in one Second of Time, and this was found fufficient to demolish the Walls of Jerufalem; with what Velocity must a Bullet, that weighs but 30lb. be moved, in order to do the fame Execution? · Answer, 66666 Feet in a Second. (280) There are two Bodies, the one contains 25 times the Matter of the other, (or is 25 times heavier) but the leffer moves with 1000 times the Swiftness of the greater; in what Proportion are the Forces by which they are moved? Anfwer, The lefs is moved with a Force 40 times greater than the other. 1 In comparing the Motions of Bodies, the Ratio, or Proportion between their Velocities, will be compounded of the direct Ratio of the Forces wherewith they are moved, and the reciprocal of the Quantities of Matter they contain. (281) A Body weighing 20 lb. is impelled by fuch a Force as to fend it 100 Feet in a Second; with what Velocity would a Body of 8 lb. Weight move, if it were impelled by the fame Force? Anfwer, 250 Feet in a Second. (282) There are two Bodies, one of which weighs 100 lb. the other 60, but the leffer Body is impelled by a Force 8 times greater than the other; the Proportion of the Velocities wherewith these Bodies move is required? Anfwer, The Velocity of the greater to that of the lefs, as 3 to 40. (283) There are two Bodies, the greater contains 8 times the Quantity of the Matter in the lefs, and is moved with a Force 48 times greater; the Ratio of the Velocities of these two Bodies is required? Answer, The greater to the lefs, as 6 to 1. 1. In comparing the Motions of Bodies, if their Velocities be equal, the Spaces defcribed by them fhall be in the direct Proportion of the Times in which they are defcribed. 2. If the Times be equal, then the Spaces defcribed will be as their Velocities. 3. If the Times and the Velocities be unequal, the Spaces will be in a Proportion compounded of the Times and Velocities. There (284) There are two Bodies, one of which moves 40 times fwifter than the other; but the fwifter Body has moved but one Minute, whereas the other has been in Motion two Hours: The Ratio of the Spaces defcribed by these two Bodies is required? Anfwer, The fwifter to the flower, as 1 to 3. (285) Again, fuppofing one Body to move 30 times fwifter than another, as alfo the fwifter to move 12 Minutes, the other only What Difference will there be between the Spaces by them described, fuppofing the last has moved 60 Inches ? Anfwer, 1795 Feet. (286) In comparing of Motions as above, the Ratio of the Times is compounded of the direct Ratio of the Spaces. defcribed, and the reciprocal of the Celerities. There are two Bodies, one whereof has defcribed 50 Miles, the other only 5; the first had moved with 5 times the Velocity of the fecond: What is the Ratio then of the Times they have been defcribing those Spaces? Anfwer, As 2 to 1. (287) When an heavy Body is weighed in any Fluid, it lofes therein fo much of its Weight, as an equal Bulk of that Fluid is found to weigh. Upon this Principle, fuppofe then, a cubic Inch of ftandard Gold in the Air, weighs 10 Ounces Troy, and that by Experiments, a folid Inch of fresh Water is found to weigh 256 Grains Troy: What will a gold Chain weigh in Water, that raifes a Fluid an Inch in a Veffel 3 Inches fquare, when put into it? Anfwer, 85 Ounces, 4 dwts. In Air 90 Ounces. (288) Again, as the cubic Inch of Silver is found to be about 4,444 Ounces Troy, lighter than one of Gold, fuppofing the Workman had adulterated the faid Chain with 14 Ounces and a half of Silver: How much higher would the Water, upon its Immerfion, have been railed in the faid Veffel? Anfwer, 12885 of an Inch higher than fo much Gold. (289) An irregular Piece of Lead Orě, taken from the Yorkfhire Pit, weighs in the Scale just 12 Ounces, but weighed in Water lofes 5 Ounces of that Weight; fo that a Quantity of Water of the Bignefs of the Ore weighs just 5 Ounces, 5 Ounces, as had been faid. From the Derbyshire Pit, a rough Fragment of Ore weighs, out of Water, 14 Ounces, and in Water 9 Oz. the comparative, or the specific Weight of these two Ores is required? Anfwer, 145 to 132, or 12 to 11 in Favour of the fecond. (290) An irregular Fragment of Glafs in the Scale, weighs 171 Grains; another of Magnet 102 Grains. In Water the first fetches up no more than 120 Grains, and the other 79. Then 51 and 23 are the feveral Weights of their comparative Bulks of Water: What then will their specific Gravities turn out to be? Anfwer, Glafs is to Magnet, as 3933 to 5202, or nearly, as 10 to 13 reciprocally. (291) Hiero, King of Sicily, ordered his Jeweller to make him a Crown, containing 63 Ounces of Gold. The Workman thought, substituting part Silver therein, a proper Perquifite; which taking Air, Archimedes was appointed to examine it, who, on putting it into a Veffel of Water, found it raised the Fluid, or that itself contained 8,2245 cubic Inches of Metal; and having discovered, that the cubic Inch of Gold more critically weighed 10,36 Ounces, and that of Silver but 5,85 Ounces, he, by Calculation, found what Part of his Majefty's Gold had been changed: And you are defired to repeat the Process. Anfwer, Alligation 28,8 Ounces. (292) In the Walls of Balbeck in Turkey, there are three Stones laid end to end, now in Sight, that measure in Length 61 Yards; one of which in particular is 63 Feet long, 12 Feet thick, and 4 Yards over: Now, if this Block was Marble, every cubic Inch of which is at least an Ounce and half in weight; what Power would balance it, so as to prepare it for moving? Anfwer, 656 Tons, the Burden of a good (293) The cubic Inch of common Glass weighs about 1,36 Oz. Troy; ditto of Salt Water ,5427; and of Brandy 48926 ditto. Suppofe a Seaman hath a Gallon of this Liquor in a Glafs Bottle, that weighs 3lb. Troy out of Water; and, to conceal it from the King's Officers, throws i it overboard: The Queftion is, if it will fink, how much Force would juft buoy it up ? Anfwer, It is 12,8968 Ounces heavier than the fame Bulk of Salt Water. (294) Another of the Mariners has half an Anchor of Brandy, of the fpecific Gravity above; the Cafk, fuppofe, measures of a cubic Foot, and the folid Inch of Oak is known to be 192 Grains Troy: What Quantity of Lead, 5,984 Ounces Troy to the cubic Inch, is juft requifite to keep the Cask and Liquor under Water? Anfwer, 84 Ounces Troy will just do it. (295) The abfolute Weight of a Body floating in a Fluid, is precifely equal to the Weight of fuch Part of the Fluid as fhall be thrust away thereby and displaced, or, in other Words, to the immerfed Part of the Body: Suppofe then it be by Measurement found, that a Man of War, with all its Ordnance, Rigging and Appointments, draws so much Water as to difplace 1300 Tuns of Sea Water, weighing ,5949 of an Ounce Avoirdupois to the cubic Inch, and that the Measure be taken according to that of London Beer; the Weight of this Veffel is required? K Anfwer, Cwt. 26287.2.19.9 A GENERAL RELEASE. NOW all Men by these Presents, That I [Henry Haveall, of London, Founder] have remised, released, and for ever quitted Claim, and by these Presents, do for me, my Heirs, Executors, and Adminiftrators, remife, release, and for ever quit Claim, unto [Lewis Lightpocket Citizen and Lorimer of London] his Heirs, Executors, and Adminiftrators, all and all manner of Actions, Cause and Causes of Actions, Suits, Bills, Bonds, Writings obligatory, Debts, Dues, Duties, Accompts, Sum and Sums of Money, Judgments, Executions, Extents, Quarrels, Controverfies, Trefpaffes, Damages, and Demands whatsoever, both in Law and Equity, or otherwise howsoever; which against the said [Lewis Lightpocket] I ever had, now have, and which I, my Heirs, Executors, and Adminiftrators, fhall, or may have, claim, challenge, or demand, for or by Reason or Means of any Matter, Caufe, or Thing, from the Beginning of the World, to the Day of the Date of thefe Prefents. In Witness whereof, I have hereunto fet my Hand and Seal, [this Tenth Day of June, in the Year of our LORD One thousand Seven hundred and Sixty-four.] Signed, Sealed, Delivered, (being firft legally stamped) Henry Haveall, (L.S.) in Presence of L. M. N. 0. K A LETTER of ATTORNEY. NOW all Men by thefe Prefents, That I [the Lady Elizabeth Goring, of the Parish of Hampton, in the County of Middlefex, Widow] have made, ordained, conftituted, and appointed, and by thefe Prefents do make, ordain, conftitute, and appoint [Edmund Wingate of Gray'sInn Efq; to be my true and lawful Attorney, for me, and in my Name, and for my Ufe, to afk, demand, and receive of, and from Henry Long of St Mary-le-bonne Efq; Peter Randal of Pancras Gent. Philip Ryley of Wandsworth, Dyer; and Jeremiah Holcomb of Iflington, Innholder] their Executors, Adminiftrators, or Affigns, as well all fuch Sum and Sums of Money as now are, or which fhall, or may, at any Time hereafter become due and owing to me, for or on Account of Rent, for the refpective Tenures, by them, or fome of them now occupied and poffeffed; and upon Nonpayment thereof, the faid Perfon or Perfons, his or their Executors and Adminiftrators, for me, and in my Name, to fue, arreft, imprison, implead, and profecute for the fame, and upon fuch Suit to proceed to Judgment and Execution; and thereupon, the faid Perfon or Perfons, their or either of their Executors and Adminiftrators, in Prifon to hold and keep, until Payment thereof be made, with all Cofts and Damages fuftained, and to be fuftained, by reafon of the detaining of the fame: And upon Payment thereof, the faid Person |