Selected quad for the lemma: life_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
life_n	age_n	live_v	old_a	4,232	5	5.4475	4	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A54611	The discourse made before the Royal Society the 26. of November, 1674, concerning the use of duplicate proportion in sundry important particulars together with a new hypothesis of springing or elastique motions / by Sir William Petty, Kt. ...	Petty, William, Sir, 1623-1687.	1674 (1674)	Wing P1919; ESTC R4342	21,001	166

Experimentation then may also be known the length of every Gun for every Bullet respectively As for example suppose a Gun that carries a Ball of 5 inches Diameter be 10 foot long in the Concave then the Content of the said Concave will be 3000 Cylindrical inches Now the question is how long must the Piece be which carries a Bullet of 7 inches Diameter I say that forasmuch as the Weight of the 5 inch Bullet to that of 7 is as 125 to 343 the Concave of the greater Gun must be in the same proportion to 3000 viz. 8232 like inches so as it may contein and fire a proportionable quantity of powder Which 8232 being divided by the Area of the Bullet 49 the Quotient will be 168 inches or 14 foot that is to speak shortly and plainly The Length of Guns must be measured by the Diameters of their respective Bullets I cannot say I have tried the effects of Gunpowder to be in the abovemention'd proportion but have credibly heard it to be so and because of the Similitude of Sails Weights Knocks and the other points above described unto this of Gunpowder I believe it and recommend it to your further thoughts and experience The Seventh Instance Of Sounds LEt there be many Equal Sounds I say that the Distances at which they may be heard are the Roots of the Numbers of such Sounds For four Musquets will be heard twice as far as one and nine thrice and so of the rest By which reckoning the hearing of some of our Fleets Engagement with the Dutch even to S. Iames's Park near this City is easily solved and the truth of that Observation doth reciprocally countenance this Doctrine For suppose both Fleets consisting of two hundred Ships great and small had about 12000 pieces of Ordnance on board them which at a Medium suppose to be Demi-Culverins Suppose also that a Demiculverin with the same circumstances of Wind and Air may be as easily heard five miles as the said Engagements were heard 160 miles Then I say that 1024 of the said 12000 Guns firing together or very near the same time might as they were be well heard 160 miles and that about 4000 such Guns might as well be heard 300 miles as one Demi-Culverin five miles which last point I add to prevent the unbelief of a probable matter when it shall happen Now what effect this had in the Popes Presage of the Battel of Lepanto I know not The Eighth Instance Of Smells I Say the same of Smells viz. that the Distances at which they are perceived are the Roots of the Quantity of the Matter out of which they are emitted which Doctrin I apply to solve what I once did hardly believe viz. that Ships coming from America towards Portugal did smell the Rosemary and other odoriferous herbs 60 miles off from the Land The which seems not only credible but very likely For if a foot square of a Rosemary-Field may be smelt one Perch or Rod whereof 320 make a mile then about 8000 Acres of Land whereon such sented Plants do grow or a piece of Land about 4 miles long and 3 miles broad or 6 miles long and 2 miles broad may be smelt 64 miles And 72000 Acres of the like Land or a parcel of such Land about 11 miles square may be smelt as many leagues or near 200 miles And this Consideration I pitch upon as one of the grounds whereupon I would build a Doctrin concerning the Influence of the Stars and other Celestial or remote Bodies upon the Globe of the Earth and its Inhabitants both Men and Brutes The Ninth Instance Concerns Visible Objects I Say also that four equal and like Candles will give light but twice as far as one and 9 thrice as far and that 16 will also enlighten but 4 times as far as one c. And if a Flag or Ships-Vane of a yard square may be seen a league off at Sea it must be 2 yards square or 4 square yards to be seen 2 leagues and so forward But whoever will make experiment hereof must first consider how many miles in thickness of a Middling Clear and Diaphanous Air do make an Opaque For we find that although a very thin plate of clear Glass seems to hinder our sight of near Objects but very little yet we also know that great number of them suppose one hundred can scarce be seen through at all Hereunto also must be added the Consideration of the Convexity of the Earth and then I doubt not but this Doctrin of Roots and Squares rectified and corrected with the two additional Considerations last mentioned will hold concerning Visible and Lucid Bodies as was above propounded The Tenth Instance In the Time of the Vibration of Pendules THe times in which the Returns of a Vibrating Pendulum are made are the Roots of the Distances between the Center of the Pendulum and the Center upon which it moves I shall need to make no application of this Truth since we all enjoy the benefit of it in our more regulated Clocks and Measures of Time which are now in common use and from whose Improvements we may most hopefully expect a better measure of Longitude upon the Surface of the Earth The further uses which may be made hereof it being a very simple and examinable Experiment is to witness and give evidence to other the more abstruse and complicate Positions which are of the like and parallel Nature The Eleventh Instance In the Life of Man and its Duration IT is found by Experience that there are more persons living of between 16 and 26 years old than of any other Age or Decade of years in the whole life of Man which David and Experience say to be between 70 and 80 years The reasons whereof are not abstruse viz. because those of 16 have passed the danger of Teeth Convulsions Worms Rickets Measles and Small-pox for the most part And for that those of 26. are scarce come to the Gout Stone Dropsie Palsies Lethargies Apoplexies and other Infirmities of Old Age. Now whether these be sufficient reasons is not the present Enquiry but taking the afore-mentioned Assertion to be true I say that the Roots of every number of Mens Ages under 16 whose Root is 4 compared with the said number 4 doth shew the proportion of the likelyhood of such mens reaching 70 years of Age. As for example 'T is 4 times more likely that one of 16 years old should live to 70 then a new-born Babe 'T is three times more likely that one of 9 years old should attain the said age of 70 than the said Infant Moreover 't is twice as likely that one of 16 should reach that Age as that one of 4 years old should do it and one third more likely than for one of nine On the other hand 't is 5 to 4 that one of 26 years old will die before one of 16 and 6 to 5 that one of 36 will die before one of

26 and 3 to 2 that the same person of 36 shall die before him of 16 And so forward according to the Roots of any other year of the declining Age compared with a number between 4 and 5 which is the Root of 21 the most hopeful year for Longaevity as the mean between 16 and 26 and is the year of perfection according to the sense of Our Law and the Age for whose life a Lease is most valuable To prove all which I can produce the accompts of every Man Woman and Child within a certain Parish of above 330 Souls all which particular Ages being cast up and added together and the Sum divided by the whole number of Souls made the Quotient between 15 and 16 which I call if it be Constant or Uniform the Age of that Parish or numerous Index or Longaevity there Many of which Indexes for several times and places would make an useful Scale of Salubrity for those places and a better Judg of Ayres than the conjectural Notions we commonly read and talk of And such a Scale the King might as easily make for all his Dominions as I did this for this one Parish The Twelfth Instance In Musick TAke a Musical String one end thereof being fastned hang unto the other over a convenient Bridg any weight which may strain it to some grave Musical Tone or Note then set some other string of near the same length Unisone thereunto Lastly instead of the first weight hang to the first String the Quadruple of the same weight and it will appear that the String with the quadruple weight shall yield a Tone of an 8 th or Diapason above it self when singly charged The reason is because the quadruple weight doubles the number of Vibrations 2 being the Root of 4 And for that the Ratio Formalis of Tones lieth in the number of the Vibrations and of the Diapasons in the doublness of such numbers By the same Method of hanging-on several weights at one end of the same String all Tones may be produced of which such String is capable The Tones or Notes also of like Bells and Drums do follow the same proportions of their Tension and Mettal so as able Artists can cast Bells in Tones assigned The Thirteenth Instance of Fire and Spirits LEt a Cylindrical Flat-bottom Vessel be filled with Water and let it be tried in what time one Lamp or Candle would make the water boyl through or come up to its greatest heat Then see in how much lesser time 2 3 or 4 more like fires will hasten the same effect I cannot speak positively hereof but know from several Observations that the Acceleration abovesaid shall not be made in Arithmetical Proportion forasmuch as I know that in Fire-works great Fires are more profitable than small as in Brewers Coppers and Iron-works may be seen wherein double Fires produce more than double dispatch or advantage I shall therefore suspend this matter and pass to the measuring of the Spirituosity of Liquors or in what proportions several Liquors contein more or less of inflameable or ardent parts Now in this case I conceive the Consideration of Roots and Squares is also material for I understand by strength or multitude of Spirits the Space greater or lesser into which such Liquors will be rarified or will fill with Spirits As for example if a Pint of Water rarified into Vapour will fill a Globe but of 3 foot Diameter and a Pint of rectified Spirit of Wine will fill a Globe of six foot diameter or 8 times as large as that of Water I shall say that there is 8 times as much Spirit or Vapour in one as in the other But if these Liquors were put into open Lamps or Vessels there the space in which the Spirits rise are the Roots whose Squares do shew the Spirituosity of those Liquors Ex. gr Let there be a Lamplike Vessel of common Aquavitae in which place a Week as high as the same will burn by the rising of the Spirit unto it suppose an inch above the surface of the Liquor Now let there be a like Equal vessel with such a Spirit as will rise up higher suppose to a Week placed two inches above the Surface in this case I say that the latter Liquor is quadruple in strength or extent of Spirit to the former for 't is certain that as the Spirit riseth double upwards so also it emitteth or rarifieth it self double also sideways and consequently the quantity of the Spirit or Vapour must be quadruple and so of other proportions The Fourteenth Instance of Rising and Falling Bodies but particularly of Waters in Pumps and River-streams LEt it be observed in the Transparent Pipe of a Forcing Pump at how many stroaks the Water is forced from the Bottom to the Top and let as many marks be made at the several places unto which the Water mounted at every stroak which stroaks we suppose to be all in Equal Times it will appear that all the said Divisions will be according to the Proportions or the Logarithms above-mentioned As for the Descents and Accelerations of falling Bodies the Times are the Roots of these Spaces which they fall in the said times respectively The great effect whereof we see in Overshot-Mills where a little water falling upon a Wheel of a large Diameter produceth wonderful Effects the which may be well computed upon the Principles we hold forth Waters also have greater forces in the above-mentioned proportions as the hole or place whereat they issue is lower from their Surface as may be seen in all Breast and Undershot-Mills where it is pleasant to divide the Sinking of the water into Equal Spaces and to count the Clacks Revolutions or Stroaks made within the Time of the waters sinking every such equal Space for therein the above-mentioned Logarithmes may also be observed Unto this head may be referred the Leakage of Ships For let there be a hole in a Ship somewhere under water then let it be seen what water comes in at the said hole within any space of Time then let the like hole be made at double the perpendicular distance from the top of the water and there shall come in four times as much as at the upper hole and let a third be at three distances and that shall admit 9 times as much c. Again let there be two Equal holes or Leaks in a Ship the one at Head and the other at Stern and let the Ship be in motion then the Leakage at the Head is composed of the pressure of the water from the Surface and of the Ships Motion together Moreover if the Ship make double way the Leakage will be quadruple if treble way non cuple c. Wherefore to stop Leaks afore the Ship must stop its motion lye by or bear up to go with the Wind and Sea c. Lastly I shall add that the Swiftnesses of Waters or River-streams are the Roots of the Power that causes them which