conftant, when q=0, eq=2, and 0, therefore * = σ, 2x. ૧ ся and q ====,q = 21, and y = 2pcx2 10 Hence the quantity of matter in the globe whofe radius is x, is to the denfity at its furface: 2x:28x2 4px three times the content of the globe to unity. Therefore, when the denfity o, x is infinite, or the fluid is of infinite extent, and its quantity of matter greater than any finite magnitude. Confequently a globe of finite magnitude of this nature, cannot have its particles at reft But to keep them together fo that the preffure may balance the elasticity or fpring, it is neceffary that it be acted upon by fome other force befides its own gravity, as the air is acted upon by the force of gravity of the earth, befides its own, otherwife the particles, being once in motion, would fly off to infinity. in the perfectly elaftic fluid above, fince the denfity is ; it must be infinite at the centre where xo. as The extent, and denfity at the furface of fuch a portion of the infinitely extended fluid, as is equal to any given finite body, as the earth, may be found thus. Let the radius of the earth, and d its denfity; then its quantity of matter 2 x pd == " and xpder I of fuch a globe. Moreover, per queftion, as : 2 and if this y, as it must be to render the fluid continuous, which being fubftituted for above, gives с 4pxr2 72 y 3825 and the radius of the globe above = Corol. As the density of the earth = 1: pedr3 1275 dr, or 1275 r when the denfity of the earth is unity. the mean denfity; and the denfity at its furface = I 12752 3 X 1275 , or its mean denfity 3 times that at its furface. This ingenious and difficult question was alfo anfwered by Mr. William Armstrong, and by Clericus of Southwold, whofe folution is in the Supplement, and by the Propofer Terricola. X 3825 NEW QUESTIONS. I. QUESTION (999) by Mr John Walton. Suppose I am out at fea in a calm day, and finding with my feet even with the fut face of the water, how many acres can I view, my eye being five feet and a half above the water, the earth's diameter being 7970 miles. H. QUESTION (1000) by Mr Wm Pearfon, North-Shields. Near Tyne's fair banks and pleafant river fide A fhady Elm erects his lotty head. The Oak's truc height when cub'd and added to, I found to be, when adde 1 in one fum, Exactly what they call a minimum. The fun of both their height's was found to be III. QUESTION (1001) by Mr Newten Bofaworth, Peterborough. Given the three angles of a triangle, 50°, 60°, 70°, and the arca 12 acres; toy find the fides of the triangle. IV. QUESTION (1002) by Mr John Hutberfal, Rochdale. Given the three perpendiculars of a plane triangle, viz, from the three angular points to the oppofite fides, equal to 10, 11, 12; to determine the tides and the area of the triangle. V. QUESTION (1003) by Mifs Nancy Mafen, of Clapham. A father dying left a fquare field to be divided among his five fons, the feld containing just 30 acres, and to be divided in fuch a manner that the oldeft fon may have 8 acres, the fecond ion 7, the third fon 6, the fourth fon 5, and the fifth or youngest on 4 acres, Now the fences are to be fo made that the oldest fon's fare fhail be a narrow piece of equal breadth all round the field, leaving the remaining tour fhares in form of a fquare; and inlike manner for each of the other fhares, leaving always the remainders in forin of fquares. one within another, till the fhare of the youngest be the innermoft iquare of all, equal to 4 acres. It is required to divide the field geometrically, and to calculate the fides of all the fences. VI. QUESTION (1004) by Mr Alex. Rowe. What plane triangle is that, the natural tangents of whofe angles are whole numbers, the radius being unity? VII. QUESTION (1005) by Mr Tho. Hornby, of Wombleton. It is the common practice in Land-furveying, for the leader and follower of the chain, at each chain's length, to fufpend it from the tops of the arrows; now fuppofing the arrows to be a yard long, above the earth's furface, and fixed perpendicularly to the horizon on horizontal ground, how long ought the chain to be in this cafe, to give exacly tatate meafure; allowing it to be ftretched till its centre of gravity defcend the loweit! poffible, or the middle point just to touch the ground? VIII. QUESTION (1006) by Mr W. Featherstonhaugh, Newcastle. Let ABCD be any parallelogram, and E F, GH any two night lines drawn parallel and equal to the fides AB, AD refpectively; then if through the points G F and E H, right lines be diawn, they will meet the diagonal AC, produced in the fame point P. Required a demonftration. E P 1 IX. QUESTION (1007) by James Glenie, Efq; On a given right line as a bafe fo to construct a triangle, that the ratio of the fum of the other two fides to their difference; fhall have to the ratio of the fum of their cubes to the difference of their cubes, the ratio of 7 to 3; whilft the area of the triangle has to the fquare of the bafe a given ratio, fuppofe that of 1 to 3. X. QUESTION (1008) by Mr J T. Connor, Kensington Acad. A very fine thread of 60 yards being wrapped quite round a pole of one foot diameter it is required to find the distance that a perfon muft walk to unfold it quite off th pole, or to find the length of the spiral defcribed by the end of the thread in unwinding, XI. QUESTION (1009) by the Rev. Mr L. Evans. A gentleman having drunk half a conical glais of wine, the diameter of which being inch, and depth 2 inches, inclined its axis to an angle of 650 with the plane of the horizon; Query the area of the furface of the wine in that position? XII. QUESTION (1010) by Mr Colin Campbell, Kendal. If one end of a block AB rest upon a horizontal plane ACD, and the other be fupported by a wedge CDE in form of a right-angled triangle; the length and weight of the block, as alfo the bale CD. and perpendicular DE of the wedge being given: Query what force must be applied to the back of the wedge parallel to the horizon to keep the block from falling, when a given part CF of the bafe of the wedge is introduced underneath it, and the extremity A fixed to as to be prevented from fliding? N XIII. QUESTION (1011) by Mr John Garnet, Esq. If an 80lb weight with a velocity of 32 feet per fecond, ftriking against a fpring, be found to bend it 2 inches; required the clatic force of the fpring to bent, with the velocity loft and the time in defcribing each 8th part of an inch. XIV. QUESTION (1012) by Amicus. In a certain annual publication, the 768th Diary question is repropofed, and an answer XV. or PRIZE QUESTION (1013) by Mr John Rodham, It Walking uniformly at the rate of four miles an hour, on a straight road, on which was a coach traveling in the fame direction at an uniform rate; one of its wheels giving a crack at every revolution, I counted or heard 70 of thefe cracks a minute before it pafled me, and only 68 afterwards; required, by a direct investigation, how many miles the coach travelled an hour; the motion of found being confidered. The prizes for the feveral folutions have been determined by Let as fullogus: First, for the Prize Queftion, to Amicus and Mr Wm. Armlirong, each 10 Diaries.-2d, for the Prize Enigma, to the Rev. Mr Baker, and Mrs. Furnafs, each 8 Diaries.-3d, for the General Arfavers to the Enigmas, to Mr John Brockbank and Mr T. R. Smart, each 8 Diaries. -4th, for the Rebufes, Queries, &c, to Mr Newton Bosworth and Mr Ra. Dutton, each 6 Diaries: all of whem will please to fend for them to Mr Horsfield at Stationers Hall, London, where allo correfpondents may direct their letters for the Diary, but with this addrefs, viz. To the Author of the Ladies' Diary, Stationers Hall, London, all which letters mut be franked or post-paid, other wife, they will not be received; and the last of them must be lent before the first of May, but thofe for the folution of the Prize Enigma and Prize Question before Candlemas Day. And along with all new Questions, Enigmas, Rem. bujes, and Charades, must be sent their answer. OR, A LOYAL ALMANACK For the Year of HUMAN REDEMPTION 1796, Being the BISSEXTILE, 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 fitted to the fame; The Rising 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, Aftrological Obfervations on the Four Quarthe Year. A remarkable CHRONOLOGY; the ECLIPSES; And other MATTERS, both curious able. With farther Observations on the Weather, in, And an HIEROGLYPHIC adapted to the TIMES. By FRANCIS MOORE, Physician. LOND Printed for the COMPANY of STATIONERS, 1796; And Sold by ROBERT HORSFIELD, at their Hall in LUDGATE STREET, [Price Eleven Pence, ftit»hed.] Let my Mufe rouse, and tell what News fhe hears If't doth affront the Turk, or make the Papist mad F. Circumcifion. D' D's Drifes Mutual Afps 2111 a 58 Frefty with 11 driving 22 23 15 6W EpiphTw.Day 16 hips 20 17 and ᎪᏏ ? 8 F Lucian. 18 thighs 28 6 25 Variable 91 19 knees 9S Day 8 2 long Day C 1 S. aft. Epiph. 20 hams 11M Plough Monday 21 legs 12 Tu Old N. Y's Day. 2z ancles 13 W Hilary C.T.beg. 23 feet 14TH Oxf. Term. beg. 24 and 15 F 16 S Night 15.42 1. S. aft. Epiph 18 M Q Char.b.d.k 19 Tu 20 W Fabian. 21TH Agnes. 22 F Vincent. arms z breaft 23 S Hil. Term begins 3 ftom. 24 28 TH 29 F Day incr. 1 12 30 SK. Ch. 1. mart, 10 loins 3 CSexagefima S. 11 fecret 12 5 53 17 8 189 29 near the 1910 39 21 16248 47 end. morn. 23 More fine 7 morn. 8 9 3 |