparation and manage- 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 wincs, used plain and burnt salt, bilter al. to thew their effects in the stomach and monds, the whites of eggs, and particularly bowels ; and, unless soon discharged and itinglais.

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 acquaint. blood and nervous system, can only be deed with these arts than our modern wine- termined by future oblervarions." 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 dust, as its density is do not find that they ever made use of ar- much greater; and Sir Edward gives a resenic, 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 this by its very fuperior gravity, will powerfylly kind : “ A hogshead of clares, which had attenuate 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, juch wines has been often succeeded with from the want of a more convenient place, fatal consequences. I shall 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 asterwards found to be disiņaion bad dran's pretty freely of whits much superior to the wine of the same

O %

growth 44

ment,

nants,

frowth, which had been imported and bot. business 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 compact 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 effcêtually 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 muft dishearten the as they are niore capable, from their superior bulk of mankind, who are reduced to ladensity and capacity, of rolifting 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 flavour, may be more ef. evident that no single cause affects it, so fectually, preserved in earthen vesels, of a much as the destructive practice which has Jarger size 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 cuskind, wbich 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 imperfe&tly vitrified; but our artists are and ends in considerable private loss, and arrived to such a perfe&tion 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 tetained in them; however pitching them externally would be a greater defence, efpecially 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 Juftrated, and new light thrown upon them, to be envied. Where this has been the pracin this work.

tice, we see a vast number of families redu. II. Hines to Gentlemen of landed Property ced to poverty and misery, the poor rates by Naib. Kert. .55. Dodney.

much increased, the small anicles of proGentlemen 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 gralles ; improving meadow and par- tendency, for as soon as the little schools of ture land ; a suitable fock 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 ; occupicro are, at once, all reduced to the advantages of small farms ; importance of fate of day-labourers; and when their health cottages ; diftrets 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 Nerberlands, 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- fmall articles of provifion, are no longer sup. to the internal state, 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 consumption ; because character of gentlemen-farmers, acquiring his wife and children will not take the Targe furtunes inerely by superintending the trouble and care of them, or condescend to

attend

1

1776. Review of New Publications.

45 attend the market, like the wives and chil- IV. The Law of Liberty, a Sermon or dren of little farmers. His views are form- American Affairs, preacbed at the opening of ed upon a large scale, and everything flows the Provincial Congress of Georgia, addressed from him in a wholesale channel. And as to obe Right Honourable the Earl of Dartno man can execute any very extensive bufin mourb, with an Appendix, giving a concise ness, so well as that which lies in a more siccount of the Struggles of Switzerland To contracted space, he must, when he has a recover ibeir Liberiy, by 7. 7. 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 stile 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 Imall farm. ro'do as they that shall be judged by the law Here tbe tenant's great dependance rests up

of liberty," Which is treated with judgon trifles merely ; and therefore it behoves

ment and perspicuiiy: him 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 prohibit all Inder his eye at any times, and seasons ; he tercourse witboebe Colonies. is. Kearly. feizes 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 considering his animal as well as vegetable opposite to that great palladium of our liberproduce, bas likewise in that a greater pro- ty, the bill of righes. portion.

VI.On Illicit Love, written among the Ruins He does great part of his work with his of Godftow Nunnery, near Oxford, by Joon own hands; and every man works more Brand, A. B. Is. 60. Wilkie. cheartully, zealously, and diligently for Godstow is at present a ruin on the marhimself, than for another. His wife and gin of the lsis, 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, Jarger 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 inftiganion of their mother, found

Upon an effate 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 160l. one of delightful recess, sacred to the moments of 1201. one of 100l, iwo 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, cach. This would be fixteen farms upon a the alarming progrels 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 dissolution of lic. Bui, 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 aso agreeable poem for our fair readers. Sert, that the poor rates will be much higher Ah hapless maid ! th' ætherial power began, in the latter, than in the former mode of al. (While pensive sadness 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 boaft 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 desire ? are deprived of this method of supporting Love's living smile ambition’s frowns devour, themselves.

And pleasure flies the rude embrace of pow'r. III. Tbe Evidence of obe Common and Sta. Could Henry's crown a charm so pow'rful tate Laws of the Realm, Usage, Records, prove, History, with the greatest and best futborities To blanch the negro front of lawless love? down in the 3rd of George III. in Proof of the Too justly blam'd! to blast wbose fame con. Rig brs of Britons througbout tbe British Em. Ipire 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, Americao cluime,

And beat a bolom, rack'd with hopeless cares;

Involte

[ted bed!

Invoke high Hear's on Henry's head to VII. Adventures of Alonso, containing some show's

Ariking Anecdotes of ibe projent prime Minister The vengeful light’nings of incensed pow's : of Poringa!, 2 vols. ss. Bew. Bare ihe red arm against th' adult'rous tlame, The most striking anecdotes we shall select And hide in doft a darling daughter's thame! next month : the adventures contain lome The pray?r's preferr'd-Nor ever move in pleasing particulars, and extraordinary events ; vain

Some of them too extraordinary to be true ; The holy lips of age, incens'd hy pain. however, at last, Alunfo is reconciled to his War's itern alarms their infant loves annoy, father, survives him, and inherits great And black remo:le lucceeds the blaze of joy. wealth. His crime was an intrigue with a da vain has Woodilock reas'd her haughty married 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 fooitteps. And conscience follows wherefoc'er she flies ! VIII. A Letter to Lord Carbcart, concera. How chang'd by absence ev'ry haunt re- ing tbe Recovery of Perfons drowned and mains !

seemingly dead, by Dr. William Cullen. 15. 60. The scene of pleasures paft, of present pains! Murray. There mourn, fair maid! till o'er the nurky The Author hath displayed great judge gloom,

ment and humanity: he obierves, that lite Repentance shine to mitigate thy doom : doth not ceafe im inediately upon the cestuijon By man unhcard, unwept; and unforgiven, of the action of the lungs and heart, and the The

mercy earth deris; draw down from coniequent ccaling of the circulation of the hcav's!

blood, baton a certain condition in the serves The dark retreats stern jealousy explores, and muscular fibres, by which they are fenfible Fire's clue conducting thro the mazy doors ! and irriiabie, and on which the action of the See guilt at once, and injur'd love arraign, heart itself depends. As long as this subsists White pity pleads, and mercy moves in vain! it is presunned, that the action of the heart Nor lighs, nor pray’rs, nor cars in torrents and lungs, the circulation of the blood, and shed,

thercfore all the functions of life may also, Avert the doom from her devoted head, though ihey have many of thun long cealed,

be again ensirely restored. The directions." Till poison's fpumy bowl avenge the spot. for the recovery of perfons drowned, are juHere paus’d the pow'r ! and having glean'd dicious, and very similar to those already reher fiore

commended by ine London fuciety for the lame From ages patt, to future fram'd her lore. purpose. Be warn’d je tuir ! (the cried) by Clifiord's IX. An Heroic Epiftle to Lord Craven, fata,

is. Wheble, What vengeful uocs on lawless love await? If his Lordship faid at the county meeting Ine phantoms, fany 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 loon her luscious sweets be dash'd with Satyrized, we think he justiy deserved fome 3.lila picature tees from guilt on Birting of the lines here bestuwd upon him, but wings,

[llings!

our poct is not a Juvenal. And 'mid her fiow'rs the serpent sorrow X. Elsgiac Verjes 10 a young Lady on Transcribe the tale that on ihis wall is ibe Deelb of ber Bras ber, by M. Robinson, wroughi,

15. Johnson The tablet hangs a toilett for

For, “ The first eslay of an early muse," Herc look no to chole titt'ning mirrors fly commendable. Where couls are poilon'd ny the plealur'd eye; X1. in Ejly on Politeness, 19 which is Nor vainly wish, to future lortunes blind, prefixed an allegorical Defiriprion of ibe Orio Lucretia's face, wi honi ber fairer mind!

gin of Politeness, by a young Gentleman, Think then! and from the cute lct Law. thought restrain,

This young grntieman Mould have much Fortranseni joys, whai lasting illo remain !

your thought !

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longer villet she iwo ciief places of inftrucThe tail in vain from honour's height you tion, “The academy of Science, and the mourn ;

univerlity of the world,"

before he vcne In vain with iears to rothless man you turn; turid to write on politeness. As soon the streams that down the vaikys Xli. A folemn Declaration of Mr. Da. diray,

niel Perreau, ad drejjed to ibe Public. is. Shall backwards to their fountains force a Evans.

In this publication, the writer solemnly Sooner ihall frost its freezing pow'rs forego, declares boin himself and his brother to be and Atric's foot be chang'd to Europe s inox', free and innocent trom every degree of crimiThan blafted beauty shut its bloom rega D, nal krewiedge in the fougeries for which they Orlemale bonvur fuli'd, remove the sain ! Luified cath, and chai they fell innocent

victims

way!

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