1776. State of the English Peerage from 1603 to 1776. 539 the duft, when they meet in a parlia ment, can do the public bufinefs with that chearfulness which might be expected from freeborn fubjects, would be a question in any other country, except that unfortunate ifland, the English inhabitants whereof have given more and greater examples of their loyalty and dutifulness, than can be fhewn in any other part of the world. What part of these grievances may be thought proper to be redreffed by fo wife and great a minifter as Sir Robert Walpole, he perhaps will please to confider; efpecially because they have been all brought upon that kingdom fince the Revolution, which, however, is a bleffing annually celebrated there with the greatest zeal and fincerity. I most humbly entreat your lordship to give this paper to Sir Robert Walpole, and defire him to read it, which he may do in a few minutes. I am, with the greatest refpect, my lord, Your lordship's Moft obedient humble fervant, For the LONDON MAGAZINE. State of the English Peerage, from 1603 to 1776. On the Acceffion of James I. the Peerage was: 1 Marquis 16 Earls 2 Viscounts 40 Barons 59 The Number in 1774. 3 Princes 13 Viscounts Among the very numerous Irish peerage, there are not, at this day, any more than three peers of old Irish families, namely, the earl of Inchiquin, of the royal blood of the O'Briens the earl of Upper Offory, (who, though of the Norman name of Fitzpatrick, is defcended from the kings of Offory, who fprang from Heremon, the first monarch of Ireland of the Milefian race;) and lord Lifle, defcended from the O'Briens, whofe ancestors being lent auxiliaries in fome of the provincial wars; obtained the name of Guil-Yfaght, or Lent-men, which has fince been contracted into the word Lyfaght, the name of his lordship. As it may appear strange that only three families of the old Irifh fhould enjoy the dignity of peerage, and as the peerage of Ireland is very nume Of English origin, rous, it may not be unpleafing to fome of your readers, to give an account, and fhew what families compofe it, The prefent peerage of Ireland confits of twenty two fpiritual, which are, four archbishops and eighteen bifhops. The temporal peerage contains one duke, fixty-five earls (including two of the royal blood) forty-fix viscounts, forty-feven barons, and four peerefles in their own right, making in the whole, one hundred and eighty-five-within fix of the number of English peers, and ninety-eight more than thofe of Scotland Taking away from the above number the twenty-two fpiritual lords, the four peereffes, and the two royal earls, the remainder will be one hundred and fifty-feven, whofe origin are as follows: To the EDITOR of the LONDON MAGAZINE. SIR, Pope. I AM not one of thofe fufty old lofophical angelick, instantly changed bachelors, who make it their bufinefs to feize every opportunity to rail against the fair fex, merely because their own perfons or favage difpofitions have excluded them from their favours, The truth is, fir, I am a widower, now got on the wrong fide of fixty, and, like many hundreds at my age, can diftinguith charms in the fair, which I am not yet willing totally to relinquish History tells me, that there are in the world many mountains, whose tops are covered with fnow, while the fun hines in the vallies. I am rich, and have no room to complain of my conftitution; but am a little angry with a trick lately put up. on me. Chance brought me acquainted with a young danfel of two-andtwenty. Love, prudence, and fincerity, feemed to be engraven on her countenance, and I thought myself happier than king David in the evening of his life. "What is the fire and impetuofity of youth, (the would fometimes fay to me) but the certain companions of inconftancy? In age, ftability and wif dom mark every ftep, and love and prudence join hand in hand. We tafte no pleasures amidst the fcorching rays of the noon-day fun; but find happiness and delight when fanned by the gentle evening zephyrs. In youth, love is a tyrant, who is brought to reafon only by time, when it becomes the gentle monarch, and rules with peace and moderation: Youth and age fhould always be united to make the prudent and the happy pair; fince the wisdom and experience of the one are neceffary to check the youthful and unbounded fallies of the other. So happy am I in my prefent fituation, that nothing but death or your difpleasure hall part us. female rovers follow my example, and Let youthful from me learn how to be happy.' How could I, fir, be fearful of too much indulging fuch a fweet and phi my old, pedantick, gothic drefs, into and, as thus newly caparifoned, I one adapted to the modern tafte, could not help thinking, that I had paft roll of my life. I accompanied cut off at least twenty years of the my charmer to all the public places of diverfion, lived high, and seldom went to bed but by the light of Aurobe permitted to speak in the language ra. "But, O! my Galatea, (if I may of Ovid) thou who art fairer than the leaf of the fnow-white pivet, gayer than the meadows, taller than the alder, brighter than glafs, and more sprightly deceitful? And why did nature give than the tender kid," why art thou thee the tongue and perfon of an angel, but the heart and falfity of a fyren? enchanting pleasures, while wafting To be fhort, fir, amidit all these. from fhore to fhore on this ocean of defudden, for the gout (that they light, my career was stopped on a told ine was my diforder) confined me ance. at home, and brought me to repentI was however ftill happy in the charmer; but how shall I express my foothings of my little philofophical horror and confternation when I received the following billet inftead of her ufual carefles!" I fly to the arms of a youth, with whom I shall enjoy the fruits of your folly, nor little cath I have now borrowed from think much of the few notes and the you. Love is not to be purchased by money: old men should take care of the latter, and give over all thoughts of rule, a young girl may flatter an old the former; for take this as a certain man, but can never love him. As winter and fummer cannot be united, fo neither can youth and old age in a and is the beft advice you ever can or mutual paffion. This will be the last, and philofophical will receive from your angelic, fweet, GALATEA." MATHE. 542 oa. MATHEMATICAL CORRESPONDENCE. Anfwers to the Questions in our Magazine for Auguft laf. [67.] QUESTION I. Anfwered by Mr. Jonathan Mabbott of Oldham in Lancashire. expreffion required. 2 Mr. Keech, Mr. Robbins, Mr. Bonnycaftle, Mr. Hampshire, Mr. Buckley, Stoke, and others answered this question. [68.] Question II. Answered By Mr. Bonnycastle. Conft. Make A B=given base, and let Ngiven fum of the fquares of the fides; bifect AB in E, and produce EB to M (by V: 18 Simp. Geo.) fo that EM x MB = N2, make ED BM, and erect the indefinite perpendicular DI; from A apply AC BM, and join BC, and ABC will be the triangle required. Dem. Erect the perpendicular EF, and join AF, now fince AC BM=2ED by Conft., BC2 + 2EC2 =2BE BM2 (Simp. Geo. III. 2.) BE2 + EC2 + BE x BM (III. 10.) therefore BE × BM + BM2 (EM × MB) = BE2 + EC 2 fum of the fquares of the fides (III. 11.) N by Construction. Alfo BF: FC :: BE: ED :: BAA : (2BE) AC (2ED), confèquently the angle B AC is bisected (IV. 18.) and is double the angle B. Q. E. D. Cor. In any triangle, when one angle at the bafe is double the other the leaft fide will always be equal to the difference of the fegments of the bafe made by the perpendicular. The fame anfwered algebraically by Mr. John Buckley of Milnrow near Rochdale. The leaft fide difference of the fegments of the bafe, as is proved in the laft. Therefore put AC x, CB=y, the bafe AB, and the given fum of the fquares of the fidesa, and we shall have (by Trig.) b : y+x :: 18-x x2 bx2 whence j2x2 + bx and x2+ by the quef2 b a 2 tion, which by completing the fquare and extracting the root gives x = Very elegant geometrical conftructions to this question were received from Mr. Johu.. Merritt, Stoke, Mr. Mabbott, Mr. Keech, Le Gos, Mr. Rob. bins, magiques, and others. Let P be the point fought, and p another infinitely near it, draw Cp, BP and the arch pq: then because PFFB is to be a maximum Ff=Pq : but Pq is to Ff in a ratio compounded of the ratio of Pq to qp and qp to Ff, that is, (letting fall CD perpendicular to the tangent PD) of PD to CD and Cp to Cf, which laft in its ultimate ftate is that of CP to CF, confequently PD × CP = CD x CF; whence this. Conft. Take Ce, ge two reciprocals to AB, BC whofe difference (Cg) is equal to BP, and bifect ge in d, then with the Center C and radius Cd describe a circle; to touch which, and the circle whofe center is B, draw the tangent DP, and P will be the point required. Dem. For make CG, CE = Cg, Ce, and draw PG, PE then by Conft. EG x EC: AB × BC 2 CB2, or ED × EC = CB2, but because CG (Cg) and BP are equal and parallel, GP CB; and GP PE from equality of the right angled triangles PDG, and PDE, therefore PE CB and ED × EC PE2; confequently by Euclid VI. 6, the triangles DEP, PEC are fimilar and therefore EPC a right angle, whence CP: PE (CF) :: CD: PD or PD x CP = CD x CF. Q. E. D. The future Favours of this very ingenious Correfpondent will be efteemed an Obligation. Mr. Le Gos, Mr. Bonnycastle, and Mr. Keech favoured us with answers to this question. NEW MATHEMATICAL QUESTIONS. [73] QUESTION I. By Cleonicus. A captain (on Long Island) has three companies under his command, Heffians, Brunswickers, and Scots; and propofes to make an affault with one of the companies on the lines of the Provincials, and promifes them, if they fucceed, 901 guineas among them, in the following proportion; each foldier that shall engage in the affault, to receive one guinea, and the refidue to be divided equally between the other two companies, Now if the Heffians make the affault each foldier of the other companies will receive half a guinea, if the Brunswickers, the others will receive one third of a guinea, and if the Scots, the others will receive one quarter of a guinea: required the number of foldiers in each company. [74] QUESTION II. By Philalethes Weft fmithfieldienfis. The income of a gentleman and his heirs for ever, is one pound at the end of one day, two pounds at the end of two days, three pounds at the end of three days, &c. for ever: he would be glad to know what equal daily payments con tinued |