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42

Mathematical Correfpondence.

This problem has no limitation. The ratio which the rectangles 10 x OE, IA x OA are to bear to each other is thus determined. Let ABC be an ifofceles triangle having the vertical angle ABC = the given, demit BD therefrom perpendicular to the bafe AC, and bifect BD in E, then the required C ratio of 10 x OEIA x OA is that of AC: DE.

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

QUESTION III. Anfawered by Mr. Todd.

If x = ac, y=de, and aG = a,

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the given line

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then jy: = = bc,and by 47.c.1, ——√x2+j2

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bd; and bd bc x a = ac x de by quest.

ay

that is,√+y=xy; which will re

ayse

y2

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a2-x2 log. where yo, when xo; and when x=a, y will be infinite, or an affymptote to the curve.

2a3x a2-x2

To find the area. Å=xj = −2ax + = flux. of adp, whofe fluent A-2ax + a' x hyp. log. correct, (for when x = 0, A=o) ..

a+x
a-x

the required area ade = xy, lefs by the preceding area. To find the length of the curve ad± 2.

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ad. It may be obferved, that A and zo, and infi

Mr. Bonnycaftle, Mr. Ogle, and others, favoured us with folutions to this queftion.

Mr. LAWSON bas defired us to infert his reduction of the four cafe of Question 17 in his Synopfis (other folutions of which have been given in our two laft Magazines and Appendix) to determinate fection as restored by Mr, Wales. As they will take up but little room, and ferve to fhew the ufe of that most excellent treatife, we willingly comply with his defire.

Reduced to

I. V. S+S.B+P. Pr. I. ep. 3.

cafe 1. of book 2. fig. 44.

II. V. S+s. BP. Pr. II. ep. 2. cafe 1. of bock 2. fig. 50. III. V. S-s. B+P. Pr. II. ep. 1. cafe 1. of book 2.

fig. 46. IV. V. S-s. BP. two cafes ift. when S-sis lefs than B P. Pr. III. ep. 3. cafe 7. of book 2. fig. 37.

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In all thefe figures AE and EU are put for S+s, or S-s, and EO always fuppofed B. The required ratio is determined from V when S is cons cerned, but from the fupplement of V when S+s is concerned.

1776.

Review of New Publications.

NEW MATHEMATICAL QUESTIONS.

QUESTION I. By T. P.

43

GIVEN one of the diameters of an ellipfis, and the periphery, to find the fide of an equilateral triangle inscribed therein.

QUESTION IL. By Mr. Robbins.

IN a plane triangle there is given the base, the difference of the fides, and the nearest distance from one of the angles at the bafe to the circumference of the infcribed circle; to conftruct the triangle.

QUESTION III. By Caput Mortuum.

TWO leffer circles being given on the plane of the ftereographic projection, to defcribe a given arc of a great circle within one of them, fo that when continued it shall touch the other.

An Impartial Review of New Publications.

ARTICLE I.

OBSERVATIONS Hiftorical, Critical, and

Medical, on the Wines of the Ancients; and the Analogy between them and modern Writers. With general Obfervations on the Principles and Qualities of Water, particularly thefe of Bath. By Sir Edward Barry, Bart. 155. Cadell.

The learned author's obfervations have great merit-all wine merchants and wine drinkers, may be much benefited by perufing them. The general properties of the wines of the ancients, are here explained from obfervation, facts, and the established principles of fermentation and philofophy. Rules are given alfo for the preparation and manage ment of vinous liquors. We are told that the ancients in depurating or fining their wines, ufed plain and burnt falt, bitter almonds, the whites of eggs, and particularly ifinglafs.

But our author obferves, "that when the wines continued more obftinately foul than ufual, they added fand, or marble finely powdered. They were much better acquaint ed with these arts than our modern winecoopers, who pretend to conceal, as valuable fecrets, fome of thefe common forms; but I do not find that they ever made ufe of arfenic, or any noxious mineral bodies, in fining down their wines, which certainly, by its very fuperior gravity, will powerfully attenuate them, and force down any lees, which will in fome time entirely fubfide, perhaps without communicating any noxious quality to the wine; but the too early ufe of fuch wines has been often fucceeded with fatal confequences. I fhall mention a remarkable inftance of this kind, which came within my obfervation. Three gentlemen of diftinction had dran's pretty freely of white

wine, which had been fined down with arfenic. Two of them died in the country in a few days, the other, who came to town, either from the strength of his conflitution, or having drank a lefs quantity, furvived: but the effects of it appeared foon in bloody fpots over the whole furface of his body; his urine, faliva, and whatever he hawked up, or expectorated, was deeply tinged with blood; thefe appearances cealed in fome time, and he became cedematous, However he recovered; but though his ftate of health was from that time very imperfect, yet he married two years after, and died in about four of a dropfy, owing to a total diffolution and acrimony of his humours, from this mineral poifon-Mineral poifons of this kind are generally fo violent as immediately to fhew their effects in the ftomach and bowels; and, unless foon difcharged and corrected by emetics, lenient purgatives, and foft plentiful diluents, excite a fatal inflammation and mortification; but how far in a lefs quantity they may more flowly affect the blood and nervous fyftem, can only be determined by future oblervations."

To preferve wines in the bings, he prefers dry fand to faw duft, as its denfity is much greater; and Sir Edward gives a remarkable inftance within his own knowledge of the benefit arifing from a defence of this kind: "A hogfhead of claret, which had been lately bottled, was heaped up in a corner of a merchant's common large cellar, with a view of removing it foon to the wine cellar. In the mean time a load of falt, from the want of a more convenient place, was thrown on the bottles, and remained there feveral months before it was removed. This wine was afterwards found to be much fuperior to the wine of the fame

G&

growth

44

Review of New Publications.

growth, which had been imported and bottled about the fame time, and had been immediately placed in the wine cellar. The large quantity of falt formed a compact vault over the bottles, which entirely defended the wine from the influence of the air, though greatly expofed to it; and probably the coldnefs of the falt contributed to this improve

ment.

The ancients certainly more effectually preferved their wine in larger earthen veffels pitched externally than we can in our bottles, as they are more capable, from their fuperior denfity and capacity, of refifting the frequent changes in the air; and it is a common obfervation, that the wine received into bottles which contain two quarts, proves better than that which had been kept in fingle quarts.

It appears very probable, that our beft modern wines, efpecially thofe of a delicate texture and flavour, may be more ef fectually preferved in earthen veffels, of a larger fize than our bottles, well glazed externally and internally. The veffels of this kind, which were formerly ufed for that purpose, were pitched externally, and lined internally, on account of their being porous, and imperfectly vitrified; but our artifts are arrived to fuch a perfection in this article of manufactory, that their glazed veffels are impervious to the air, and incapable of communicating any bad tafte to any liquors contained in them; however pitching them externally would be a greater defence, especially when the glazing is not equally firm."

We cannot conclude this article without obferving, that claffical fcholars will find Leveral paffages in Horace, &c. agreeably illuftrated, and new light thrown upon them, in this work.

II. Hints to Gentlemen of landed Property by Nath. Kent. 55. Dodfley.

Gentlemen and farmers will find in this volume, many valuable hints on the following particulars. Of the application of foil to its right ufe; draining; natural and artificial graffes; improving meadow and pafture land; a fuitable ftock of cattle; mamures; turneps; cole and rape feed; hops; building and repairs; timber and planting; advantages of fmall farms; importance of cottages; diftrets of the poor, and increase of rates.

Of the advantages refulting from small farms, and thofe of the most profitable fize defcribed, Mr. Kent thus fpeaks, "Every fpeculative Englishman who travels through the Auftrian Netherlands, is aftonished at the great population of that country, and at the fight of the markets, which are plentiful beyond defcription. Upon enquiring into the internal state, and regulation of the country, he finds that there are no large farms, no clafs of men who pafs under the character of gentlemen-farmers, acquiring large fortunes merely by fuperintending the

Jan

bufinefs of farming, but that the whole country is divided into much smaller portions than land is with us, and occupied by fet of laborious people, who in general work for themselves, and live very much upon a footing of equality.

This feems a prefumptive proof, that agriculture, when it is thrown into a number of hands, becomes the life of industry, the fource of plenty, and the fountain of riches to a country; but that monopolized, and grafped into few hands, it must dishearten the bulk of mankind, who are reduced to labour for others instead of themselves; muft leffen the produce, and greatly tend to general poverty.

I fhall not attempt wholly to account for the amazing increafed price of provifion's with us. There are, undoubtedly, many

caufes which contribute to it; but it is very evident that no fingle caufe affects it, fo much as the deftructive practice which has prevailed, for near half a century back, of demolishing fmall farms. This abfurd cuftom, which is not without its advocates, draws its birth from ill-digefted calculations; is attended with great cruelty to individuals; and ends in confiderable private lofs, and public calamity.

The fpecious inducements are, to avoid trouble, to fave expences in repairs, and to fecure the rent by having more capital te

nants.

Granting these arguments their utmost weight, they may be eafily confuted.

Those who contribute towards the deftruction of fmall farms, can have very little reflection. If they have, their feelings are not to be envied. Where this has been the practice, we fee a vaft number of families redu

ced to poverty and mifery, the poor rates much increased, the fmall articles of provifion greatly diminished in quantity and number, and confequently augmented in price.

The increase of farms has a general bad tendency, for as foon as the little schools of industry are grafped into the hands of an over-grown, rapacious farmer, the former Occupiers are, at once, all reduced to the ftate of day-labourers; and when their health or frength fails, there is but one resource; they, and their children, are thrown upon the parish. This has undoubtedly fwelled the rates to their prefent enormous height, more than any cause whatever.

The mechanic and manufacturer next feel the blow. The market wears a different face. The vast number of poultry, the quantity of pork, and a variety of other mali articles of provifion, are no longer fup. plied in their former abundance. The great farmer railes no more of thefe, than are ne ceffary for his own confumption; because his wife and children will not take the trouble and care of them, or condefcend to

attend

1776.

Review of New Publications.

attend the market, like the wives and children of little farmers. His views are formed upon a large scale, and every thing flows from him in a wholefale channel. And as no man can execute any very extensive bufinefs, fo well as that which lies in a more contracted space, he muft, when he has a great deal upon his hands, neglect many imall objects, partly for want of time, and partly because they appear trivial in their nature and many trifles added together, make a large deficiency upon the whole.

The cafe is different upon the Imall farm. Here the tenant's great dependance refts upon trifles merely; and therefore it behoves him to make the most of every thing. As he has no great space to fuperintend, it lies under his eye at a times, and feafons; he feizes all minute advantages; cultivates every obfcure corner; generally accumulates more manure in proportion to his land; and confidering his animal as well as vegetable produce, has likewise in that a greater proportion.

He does great part of his work with his own hands; and every man works more chearfully, zealoufly, and diligently for himself, than for another. His wife and children are likewife of great fervice to him, efpecially if his gains depend much upon a dairy. And, in general, the children of thefe little farmers prove the moft ufeful people the country produces. The girls make the beft dairy-maids; the boys the best gentlemen's bailiffs; the best head-men in larger farms; the best perfons to fuperintend, and manage cattle; and, in a word, the moft regular fervants, in moft capacities.

Upon an eftate of one thousand pounds a year, I wish to fee fomething like the following proportion: one farm of 160l. one of 1201, one of tool, two of 8cl. two of 60l. two of 50. three of 401. and four of 30l. each. This would be fixteen farms upon a thousand pounds a year, and would be a profitable,divifion to an owner, and to the public. But, inftead of this, the generality of large eftates do not support above a third part of these families. And I will venture to affert, that the poor rates will be much higher in the latter, than in the former mode of allotment; because a great many families, which would get a decent livelyhood upon the farms of 301. 401. and 50l. a year, come to the parifh, as I have before obferved, when they are deprived of this method of fupporting themselves.

III. The Evidence of the Common and Statute Laws of the Realm, Ufage, Records, Hiflory, with the greatest and beft Authorities down to the 3d of George III. in Proof of the Rights of Britons throughout the British Em pire. 25. Williams.

Great authorities and a number of good evidences are here produced in favour of the American claime,

45

IV. The Law of Liberty, a Sermon on American Affairs, preached at the opening of the Provincial Congrefs of Georgia, addreffed to the Right Honourable the Earl of Dartmouth, with an Appendix, giving a concife Account of the Struggles of Switzerland to recover their Liberty, by J. J. Zubly, D. D. Is. 6d. Almon.

6

By the addrefs already inferted p. 35, the reverend writer's ftile and fentiments must be fufficiently known to our readers. His text was James ii. 12. "So fpeak ye and fo do as they that shall be judged by the law of liberty," Which is treated with judgment and perfpicuity,

V. The Speech of bis Grace the Duke of Manchester, against the Bill to prohibit all Intercourse with the Colonies. Is. Kearfly.

This noble Duke fhines as a patriot, and brings a variety of arguments to prove that the late bill which he oppofed was directly oppofite to that great palladium of our liberty, the bill of rights.

VI.On Illicit Love, written among the Ruins of Godstow Nunnery, near Oxford, by John Brand, A. B. Is. 6d. Wilkie.

Godftow is at prefent a ruin on the margin of the Ifis, at a fmall diftance from Oxford. It was formerly a house of nuns, famous perhaps on no account so much as for having been the burial place of Rofamond, daughter of Lord Clifford, the beautiful paramour of Henry the fecond. This monarch is faid to have built a labyrinth at Woodstock to conceal her from his jealous queen, who, daring his abfence, when he was called away by an unnatural rebellion of his fons, at the fuppofed inftigation of their mother, found means to get access to her, and compelled her to fwallow poison. Frequent walks in this delightful recefs, facred to the moments of contemplation, fuggefted the following thoughts, for the publication of which, the alarming progrefs of lewdness, and confequently of licentioufnefs of manners, which indeed threatens the diffolution of cur ftate, fhould be accepted as an apology.

The following extract is felected from this agreeable poem for our fair readers. Ah hapless maid! th' ætherial power began, (While penfive fadnefs thro' my bofom ran!) What mov'd thee first thy father to difgrace? The boaft and brand of Clifford's noble race! Cou'd icy age thy youthful breaft infpire, Or e'er grey hairs enkindle green defire? Love's living fmile ambition's frowns devour, And pleasure flies the rude embrace of pow'r. Could Henry's crown a charm fo pow'rful prove,

To blanch the negro front of lawless love? Too justly blam'd! to blast whose fame confpire

A lover old, wrong'd Queen, and injur'd fire!

I fee the father tear his hoary hairs, And beat a bofom, tack'd with hopeless cares;

Involée

46

Review of New Publications.

Invoke high Heav'n on Henry's head to

fhow'r

The vengeful light'nings of incenfed pow'r
Bare the red arm against th` adult'rous flame,
And hide in duft a darling daughter's fhame!
The pray'r's preferr'd-Nor ever move in
vain

The holy lips of age, incens'd by pain.
War's ftern alarms their infant loves annoy,
And black remorse fucceeds the blaze of joy.
In vain has Woodstock rear'd her haughty
tow'rs,

In vain immur'd thee in meand'ring bowr's:
Eludes no lab'rinth guilt's intrufive eyes,
And confcience follows wherefoc'er the flies!
How chang'd by abfence ev'ry haunt re-
maina!

The fcene of pleafures paft, of prefent pains!
There mourn, fair maid! till o'er the murky
gloom,

Repentance fhine to mitigate thy doom:
By man unheard, unwept; and unforgiven,
The mercy earth denis, draw down from
heav'n!

The dark retreats ftern jealousy explores,
Fate's clue conducting thro the mazy doors!
See guilt at once, and injur'd love arraign,
While pity pleads, and mercy moves in vain!
Nor fighs, nor pray'rs, nor tears in torrents
fhed,

Avert the doom from her devoted head,
[ted bed!
Till poifon's fpumy bowl avenge the spot.
Here paus'd the pow'r ! and having glean'd
her fiore

From ages pait, to future fram'd her lore.
Be warn'd ye fair! (the cried) by Clifford's

fate,

What vengeful woes on lawless love await?
The phantoms, fanty pleasure rais'd, _ shall
[gall!
fail,
And foon her lufcious fweets be dafh'd with
flitting
Stil picature flies from guilt on
[dings

wings,
And mid her flow'rs the ferpent' forrow
Tranfcribe the tale that on this wall is
wrought,

The tablet hangs a toilett for your thought!
Here look-nor to thofe fitting mirrors fly
Where fouls are poilon'd by the pleasur'd eye;
Nor vainly with, to future tortunes blind,
Lucretia's face, without her fairer mind!

Think then! and from the crime let

thought restrain,

For transient joys, what lafting ills remain !
The fall in vain from honour's height you

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Jan.

VII. Adventures of Alonso, containing fore Ariking Anecdotes of the prefent prime Minifter of Portugal, 2 vols. 5s. Bew.

The most striking anecdotes we shall fele next month: the adventures contain fome pleafing particulars, and extraordinary events; fome of them too extraordinary to be true; however, at laft, Alonfo is reconciled to his father, furvives him, and inherits great wealth. His crime was an intrigue with a married lady, and running away with her, which involved both in numerous evils. Warned by their errors and fufferings, may others avoid their evil footsteps.

VIII. A Letter to Lord Cathcart, concern ing the Recovery of Perfons drowned and feemingly dead, by Dr. William Cullen. 1s. 6d. Murray.

The Author hath difplayed great judgment and humanity: he obferves, that lite doth not ceafe immediately upon the ceffation of the action of the lungs and heart, and the confequent ceafing of the circulation of the blood, but on a certain condition in the nerves and mufcular fibres, bywhich they are fenfible and irritable, and on which the action of the heart itfeif depends. As long as this fubfifts it is prefumed, that the action of the heart and lungs, the circulation of the blood, and therefore all the functions of life may alfo, though they have many of the long cealed, be again entirely restored. The directions for the recovery of perfons drowned, are ju dicious, and very inilar to thofe already recommended by the London fociety for the fame purpole.

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IX. An Heroic Epifle to Lard Craven. Is. Wheble.

If his Lordship faid at the county meeting at Abingdon, "I will have it known there is refpect due to a Lord," for which he is here fatyrized, we think he juftiy deferved fome of the lines here beftowed upon him, but our pact is not a Juvenal.

X. Elegiac Verfes to a young Lady on the Death of her Brother, by M. Robinson, 15. Johnson.

For, "The first effay of an early mufe," commendable.

XI. An Efay on Politeness, to which is prefixed an allegorical Description of the Origin of Politeness, by a young Ge■rleman.

Law.

This young gentleman fhould have much longer vilted the two chief places of inftruction, "The academy of fcience, and the before he ven univerfity of the world," tured to write on politeness.

XII. A folemn Declaration of Mr. Daniel Perreau, addreffed to the Public. 15. Evans.

In this publication, the writer folemnly declares both himfelf and his brother to be free and innocent from every degree of criminal knowledge in the forgeries for which they fuffered death, and that they fell innocent

victims

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