fig. 1ft of the 1ft fpecies, where AD is lefs than the greateft root ap, when the conic hyperbola coincides with its afymptotes, it is evident without farther illuftration, that the hyperbola whofe vertex is t mo be wholly within the afymptotes D8, Dd, whilst the other two cut them (as in fig. 21ft) and the oval ftill remains within the triangle D d♪ (as in the 10th fpecies) bifected by the diameter AD; and this is Mr Stirling's 11th fpecies: and when, the two lefs limits being equal, the oval vanishes into a conjugate point, it is his 15th, and the fame in appearance with Sir Ifaac's fig. 21ft, 15th fpecies. And when, in the limiting equation ax3 + bx2 + cx + d = 9, 4acb2, or the curve has three diameters, it is manifeft. that the only difference this can make, will be, that the hyperbolas c and r will be wholly within the angles at d and, as t is within D; the oval muft remain fo long as the two less roots of this equation are real and unequal, which is Mr Stirling's 24th fpecies, when they are equal the oval becomes a conjugate point, and this is his 25th fpecies, and the appearance as in Sir Ifaac's Eg. 28th, fpecies 22d. As to the curves expreffed by the equation xy2 = bx2 +,cx + d, when it takes the form xy2x2 + b + d. x + bd; the first difcovery of them is not due to Mr Stone, for there is not one word about them in the first edition of his Dictionary, but to M. Nic. Bernoulli, who died in 1726, the year in which that edition was published. They confift of two hyperbolo-parabolic curves like thofe in Sir Ifaac's 57th fig. with an oval on the contrary fide of the afymptote, if b and d be unequal; but with a conjugate point only, if they be equal, For, in the equation xy2 = cxx+6xx+d, y is evidently equal o, both when xb, and when x-d. This queflion was also ingeniously anfivered by Plus Minus NEW QUESTIONS. I QUESTION 878, by Mr Geo Befwick, Coalfhaw Green. 2x3 A Beautiful couple have lately been ty'd, The groom was right lufty, and lovely the bride; A fimple equation will eafily fhew The age of this couple, as noted below. x4 x2 + 2 x 2 y — y2 = √x5 y — √x3 y=2xy, where x+y and y denote their ages in years. II QUESTION 879, by Mr Tho Nield, Writing Mafter, Hawarden. Measuring a fimall inclofure of a rectangular form, I obferved that if 2 poles were added to the breadth and 5 to the length, the area would be increased by 430; but if 5 were added to the breadth and two to the length, it would be increafed by 445. It is required from hence to find the length and breadth of the inclofure. III QUESTION 880, by Mr Jonath. Hornby, Weferdale School. Obferved in the fpring quarter, in latitude 22 deg. north, when the un was due eaft, the difference between his altitude and hour from 6, in degrees, a maximum. Query the time of obfervation. `IV QUESTION 881, by Mr Timothy Simpson, Papplewick. A certtain gamefter is willing to take the odds to a guinea, that he, with 9 halfpence, brings up 3 heads precifely, 4 times in 5 throws: what ought the odds to be? V QUESTION 882, by Mr Matthew Terry, Land-Surveyor. What must be the length of a pendulum vibrating feconds at the the distance of 4 radii from the earth's center? VI QUESTION 883, by Mr Tho Trufwell, of Nuneaton. If a given cone, whofe altitude is 10, and bafe 8, be cut by two planes, the one of which is parallel to the fide, and the other to the bafe; required the point in the fide where the two planes meet, when the area of their fections are equal to each other... VII QUESTION 884, by Mr John Dalton, of Kendal. In the femicircle ACB, whole diameter is AB, and OC perpendicular to it from the centre, from B there is drawn a.chord BF to cut OC in E, and on the fame chord there is taken BD equal to the radius of the femicircle; it is required to determine the rectangle DE. EF, à maxinum. VIII QUESTION 885, by Amicus. A block of marble, in the form of the fruftnm of a hexagonal pyramid, the fide of the lefs end being 6, and of the greater 9 inches, has fix points on the external furface, one foot from the leis end, upon any one of which it will reft in equilibrio, on the point of a odle fixed perpendicular to the horizon. The length of the block is required. IX QUESTION 886, by Mr Thomas Todd, of Darlington, late of Weft Smithfield, London. if the debts a, b, c, d, &c. in pounds, payable at the end of n, n', n', a", &c. t years, &c. Then I fay the equated time from the firft term, by compound in tereft, will be equal to the difference of the logarithm, of the fum of the debts, and lo garithm of the fum of the prefent worths divided by the logarithm of one pound and its intereft for one year; whether it be computed by the old method, by Kerfey's, or by Malcolm's; all giving the fame anfwer. Query the investigation by each method. X QUESTION 887, by Mr John Farey, London. Let GB be a defective hyperbola of Sir Ifaac Newton's 44th fpecies, A its conjugate point, B the vertex, and CH its afymptote; draw BI a tangent to the vertex parallel. to the afymptote, on AB defcribe a femicircle, and draw any line AF, cutting the circle in D, the curve in E, and the tangent BI in F. Then I fay ACACB::DE EF. Required a demonstration. XI QUESTION 888, by Mr John Cullyer, Affiftant at Mr M'Kain's School, Bungay, Suffolk. Being in a thunder ftorm, and having a cylindrical walking ftick, 5 feet long; I' held one end of it in my hand, and caufed it to turn round in a conical motion, in which the other end defcribed circles, parallel to the horizon, 6 feet in diameter; and the tick made 7 revolutions from the inftant of my feeing the lightning till I heard the thunder. From which I defire to know the distance of the thunder-cloud from me. XII QUESTION 889, by the Rev Mr John Hellins. If there be four numbers A, B, C, D, in arithmetical progreffion, whofe common difference is 1, that is, AIB, BIC, and D; and if s a +22=p, and the modulus of Briggs s lathere be put ca, 2a+1 garithme M; and if a be not lefs than 100, S M exprefs the third difference of the logarithms of then fhallpa-thofe numbers, true to 18 places of figures, Query the demonftration, XIII QUESTION 890, by Lieut. Wm Mudge, of the Royal Artillery. If a ftring with the weights W, w, one at each end, be hung on a pulley, and the greater weight W touch the pulley, fo that the lefs may have the whole length of the thread to vibrate by ; and if, at the inftant when it has completed one vibration, and is about to defcribe another, the weight W be fuffered to defcend; query the time of vibration, and the nature of the curve. XIV QUESTION 891, by Major Edzu Williams, of the Royal Artillery . It is required to affign the time of exhaufting the ditches of a fortiefs of water, te within one inch of the bottom, by means of a rectangular cut or notch in the fide from top to bottom, of 2 feet wide; the depth of the ditch or water being 9 feet, the breadth at top 30 feet, at bottom 32 feet, and the whole length of the ditches one mile. XV OF PRIZE QUESTION 892, by Mr Ge Sanderson, London: (Whoever anfwers it before Candlemas Day has a chance for 10, and another for 8 Liaries.) In confidering the prize queftion for last year, I find that fig. 20 of Newton's catague confifts of two infcribed hyperbolas at d and 8, and one containing its afymptotes within its own pace at D; and that fig. 21 canlifts of two ambigenous hyperbolas at d and, and one inferibed at D, without oval or conjugate paint. But between thefe two there are five more curves, effentially different from either; two of which have been defcribed by Mr Stirling at pages 9 and 100. It is therefore required to determine the other three, with an example of a numeral equation for cach." QUERY by Terricola. At what distance from the fun will a given burning glafs make no alteration in the density of the folar rays? The prizes for the feveral folutions have been determined by lot as follows First, for the Prize Queftion, to Amicus 10. and Mr Geo Sanderion 8 Diaries.---2d, for the Prize Enigma, to Mr J Townsend and Mr John Cullyer cach & Diaries and Supplements.3d, for the general Anfwers to the Enigmas, to Mifs Betty Smales and Mr Henry Lee each 8 Diaries and Supplements.---4th, for the Rebufes, &c, to Mr M Fleck and Mr John Rufher each 6 Diaries and Supplements. All of whom will pleafe to fend for them to Mr R Horsfield, Stationers Hall. But all letters containing any matter for the ufe of the Diary, must be directed thus, The Author of The Ladies Diary, Stationers Hall, London." And they must be franked or poft paid, or they will not be received. Several were rejected this year by the postage not being paid." Erratum in the laft Diary. In the fig, page 38, the oblique circle passing through A and R, fhould alfo pafs through the point G. Several Letters came too late to hand; viz. thofe of Meff. Ball, Walton, Wilding, and fome others. OR, A LOYAL ALMANACK For the Year of HUMAN REDEMPTION, BEING THE BISS BXTILE or LEAP YEAR. IN WHICH ARE CONTAINED All THINGS fitting for fuch a WORK; as, A TABLE of TERMS and their RETURNS, The Full, Changes, and Quarters of the Moon; The Rifing, Southing, and Setting of the SEVEN STARS, and other Fixed Stars of Note; the Moon's Age, and A TIDE TABLE fired to the fame, The Rifing and Setting of the SUN; the Rifing, Southing, and Setting of the MOON, Mutual Afpects, Monthly Obfervations; and many other Things, useful and profitable. UNTO WHICH ARE ADDED, Arological Obfervations on the Four Qadded of the Year. An HIEROGLYPHIC, alluding to thefe prefent Times; A remarkable CHRONOLOGY ACPSES; And sher MATTERS, both cu With a particular judgement rofitable. ipfes, and many other Things relaplogy. By FRANCIS MOORE, Physician. L QNDON, Printed for the COMPANY of STATIONERS, 1788. And Sold by ROBERT HORSFIELD, at their Hall in LUDGATE STREET, [Price Nine Pence, ftitched.] A plan and eafy TABLE, fhewing the Time of HIGH WATER. 345 96 เค NOTE, That the Moon's Age being taken noticej of in the TABLE, yo have the Time of HIGHWATER at all,the undernamed Places. Queenborough, Portsmouth, Southampton,Kentish- H h h 16 12 48 2 I 18 2 24 19 3 20 4 12 4 6 21 448 + 26 7 6 24 12 24 7 12 15 30 12 ON 18 3 6 54 5 24 7 398 54 I 24 3 39 4 12.12 42 3 12 4 27 30 3 0 24 6 The for going Table explained. OTE, That tire Moon's Age being taken notice of by the Rule in this TABLE, you may obtain the Time of HIGH WATER at all the Places abovenamed. Obferve, When the Moon is one or fixteen Days old. it is HIGH WATER at London, Tinmouth, Hartlepool, &c. at 3 o'clock, and 48 Minutes past. Obferve the fame of the re, which is plain to the meanelt Capacity. The Day of the Moon's Ageyou have the fixth Column on every Left hand Page of the Calendar. 34 532 1 9753 78 9 96 54 10 39 12 1510 18 I 3 3 36 F2 4 4 54 239 12 5.42 3. 27 9/12 C London, Tinmouth, Hartlepool, Amsterdam, Newcastle, Humber, Falmouth, Severn-mouth, Plymouth, Antwerp, Hull, St. David's, Holms Hague, Peter-port, Dublin, between Beachy and the Ifle of Wight, Yarmouth, St. Magnus's Sound, Combay, without the Cafkets in the Channels. |