516 Swift's Tale of a Tub, curiously confidered. νόμων, a part of the worship or refpect paid to the immortals. Tis not the firft tranflator that foisted in an oath here." It was fo understood by one of the first commentators on thefe verfes, Hierocles, who has illuftraved it in a beautiful manner, calling it the keeping of the JaLov divine laws, τήρησις των phrafe fimilar to St. Paul's, 1. Cor. vii. 19. τήρησις ετόλων 9. By Me L's own distinction of deities, the infernal are mentioned here; fo that to take Orcus for Pluto, would be a tautology. Pythagoras's order is celeftial or fupreme deities, heroes or intermediate ones, and infernal or loweft, a distinction to which St. Paul perhaps refers, Philip. II. 10. Le Clerc indeed on Heliod's Theog. 1. 231, pretends that "the Platonist, as appears by this comment of Hierocles, perfonified Opsos as the God of oaths": but no fuch meaning can be gathered from Hierocles's words. Mr. URBAN, H. D. S Dr. Swift has found a place in A the Catalogue of eminent Free thinkers &c." for being author of the “Tale of a Tub. Your inferting in your Magazine the following thort cha⚫racter of that work, from the unanfwered "Effays on the Characteristicts”, will oblige Your bumble Servant, guage a bolder or ftronger ridicule, than the well known Apologue of "The Tale of a Tub". Its manifeft defign is to recommend the English church, and to disgrace the two extremes of Popery and Puritanism". *" Some indeed have pretended otherwife. Thus Mr. Wotton, in his Reflections on Learning, fays, "It is a defigned banter upon all that is esteemed facred among men." And the pious author of the Independent Whig, affirms, it was "the fole open attack that had been made upon Chriftianity face the revolution, except the Oracles of Reafn, and was not inferior in banter and malice, to the attacks of Celfus, or Julian, Where or Porphyry, or Lucian", p. 399. by the way, the oddity of the contraft is rema kable enough; that he should pronounce the Tale of a Tuh to be a libel on Chriftianity, while it is in fact a vindication of our ecclefiaf Lical eftablishment; and at the same time entitle his own book a Vindication of our EccleHaftical Eliablishment, while in fact it is a Libel on Chrift anity." Effays on the Characteristics p. 100. The way of dying leather red and yet 1. THE first preparation of the skins, « ་་ 2. Second preparation of the skins for both the dyes. After fqueezing the water out of the fkins, put them into a mixture of bran and water new milk warm, in this pro portion, viz. three pounds of bran for five fkins, with about a gallon of water Here drench to each pound of bran. them three days; at the end of which work them well, and then return them into the drench two days longer, after which take them out and rub them between the hands; fqueeze out the water, and fcrape the bran clean off from both fides, and then wash them again ten times in clean water, and fquecze the water out. Thus far preparatory to both colours; but afterwards thofe that are to be red must be treated as follows 3. Preparations in honey and bran. Mix one pound of honey with three pints of luke warm water and stir them well till the honey be diffolved. Then add two double handfuls of bran; and taking four skins (for which this quan tity will fuffice) work them well in it feparately. Then fold each feparately into a round form, the flesh fides outs ward, and lay them in an earthen pan, fide by fide, if in fummer, and in winter on top of each other. Place the pan floping that the fluid may run fpontaneously Turkish manner of ftaining Leather. taneously from them. An acid fermen- 4. Preparations in falt. After the laft mentioned fermentation, take the skins out on the ninth or tenth day, and rub them well with dry common falt, about half a pound to each, which must be well worked into them. Then they will contract again, and part with a confiderable further quantity of liquid, which squeeze out by drawing each through the hands. Next fcrape them clean on both fides; after which trew dry falt over the grain fides and rubbed well. Then double them length-wife, from tail to tail, the flesh fide outward, and ftrew more falt thinly on the flesh fide, rubbing it in. For which two laft operations a pound and half may fuffice to each skin. Then put them, folded on each other, between two clean boards, placed floping breadthwise, and a heavy weight laid on the upper board, in order gradually to prefs out the moisture they will thus part with. They fhould be continued fo preffed two days or longer, when they will be duely prepared for dying. 5. Preparation of the red dye, in the proportion for four skins, and the manner of applying it to the skins.. To eight gallons of water in a copper, put feven ounces of Shenan* tied up in a linnen bag. Light the fire, and when the water has boiled a quarter of an hour, take out the bag, and put into the water ftill boiling two drams of alum, three quarters of an ounce of turmeric, three ounces of cochineal, and two ounces of loaf fugar. Then let the whole boil fix minutes longer. Put two pints of this liquor into a flat earthen pan; and when cool as new milk, take one skin folded lengthwife, grain fide outward, and dip it in the liquor, rubbing it gently with the hands, then take it out and hang it to dry. Proceed thus with the rest of the * Shenan is an eaftern drug for dying, eafy to be procured at any of the ports of Afia, Africa, or the Levant. It is the joined Kali, by botanists called Selicrnia, of which we have a leffer fpecies in Lincolnshire, but of inferior quality, which yet perhaps may be owing to fome unattended circumstance in the collecting. 517 fkins, feperately, eight times before, cach fred, dipping, fqueezing them by drawing through the hands. Then lay them on one side of a large floping pan for as much of the water to drain as may be without preffure in two hours; or till cold. 6. Of tanning the red fkins.se Powder four pounds of fine white: galls in a marble mortar, fift them fine, and mix them in three quarts of water. Work the skins well in this mixture half an hour or more; then folding them fourfold, let them lye in it twenty four hours; then work them again as before; when taken out and scraped clean on both fides, put them into the like quantity of fresh galls and water. Work them here again three quarters of an hour, fold them up as before, and leave them in this fresh tan three days. On the fourth, take them out again, wash them clean from the galls in feven or eight waters, and hang them up to dry. 7. Manner of dreffing the red-fkins after tanning. When near dry fcrape them with a proper fcraper, on the flesh fide to a requifite thickness. Lay them on a fmooth board, and glaze them with a fleek-ftone. After this, rub them with olive oil, and linnen rag, an ounce and half of oil to four fkins; then grain them on the graining board, lengthwife, breadthwife, and crofswife from corner to corner. 8. Preparation with galls, of the fkins for the yellow dye. When the four fkins are taken out of the bran drenched and clean washed as before directed, Art. 2d. work them very well half an hour more, in a mixture of one pound and half of fine white well powdered galls, with two quarts of clean water. The fkins are then to be feparately doubled lengthwife, rolled up the flesh fide outward, laid in the mixture, and close preffed down on each other, fo to continue two days, the third day work them well again in the tan, and afterwards fcrape them clean from the galls with an ivory or brafs fcraper, but not an iron one. Put them again into a fresh tan, made of two pounds of galls with three quarts of water, and work them well in it fifteen times. ter this double and roll them up as before, and lay them in the fecond tan two days; on the third, work a quarter of a pound of white fea-falt into cach kin, and double and roll them up as Af before 518 Plan for reducing the National Debt. before to be returned into the tan till the day following, when they must be taken out and well wathed fix times in cold water, and four times in luke warm. Squeeze the water by keeping the fkins under preffure between boards half an hour with two or three hundred pounds weight on the upper board, then they will be ready for the dye. 8. Preparation and application of the yellow dye for four skins. Mix fix ounces of Caffiari Gehira, or Dgehirat with the fame quantity of allum, and pound them together till fine, in a marble mortar with a brafs pele. Thus powdered, divide them into three equal parts, one of which put into a pint and half of hot water in an earthen veffel and ftir the mixture. Let the boiled fluid cool till the hand can bear it. Then fpread one of the kins on a flat table in a warm room, the grain fide upward; and pour a "quarter of the tinging liquor, prepared as here directed over the grain side, preading it equally over the fkin with the hands, and rubbing it well in. Do 'the like with the other three fkins, for which the mixture firft made will fuffice. Then repeat the operation twice more feparately on each fkin, with the remaining eight ounces of powder of berries and alum, with the aforefaid proportions of hot water put to them as before. Hang the fkins when dyed, upon a wooden frame, the grain fide outwards, without folding, and let them drain three quarters of an hour, then wash them fix times, or more, in a running tream; which done, prefs them about an hour to fqueeze out the moisture, and hang them up to dry in a warm room. Laftly, drefs and grain them, as directed for the red ones; except that thefe must not be oiled. 'tis true, he was honeft, and took car to employ honeft men under him, and Henry the Great had the firmness to keep him in power, in fpite of all op pofition. My plan is a very plain one. The income of the finking fund was in the year 1746, full fourteen hundred thousand pounds per annum, it has fince been augmented five hundred and eighty thousand pounds, by the reduction of the four per cents to three. And the revenue of the excife, and cuftoms on tea, is, fince that period, encreafed confiderably more than half a million I fhould therefore think, as most of the unfunded debt at the clofe of the war is paid off, that one million might be applied out of the finking fund; and hrlf a million raifed by leafes of the foreft lands upon fines with fmall quit rents. The intereft of thofe who hold places in the forefts, might be very eafily taken care of, without which nothing can be expected to fucceed. Another half million, and, perhaps a great deal more, might be raised by a tax of five per cent. on all legacies (except thofe to children, and grand children) and one year's rent of every real estate, which is left from the right heir, which though I did not know it, I find has long fince been practifed in Holland, and answers the purposes of a land tax; indeed, they take ten per cent. but I think it belt to begin with five, it is next to impoffible even to guefs at what fuch a tax would bring in, as there is no accounting for the whims of humourifts, or the 'fordid ill nature of avarice, which will difinherit a deferving heir for lighting his pipe with a piece of clean paper; and I have heard of a man, who, if the money had not been lent him to pay off his bond to his uncle, would have been totally undone for treating a country cuftomer with a lobster for fupper. From the price that tickets bore în the last lottery, and are like to do in the prefent, it is very evident, that a lottery bearing an intereft of four per cent. per ann. upen lives for a million, would certainly fill, and especially if the blanks and prizes were, after the drawing, thrown into claffes of twenty thousand pounds each, with benefit of furvivorship. I could mention other helps, but as the above will pay off two millions per ann. and convert a third into annuities upon lives, I think I have done enough. Anfiers Mathematical Quefiions answered. Answers to the Mathematical Queflions page 427. D I. QUEST. (22) answered by Mr. Crakelt, of the Charterhouse. Let ZONH reprefent an orthographic projection of the fphere, wherein Z is fuppofed to be the zenith of the required place; P the north pole; HO the horizon; the equator, and DE the parallel of the fun's required declination; and put o a the fine of 18° (1 hour 12 minutes, the fun's afcenfional difference) —s, and x for E G the fine of the midnight depreffion: then by a property of the projection we fhall have Q (1): ao(s) : : Ec: ec, or by compofition and divifion Æa (1+s): Qa (1 − s) : : De: Ee:: (by fim. triangles) D F ( = 2 by pa. 15 of my tranflation of Mauduit's queftion): E G (x): confequently x= of 18° 41′58′′ nearly the depreffion at altitude = 37° 23′ 56′′; the latitude (=90° I-X 2 S N 519 E Trigonometry, and the nature of the 11 I + s 2-25 2 .32060317 the fine midnight; and therefore the meridional 37° 23′ 56′′ + 18° 41′ 58′′) 2 57′ 3′′, and the declination (=37° 23′ 56′′-18° 41′ 58′′) — 9° 20′ 59′′. 2 =619 Mef. Barker, Burrow, Edwards, Ogle, Renshaw, and Reynolds, favoured us alfo with true and concife folutions to this question, II. QUEST. (23) answered by Mess. Barker and Edwards. Put a for the fine of (60°) double the first elevation; e for that of (66°) dou ble the fecond; m tor 50 paces; n for 18, and x for the distance required. Then. by the doctrine of projectiles we shall have a : : : x − m : x + n, and = an+cm 1289. 2593 &c. paces; from whence the elevations ncceflary to hit the mark will be eafily found 32° 9', 57° 51'. c-a The answers given by Me. Burrow, Hale (the propofer) and Renshaw, are nearly the fame. III. QUEST. (24) anfwered by Mr. Stephen Ogle. Let A, B denote the two fides of the triangle; D, E the fegments of the base, and M, N the two given fums: then will A+B+DEM, and A – B + D+EN, and confequently, by addition, 2 A+ 2 D≈M+N: alfo D +, is univerfally to AB as A+B to DE, and therefore by composition, &c. DE will be to A+B as D +E+A−B (N) to A+B+D-E (M); whence the following CONSTRUC. Defcribe a triangle ABC, by prob, I. of Simpson's algebra, whereof AC may be any affumed line, the angle at B equal to the given one, and AB+BC a fourth proportional to N M, and AC: then on C A produced take A G= A B, and DH = M+N. i and having joined the points, G, B, draw HE, E P and E F parallel to G B, B A and B C refpectively, and P EF will be the required triangle. For fince PEF and A B C are fimular, it will be PF: PETEFAC:AB+B C : : N : M; and as DG = A B † AD, DH will be =PE+PD_M+N 2 2 CALCULA, Having obtained the feveral parts of the triangle ABC from Simpson's conftruction, it will be as AB+ AD: A B, B C, A C respectively :: M+N .: PE, EF, PF respectively. 2 Me. Crakelt and Lawfon conftructed this queflion likewife; and Mr. T. Barker (the proposer), Mr, R, Burrow, and Mr. W. Renshaw, anfwered it algebraically. 520 Mathematical Questions answered. IV. QUEST. (25) anfwered by the Rev. Mr. Lawfon. CONSTRUC. Bifect the line joining the two given points, A, B, with a perpendicular meeting the given indefinite line in the point D, and draw the line A D: then demit from C on the faid indefinite line the perpendicular C E, and having made the angle E C F equal to the leffer given one (which, in order to render the problem poffible, muft manifeftly be the fupplement to the greater given angle), apply to A D (from C) C G C F, and draw A H parallel thereto to meet the perpendicular D C produced in H; then with H A as ra dius defcribe a circle, and to the points of its interfection with the given indifinite line, draw A I, A L, BI and B L, and the thing will be done. = L K E C H DEMONSTRA. Demit on L D the perpendicular H K, and through H draw a parallel to CF, meeting L D in fome point I: then by fimilar triangles we shall have CF: HI:: DC: DH:: CG: HA; but (by construct.) ČF = CG, wherefore HI=HA, and I a point in the circumference of the defcribed circle; and the angle I BLIHK= (by the nature of parallels) E C F = the leffer given angle (by conftruc.) and fupplemental to I A L. The calculation will eafily appear from the conftruction. If CF cannot be applied from C to A D the problem will be impoffible. In a manner not greaily different Mess. Crakelt and Ogle gave the conftruction V. QUEST. (26) answered by Mr. Todd, the proposer. In the given right-angled triangle A B C, put AB=m; BC=n; BDx, and DF (perpendicular to A B and per question) =BE≈y: then by fimilar triangles we have, m:n :: m+x: n nx 212 D E, and (by Euc. 47. 1.) y2( = D F2 or B E ́ F F F E bola, let the fides of the triangle be what they will. Now when y or D F is a minimum, B E will manifeftly become perpendicular to A C, and in that cafe H gate diameter or, per common property of the hyperbola we have, G. X GH+H=GH-HXGH+HGH2 HC B 2 2 2 -2 G C2orec2: : eB2: 072; but by fimilar triangles Ce": 2 •2 wherefore or2e H, and ore H= mn The method of finding the 2 area of an hyperbola when the abfciffa is any given quantity being hewn by moft fluxionary writers, it would be needlefs to fpecify it here. SCHOL. This question ftands propofed in Stone's dictionary, 2d. edition; in which it is erroneously obferved, that the curve will be that of an ellipfis, hyperbola or parabola, according as A B is greater, lefs than, or equal to, BC; the equation above given plainly indicating it to be an hyperbola in every cafe. Mr. Emerfon hath alfo given this problem in his treatife of Algebra, but hath only expressed the equation without telling us to what fection it belongs. With equal elegance Me, Barker, Burrow, Ogle, Renshaw, and Reynolds, anfwered this question. NEW |