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1776.

Anecdote of an Ancestor of the Leeds Family.

The Americans have always fhewn an affectionate regard to the king, and they are truly fenfible of the neceflity and advantage of a perpetual union with the parent state; but undeserved feverities cannot be productive of any pleafing returns. The Americans firmly believe that the claim at prefent endeavouring to be enforced, would render them mere flaves, and it is their general motto, death or freedom. The parliamentary, or, as they fay, ministerial claim is now written in letters of blood, and that will be far from making it more acceptable to American readers.

On the whole, my lord, fhould this addrefs be deemed impertinent and intrufive, I hope it may still be excufable from the importance of the caufe, and the fincerity of its motive. In the event of the prefent difpute I look upon all mankind as interested, and though not natural born, his majefty has not another fubject who more ardently witheth that his own repofe and happiness and that of all his fubjects may never meet with any interruption. Whether British troops fhall now drive liberty from out of the greater part of the British empire, and bury her remains in the American wilderness, or whether that wilder nefs fhall flourish and chearfully contribute to make Great Britain the greatest empire of the univerfe, is the queftion now to be decided; and it is not fo unimportant, but it may be expected he that is higher than the highest, and taketh up the ifles like a very little thing, will interpofe in the decifion. The whole American pro

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cefs, my lord, is liable to a revifion, and when righteoufnefs and judgment come once to make an impreffion, many a Felix will tremble.

To reftore peace and harmony no. thing is neceffary than to fecure to America the known bleflings of the British conftitution. This may be done in a moment, and without any disgrace or risk. Let the Americans enjoy, as hitherto, the privilege to give and grant by their own reprefentatives, and they will give and grant liberally; but their liberty they will never part with but with their lives. The day that reitores their liberty, reftores every thing to their former channel ; to enforce the contrary claim, ages may be infufficient, and every day encreases the danger of " a mother's being dashed to pieces on her own children."

That your lordship, in the hand of Providence, may be a happy inftrument to bring the prefent unnatural conteft to a speedy, juít, and honourable iffue; that you may live to fee much of that happiness which must be the refult; is no less my fervent prayer, than that God would blaft every counfel and measure that may have a contrary tendency-that would feparate Britain and America, whom God has joined together that would abridge the rights, liberties, and happiness of the nation, our rightful fo vereign, whom God ever preferve, or any of his fubjects!

I am, my lord,
Your lordship's
moit humble servant,
J. J. ZUBLY.

Sept. 3, 1775.

Genuine Anecdote of an Anceflor of the Duke of Leeds. IR William Hewet, who was Lord Mayor of London in the year 1559, the second year of queen Elizabeth, was a merchant of great eminence in those days, and poffeffed an eftate valued then at more than 6000l. a year. He had three fons and one daughter, to whom the following mifchance happened (Sir William living then upon London Bridge) a female fervant playing with her out of the window over the river Thames, by chance dropt her in, almoft beyond expectation of being faved. A young gentleman named Oborne, an anceltor of the prefent duke of Leeds, in a direct line, being then apprentice to Sir William, at this calamitous acci4

dent leaped in bravely, and faved the child. In memory of which deliverance, and in gratitud, her father afterwards beftowed her in marriage on Mr. Ofborne, with a very great dowry, although feveral young perfons of quality then courted her, particularly the earl of Shrewsbury; but Sir William was pleased to fay, Ofborne has faved her, and Osborne fhall enjoy her.' The Leeds family preferve the picture of the faid Sir William in his habit of mayor, at their feat at Kniveton Hall in Yorkshire, and put a great value upon it. Mr. Ofborne ferved fheriff in 1575, was afterwards knighted, and ferved Lord Mayor in 1583.

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IN

A Defcription of the Counties of Sterling and Clackmannan. (Illuftrated with a Map.)

WN former numbers we have prefented our fubfcribers with Maps of all the counties in England and in Wales, and fome of the counties in Scotland. We intend to finish the furvey of thofe which remain, as foon as poffible, and therefore begin this year with the counties of Sterling and Clackman

nan.

This county is 23 miles long, and 18 miles broad, and contains about 289 fquare miles. Sterling is the capital or principal place in the county, the Vindovera of Ptolemy, and formerly called Striveling, from its fituation. It is placed on a ridged hill, or rock rifing out of a plain, having the caftle, which is reckoned the second in Scotland, at the upper end on a high precipitous rock. It was reckoned the key of Scotland, commanding the paffes between the N. and S. of Scotland. The town is inclosed with a wall, the ftreets are irregular and narrow, except that which leads to the caftie. The Highlanders, in the rebellion of 1715, ftrove to poffefs themselves of this fortrefs, but were prevented by the duke of Argyle; and in 1745 it held out against all the efforts of the rebels of that day, under General (afterwards Lord) Blakeney.

From the top of the caftle, is the fineft view in Scotland, according to the late traveller Mr. Pennant. To the east is a vaft plain, rich in corn, adorned with woods, and watered with the river Forth, whofe meanders, before it reaches the fea, are fo frequent and large, as to form a multitude of beautiful peninfulas: in many parts the windings approximate fo close as to leave only an ifthmus of a few yards. In this plain is an old Abbey, a view of Alloa, Clackmannan, Falkirk, the firth or bay of Forth, and the country as far as Edinburgh, which is 30 miles. On the north, you see the Ochill hills, and the Moor where the battle of Dumblain was fought. To the Weft, the ftraith of Menteith, as fertile as the eaftern plain, and terminated by the Highland mountains, among which the fummit of Ben Lomond is very confpicuous. The Sylva Caledonia,

Jan.

or Caledonian Foreft, began a little north of Sterling.

Several of the Scottish kings refided in this place. The palace is still ftanding, a fquare building, ornamented on three fides with pillars refting on grotefque figures projecting from the wall, and on the top of each pillar is a ftatue, feemingly the work of fancy. Near it is the old parliament house, a large room 120 feet long, very high, with a timbered roof, and formerly had a gallery running round the infide. Below the caftle are the ruins of the palace belonging to the earls of Mar, whofe family had once the keeping of this fortrefs. A confiderable manufacture of coarfe carpets is now carried on in Sterling.

A mile fouth of Sterling, is St. Ninian, remarkable only for its church having been the powder Magazine of the rebels in 1746; who, on their retreat northward, blew it up in fuch hafte as to deftroy fome of their own people, and about 15 innocent fpectators.

Five miles east of Sterling is Alloa, a fmall town, but hath a handfome castle, and a good harbour in the firth of Forth, and feveral coal mines near to it.

Eight miles fouth of Sterling, is another town, which though ill built, is worthy of notice, Falkirk. Near. this place, anno 1298, the English, under Edward I. defeated the Scots, and January 17, 1746, there was another battle as difgraceful to the Englih, as the other was fatal to the Scots. The firft was a well difputed combat, the last a panic on both fides; for part of each army flew, the one weft, the other eaft; each carrying the news of their feveral defeats, while the deftruction of our forces, under General Hawley, was prevented by a gallant officer, who with two regiments faced thofe rebels that kept the field, and prevented any further advantages. Falkirk is fupported by the great fairs for black cattle from the Highlands: about 24000 are annually fold there. They get alfo confiderably by the carriage of goods, landed at Carron wharf, to Glasgow.

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1776.

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MATHEMATICAL CORRESPONDENCE.

Anfwers to the Queftions in our Magazine for November.

QUESTION I. Answered by the Propofer.

Rin the multiplier, and from thence fubtract the multiplicand, the ques ULE. To the multiplicand annex as many cyphers as there are figures ber refulting multiply by the first figure of the multiplier, and the product divided by 9 will give the answer required.

Dem. Call the multiplicand a, the multiplier b, and the first figure thereof

c: then will the product ab = a × 111, &c. x c = ax 1000, &c.—

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9

с

XC = 1000, &c. x a-ax

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999, &c.
9

XC=

QUESTION II. Anfwered by the Propofer, Mr. Bonnycastle, Mafter of the

Conft. On A B the given bafe, let a fegment of a circle bedescribed to contain the given angle. Bifect AB with the perpendicular GE, meeting the circle completed in G and E. Join AE, and find two reciprocals A to EG and GL, whofe difference (hall be 2AE; and from G apply GF

to meet AB produced,

Academy at Hackney.

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greater of thofe reciprocals; and to C, the point where it cuts the circle, draw A, C and B, C, and ABC is the triangle required.

Demon. Join EC, and let fall the perpendiculars ED and CI. The triangles ECG and FGL are fimilar.. EG : GC :: FG: GL, confequently as FG is one of the two reciprocals to EG and GL, GC will be the other, and their difference FC 2 AE by conft. but the triangles EAD and FCI are fimilar, and CF has been proved 2AE, .. CI = 2AD, which is well known to be the difference of the fides of the triangle.

The fame anfwered by Mr. Lawson.

Analyfis. Since the vertical angle is given, the fquare of the bafe- the

I

A

Q.E. D.

B

fquare of the difference of the fides has to the area of the triangle a given ratio, by Euclid's Data, Simfon's Edit. 76. pr. 76. cor. But here the difference of the fides is to be equal to the perpendicular; hence if we put IA the given bafe, and fuppofe OA the difference of the fides or the perpendicular, we fhall have IA-OA2 to IA x OA in a given ratio, and putting AE = AI, by Euc. II. 5. IA2 — OA2 = 10 x OE... the ratio of IO × OE: IA × OA is given, and the problem reduced to determinate fe&tion, viz. to Booke I. pr. 5. Ep 2. Cafe 3. of Mr. Wales's Reftitution, published with my book of Tangencies.

The fynthefis is the conftruction of that cafe in determinate fection. This was the method of the antients; for when they had reduced any problem to a cafe of those tracts which were called the SECOND ELEMENTS, they accounted it fully folved.

Jan. 1776,

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