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The Americans have always Mewn cess, my lord, is liable to a revision, an affectionate regard to the king, and and whien righteousness and judgment they are truly senlible of the necessity come once to make an impreslion, and advantage of a perpetual union many a Felix will tremble, with the parent state ; but undeserved To restore peace and harmony no. leverisies cannot be productive of anything is necessary than to secure to Ame-' pleasing returns. The Americans rica the known blessings of the Britiíh firmly believe that the claim at pre- constitution. This may be done in a fent endeavouring to be enforced, moment, and without any disgrace would render them mere Naves, and or risk. Let the Americans enjoy, as it is their general motto, death or hitherto, the privilege to give and freedom. The parliamentary, or, as grant by their own reprefentatives, they say, miniiterial claim is now and they will give and grant liberally; written in letters of blood, and that but their liberty they will never part will be far from making it more ac with but with their lives. The day ceptable to American readers.

that reitores their liberty, reftores On the whole, my lord, should this every thing to their former channel ; address be deemed impertinent and to enforce the contrary claim, ages intrusive, I hope it may itill be excu may be insufficient, and every day en. sable from the importance of the creases the danger of “ a mother's cause, and the fincerity of its motive. · being dashed to pieces on her own In the event of the prelent dispute I children." look upon all mankind as interelted, That your lordship, in the hand of and though not natural born, bis ma- Providence, may be a happy inftrujelty has not another subject who more inent to bring the present unnatural aruently witheth that his own repose conteft to a speedy, juít, and honourand happiness and that of all his lub- able issue; that you may live to fee jects may never meet with any inter- much of that happiness which must be ruption. Whether British 'troops the result; is no less my fervent shall now drive liberty from out of the prayer, than that God would blait greater part of the British empire, and every counsel and measure that may bury her remains in the American have a contrary tendency-that would wilderness, or whether that wilder: separate Britain and America, whom ness fall flourish and chearfully con God has joined together-that would tribute to make Great Britain the abridge the rights, liberties, and hapgreatest empire of the universe, is the piness of the nation, our rightful foquestion now to be decided; and it is vereign, whoin God ever preserve, or not lo unimportant, but it may be any of his subjects ! expected he that is bigher than the I am, my lord, highest, and taketh up tlie illes like a

Your lordlip's very little thing, will'interpose in the

moit humble servant, decision. The whole Ainerican pro Sept. 3, 1775

J. J. ZUBLY. Genuine Anecdote of an Anceflor of the Duke of Leeds. S'Mayor on Bencion in the chindle and memory of which delive 1559, the second year of queen Eliza- rance, and in gratieuda, her father beth, was a merchant of great emi- afterwards bestowed her in marriage nence in those days, and poßeffed an on Mr. Olborne, with a very great eftate valued then at more than 6000l. dowry, although several young pera year. He had three sons and one sons of quality then courted her, pardaughter, to whom the following mis. ticularly the earl of Shrewsbury; but chance happened (Sir William Jiving Sir William was pleased to fay, · 0fthen upon London Bridge) a female borne has saved her, and Onborne shall fervant playing with her out of the enjoy her.' The Leeds family prewindow over the river. Thames, by serve the picture of the said Sir Wilchance dropt her in, almost beyond liam in his babit of mayor, at their expectation of being saved. A young feat at Kniveton Hall in Yorkfhire, gentleman named Osborne, an ancel and put a great value upon it. Mr. tor of the present duke of Leeds, in a Ofborne served sheriff in 1575, was direct line, being then apprentice to afterwards knighted, and served Lord Sir William, at this calamitous acci. Mayor in 1583.

A Description of the Counties of Sterling and Clackmannan.

(Illustrated with a Map.) I ne forme Subscribers with me apresenti northlef Sterling:

or Caledonian Forest, began a little the counties in England and in Wales, Several of the Scottish kings resided and some of the counties in Scotland. in this place. The palace is still We intend to finish the survey of those' ftanding, a square building, ornawhich remain, as soon as pofáble, and mented on three sides with pillars resttherefore begin this year with the ing on grotesque figures projecting counties of Sterling and Clackman from the wall, and on the top of each nan.

pillar is a statue, seemingly the work This county is 23 miles long, and of fancy. Near it is the old parlia18 miles broad, and contains about ment house, a large room 120 feet 289 square miles. Sterling is the ca- long, very high, with a timbered pital or principal place in the county, roof, and formerly had a gallery runthe Vindovera of Ptolemy, and former- ning round the inside. Below the ly called Striveling, from its situation. cattle are the ruins of the palace beIt is placed on a ridged hill, or rock longing to the earls of Mar, whose rising out of a plain, having the castle, family had once the keeping of this which is reckoned the second in Scot. fortress. A considerable inanufacture land, at the upper end on a high pre- of coarse carpets is now carried on in cipitous rock. It was reckoned the Sterling. key of Scotland, commanding the paso A mile south of Sterling, is St. Nises between the N. and S. of Scotland. pian, remarkable only for its church The town is inclosed with a wall, the having been the powder Magazine of Streets are irregular and narrow, ex the rebels in 1746; who, on their recept that which leads to the castie. treat northward, blew it up in such The Highlanders, in the rebellion of hafte as to destroy some of their own peo1715, ftrove to possess themselves of ple, and about 15 innocent fpectators. this fortress, but were prevented by the Five miles east of Sterling is Alloa, duke of Argyle; and in 1745 it held a small town, but hatb a handsome out against all the efforts of the rebels castle, and a good harbour in the firth of that day, under General (after- of Forth, and several coal mines near wards Lord) Blakeney.

to it. From the top of the castle, is the Eight miles south of Sterling, is anfinest view in Scotland, according to other town, which though ill built, the late traveller Mr. Pennant. To is worthy of notice, Falkirk. Near. the east is a vast plain, rich in corn, this place, anno 1298, the English, adorned with woods, and watered under Edward I. defeated the Scots, with the river Forth, whose mean- and January 17, 1746, there was anders, before it reaches the sea, are so other battle as disgraceful to the Eng. frequent and large, as to form a mul- lish, as the other was fatal to the titude of beautiful peninsulas : in Scots. The first was a well disputed many parts the windings approximate combat, the last a panic on both sides; so clole as to leave only an isthmus of for part of each army few, the one a few yards. In this plain is an old west, the other east; each carrying Abbey, a view of Alloa, Clackman- the news of their several defeats, while nan, Falkirk, the firth or bay of the destruction of our forces, under Forth, and the country as far as Édin- General Hawley, was prevented by a burgh, wbich is 30 miles. On the gallant officer, who with two regiments north, you see the Ochill hills, and faced those rebels that kept the field, the Moor where the battle of Dum. and prevented any further advantages. blain was fought. To the West, the Falkirk is supported by the great fairs fțraith of Menteith, as fertile as the for black cattle from the Highlands : eastern plain, and terminated by the about 24000 are annually fold there. Highland mountains, among which They get also considerably by the the summit of Ben Lomond is very carriage of goods, landed at Carron conspicuous. The Sylva Caledonia, wharf, to Glasgow.

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MATHEMATICAL CORRESPONDENCE.
Answers to the Questions in our Magazine for November,

QUESTION I. Answered by the Proposer.
ULE. To the multiplicand annex as many cyphers as there are figures

, ; ber resulting 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 = 2 X 111, &c. x <= ax

XC 1000, &c.

9 а Х

x= 1000, &c. Xa-a 9

999, &c.

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QUESTION II. Answered by tbe Proposer, Mr. Bonnycastle, Master of the

Academy at Hackney. Conf. On A B the

G given base, let a segment of a circle be described to contain the given angle. Bisect AB with the per. pendicular GE, meeting the circle completed in G and E. Join AE, and find two reciprocals A

I/B to EG and GL, whose difference hall be 2AF; and from G apply GF to meet AB produced, = greater of those 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 similar :. EG: 6C :: 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 fimiJar, and CF has been proved = 2AE, :: CI = 2AD, which is well known to be the difference of the sides of the triangle.

Q. E. D. The same answered by Mr. Lawson. Analysis. Since the ver.

A

B tical angle is given, the Square of the base - the Square of the difference of the sides has to the area of the triangle a given ratio, by Euclid's Data, Simson's Edit. 76. pr. 76. cor. But here the difference of the sides is to be equal to the perpendicular; hence if we put IA = the given base, and suppose OA = the difference of the sides or the perpendicular, we Thall have IA-OAż to IA X OA in a given rario, and putting AE = AI, by Euc. II. S. IA2 - 0A2 = 10 x OE.. the ratio of 10 OE: JA XOA is given, and the problem reduced to determinate siEtien, viz. to Booke I. pr. s. Ep 2. Cale 3. of Mr. Wales's Restitution, publithed with iny book of Tangencies.

The synthesis is the conftruction of that case in determinate fe&tion. This was the method of the antients; for when they had reduced any problem to a case of those tracts which were called the SECOND ELEMENTS, they accounted it fully solved. Jan. 1776.

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