(247) A certain Body on the Surface of the Earth, weighs 112 lb. the Queftion is, whither this Body muft be carried that it may weigh but 10lb. Anfwer, To 3,3466 Semi-diameters from the Earth's (248) If a Body weighs 16 Ounces upon the Surface of the Earth, what will its Weight be 50 Miles above it, taking the Earth's Diameter at 7970 English Miles? Anfier, 15 Ounces, 9 Dr. 111228. (249) The lefs porous a Body is, the greater its Density; now the Moon's Denfity or Compactness is to that of the Earth as 123 to 100: What Proportion then is there between the Quantity of Matter in the Earth, and that in the Moon, fince the Earth's Diameter is 7970 Miles, and that of the Moon 2170? Anfwer, There is 4c times more Matter in the Earth than in the Moon. (250) There is a vaft Country in Ethiopia Superior, to whose Inhabitants the Moon doth always appear to be most enlightened when she is leaft enlightened; and to be least when moft, according to the 21ft Paradox of Gordon's Geographical Grammar; admitting the mean Distance of the Earth and Moon's Centers 240,000 Miles: In what Proportion is this Illumination? Anfwer, The Side turned from the Earth, at the New, is more enlightened than that obverted to the Earth at Full, in the Proportion of 4152 to 4076 nearly. (251) The Cubic Inch of Marble is 1,5688 oz. Avoirdupoiz; what Difference is there, in Point of Weight, between a Figure, containing a folid Foot and half of Stone, and another of equal Dimenfions in Brafs, 4,63 Ounces whereof make a Cubic Inch? Anfwer, Cut. 4.1.19. (252) The Sum Total of any Rank of Numbers equally increafing, is found by multiplying the Sum of the firit and laft, by half the Number of Terms. How many Strokes do the Clocks of Venice (which go on to 24 0'Clock) ftrike in the Compass of a natural Day? Answer, 300. (253) The Length of my Garden is 94 Feet; now if Eggs be laid along the Pavement a Foot afunder, and be fetched up fingly í fingly to a Basket, removed one Foot from the laft: How much Ground muft he traverse that does it? Anfwer, 1 Mile, 5 Furl. 21 Pol. 3 Feet. (254) By multiplying 16 Feet, the Defcent of an heavy Body, near the Earth's Surface, in one Second of Time, by as many of the odd Numbers, beginning from Unity, as there are Seconds in any given Time, viz. by 1 for the first; 3 for the fecond; 5 for the third; 7 for the fourth, and fo on'; the Sum total will give the Space it has paffed, any where on this Side the Center of the Earth, in that Time: Suppose a Stone let go into an Abyfs, fhould be stopped at the End of the 11th Second, after its Delivery, what Space would it have gone through? Anfwer, 1936 Feet. It may also be proved, that the Velocities acquired by Bodies in falling, are in Proportion to the Squares of the Times in which they fall. For Inftance, let go three Bullets together; ftop the firft at one Second, it will have paffed 16 Feet as before: Stop the next at the End of the Second; it will have fallen four times 16 Feet, or 64; and ftop the lat at the third Second, and the Distance will be 144, or 9 times 16; and so forward. (255) What then is the Difference between the Depth of 2 Wells, into each of which, fhould a Stone be droped at the fame Inftant, one will meet with the Bottom at 6 Seconds, the other at 10? Anfwer, Difference 1024 Feet. (256) If a Stone be 19 Seconds in defcending from the Top of a Precipice to the Bottom; what is the Height of the fame, according to the foregoing Canon? Anfwer, 1014 Fathoms. On the contrary; to determine in what Time a heavy Body will, by Virtue of its natural Tendency towards the Center of the Earth, reach any Place affigned, on this Side of the fame; fay, as 16 Feet are to the Square of one Second, or 1, fo is any given Distance, to the Square of the Seconds required. (257) In what Time will a Mufquet-Ball, droped from the Top of Salisbury-Steeple, faid to be 400 Feet high, be at the Bottom? Anfwer, 5 Seconds. (258) If a Hole could be bored through to the Center of the Earth, and the half Diameter of this Planet was proved to be 3923 times 5000 Feet; in what Time, after the Delivery of a heavy Body on its Surface, would it arrive at its Center? Anfwer, 18 Min. 27 Sec. 48, 7207 (259) The (259) The Length of Pendulums are to one another reciprocally as the Squares of the Number of their Vibrations, made in the fame Space of Time. If then a Pendulum, 39,2 Inches long, in our Latitude, fwings Seconds, or 60 times in a Minute; what Difference is there between the Length of one, that vibrates half Seconds, or 120 times in a Minute; and another that swings double Seconds, or 30 times in a Minute? Anfwer, 12 Feet, 3 Inches. (260) Again, What Difference will there be in the Number of Vibrations made by a Pendulum of 6 Inches long, and another of 12 Inches long, in an Hour's Time? Answer, 2695,14. (261) What Difference is there in the Length of two Pendulums, the one fwings 30 Times, the other 100 Times in an Hour? Answer, 6036 Feet. (262) Give the Length of a Pendulum that will swing once in a Third; Ditto in a Second; Ditto in a Minute; Ditto in an Hour; Ditto in a Day. 2. Anfwer, In a Third ,653 Inch; Second 39,2 Ditto; Minute 196 Feet; Hour 2 Miles; Day 53 Ditto. (263) Observed, that while a Stone was defcending to measure the Depth of a Well, a String and Plummet (that from the Point of Sufpenfion, or the Place where it was held, to the Center of Ofcillation, or that Part of the Bob, which being divided by a circular Line ftruck from the Center abovefaid would divide it into two Parts of equal Weight) measured just 18 Inches; had made 8 Vibrations: Pray what was the Depth, allowing (1150 Feet Second) for the Return of Sound to the Ear? Anfwer, About 400 Feet. The Sum Total of any Rank of Numbers, not equally progreffive, but multiplied from firft to laft, by one common Factor, may be univerfally found by multiplying the last of the Terms by the common Multiplier, and from the Product deducting the first Term, divide the Remainder by the faid Multiplier lefs; the Quotient will be the Total fought. (264) On New-Year's Day, a Gentleman married, and received of his Father-in-law a Guinea, on Condition that he was to have a Prefent on the first Day of every Month, for the first Year, which fhould be double ftill to what he had the Month before: What was the Lady's Portion? Anfwer, 42991. 155. (265) What is an Annuity to expire in a Dozen Years worth, difcounting 10 Cent. Annum, by compound Intereft? Anfwer, 6 Years, 297 Days Purchase. The Form of an English BOND, to which may be put any CONDITION. NOW all Men by these Presents, That I [Benjamin K Bidfair of Stepney, in the County of Middlefex, Rope maker] am held and firmly bound to [William Wellmeant, of Sutton-Colefield, in the County of Warwick Efq;]` in One hundred Pounds, lawful Money of Great Britain; to be paid to the faid [William Wellmeant] his certain Attorney, Executors, or Adminiftrators: For the Payment whereof, I bind myself, my Heirs, Executors and Adminiftrators, firmly by these Presents: Sealed with my Seal Dated this [firft Day of September] in the [Fourth] Year of the Reign of our Sovereign Lord [GEORGE THE THIRD] by the Grace of God, of Great Britain, France, and Ireland [KING] Defender of the Faith, and fo forth. And in the Year of our LORD [One thoufand Seven hundred and Sixty-four.] TH A CONDITION for Money lent. HE Condition of this Obligation is fuch, That if the above bounden [Benjamin Bidfair] his Heirs, Executors, or Adminiftrators, do well and truly pay, or cause to be paid, unto the above-mentioned [William Wellmeani] his Executors, Adminiftrators, or Affigns, the full Sum of [Fifty Pounds] of good and lawful Money of Great Britain, on the [First Day of December] next enfuing the Date hereof, with lawful Intereft for the fame; then this Obligation to be void, or elle to remain in full Force. Sealed and delivered, (being first legally ftamped) in Prefence of A. B. C. D. Benjamin Bidfair, (L. S.) When a Bond is given in Confideration of the Value received the Obligation is always to be made for double the Value in the Condition. The Dates of legal Inftruments, Sums of Money, and the Number of all other Things Specified in them, must be written in Words at length, never in Figures, for fear of Alterations. The Inftruments themselves, as well as all Proceedings at Law, must be written wholly in English, according to a late Act of Parliament. A CONDITION to ftand to the AWARD` of T Arbitrators. 2 Jan. 1. 1764. HE Condition of this Obligation is fuch, That if the above bounden [Benjamin Bidfair of London, Merchant] his Heirs, Executors, and Adminiftrators, and every of them, do and fhall in all Things well and truly ftand to, obey, abide by, perform, fulfil, and keep the Award, Order, Arbitrement, final End and Determination of [Anthony Aimwell, and Michael Makepeace of London, Merchants] Arbitrators indifferently named, elected, and chofen, as well on the Part and Behalf of the above bounden, [Benjamin Bidfair] as of the above named [William Wellmeant] to arbitrate, award, order, judge, and determine of, and concerning all Manner of Action and Actions, Caufe and Caufes of Actions, Suits, Bills, Bonds, Specialties, Judgments, Executions, Extents, Accompts, Debts, Dues, Sum and Sums of Money, Controverfies, Trefpaffes, Damages, and Demands whatfoever; at any Time or Times heretofore had, made, moved, brought, commenced, fued, profecuted, done, fuffered, committed, or depending by or between the faid Parties, so as the Award may be made and given up in Writing, under their Hands and Seals, ready to be delivered to the faid Parties, on or before the [firft of February next enfuing the Date hereof.] But if the faid Arbitrators do not make fuch their Award of and concerning the Premifes, by the Time aforesaid, that then, if the faid [Benjamin Bidfair] his Heirs, Executors, and Adminiftrators, for his and their Parts and Behalf, do in all Things, well and truly ftand to, obey, abide by, perform, fulfil, and keep the Award, Order, Arbitrement, Umpirage, final End, and Determination of [Ferdinando Finishall of London Efq;] Umpire indifferently chofen between the faid Parties, to end the faid Matter and Differences, fo as the faid |