[85]Chalmer describing a Whirlwind, which is aStormofcollectionandAscentofhotAir, &c. by Rarefaction, says, “as the Wind ceased, presently after the Whirlwind passed, thebranchesand Leaves of various Sorts of Trees, which had been carried into the Air, continued tofallforhalf an hour; and, in their Descent, appeared like Flocks of Birds of different Sizes.”This Circumstance proves that Columns ofhotAir must have been raised in a Body, in Succession, to so considerable a Height, thatBranchesof Trees carried up by them, tookhalf an Hourin falling.[86]It may be from this Principle, that in the East, Liquids are keptcoolby being hung in the Shade, in theopenAir, suspended inwet Cloths: there being a continual Breeze and Succession ofcool drySpunges(as it were) of Air, in Contact with thewettedCloths, whose Moisture will thus be more quickly evaporated.[87]Historia Ventorum, Pag. 48, Art. 33.[88]“Cum enim (Venti) Choreas ducant, Ordinem Saltationis nosse jucundum fuerit. Art. 18.”[89]On the Action of the Sun and Moon over Animal Bodies, by Dr. Mead, Miscell. Cur. Vol. 1.P. 372, 373.[90]For these Observations seeGassendus’s Natural Philosophy.De Chales’s Navigator. AndAstro-Meteoro-Logica, per J. Goad.[91]SeeMaclaurin’s Newton, Page 376.[92]Air at a Medium is 800 Timesrarerthan Water: so that if 800 Times the Quantity of Airnaturallycontained in a Vessel whose Dimensions are those of a cubic Foot, were pressed into it by a Syringe orCondenser, the Air woud differ nothing from Water in Density.[93]SeeWilson on Climate, Chap. 15. Pages 46, 54.[94]55.[95]By reducing 10 Feet 6 Inches, and 6 Feet 7 Inches, into Inches, and dividing by common Divisors, as 3 and 2; it is found that 10 Feet 6 Inches, will be to 6 Feet 7 Inches, as 3 to 2 nearly: that is, as 15 Miles to 10 Miles.[96]White’s Ephèmeris, Page 38, for the Speculum Phenomenorum, or Mirror of the Heavens.[97]See the Book which gives an Account of Walker’s Eidouranion.TheintelligentReader will easily distinguish the Effects, attributed to the Planets, viz. their mutual Attractions, owing to natural Causes only;—from the futile Ravings of judicial Astrology.[98]SeeLondon Chronicle, 26th July, 1785.[99]To find the Direction of an upper Current, without the Inconvenience of rising above the Level which the Aironaut has fixed on.This the Abbé Bertholon has hinted at, by Means of a smaller Balloon.The Dimensions of which, must however be so large; that, allowing for the Evaporation of Gass, it willjustrise with the Weight of a Quantity of Cord, a Mile and half, for Instance, in Length: and have sufficient Room left within, to admit of the Expansion of Gass without Rupture.The Pioneer-Balloon may be taken up,empty, and filled with Gass necessarily escaping fromthe mouthof thegreat Balloon, when stationary: and may be sent up with a Cord, fastened to the Center above the Car of thegreat Balloon, to reconnoitre thesuperiorCurrents: or it may be only filledin Part; and made todescend, anddiscoverthelowerCurrents.See“Des Avantages de Ballons, &c. Page 72.”[100]As theHeightsof the Atmosphere encrease in anarithmeticalProgression; the Densities are said to encrease in ageometricalProgression: which is a mathematical and pedantic Mode of Expression.ForarithmeticalProgressionheremeans no more than the Height of 1, 2, 3, 4, 5, 6, &c. &c. Yards, Fathoms, Roods, or any other equal Interval.If then at the Height of one Yard, the Balloon has acquired (suppose) the Levity of 1 Pound; then, if this Levity encreases in geometrical Progression; (as twice 1 is 2,) it will, at the Height of 2 Yards, have encreased to 2 Pounds: and, as twice 2 is 4;) it will, at the Height of 3 Yards, have encreased to 4 Pounds: and, as (as twice 4 is 8;) it will, at the Height of 4 Yards, have encreased to 8 Pounds: and, (as twice 8 is 16;) it will, at the Height of 5 Yards, have encreased to 16: and, (as twice 16 is 32;) the Levity will, at the Height of 6 Yards, have encreased to 32 Pounds; and so on,doublingthe preceding Number; at the Height of each Yard, Fathom, Rood, Mile, &c. &c.[101]Whiston’sTacquet’s Euclid, Book XI. Definition of arightCylinder, Art. 3, Page 166.[102]Archimedes’s Theorems. Proposition 33, 34; at the End ofWhiston’sEuclid, Page 42.[103]Inferred in theChester Chronicle, Sept. 30, 1785.[104]The Writer not having yet been able to procure it from the London Booksellers.[105]SeeChambers’s Dictionaryunder the Articleresistence.[106]See his“Navires des Anciens.”[107]See“Gordon’s Principles of Naval Architecture.”Also the Balzaes and Guaraes, inUllòa’s Voyage to America, Book 4, Chapter 9, Vol. 1, Page 183.[108]Mons. Carra proposed to ascend with two Balloons. One, a seventh Part less than the other, is to be connected by a Rope, throu’ a Pulley fixed in the equatorial Hoop of the great Balloon, to a Reel in the Center of the Car: in descending, the Reel is to be unwound: the great Balloon and Car will therefore descend, while the small Balloon remains in the Air. The Scheme is certainly practicable. See the Cut in theLondon Magazinefor June, 1784.[109]See“Lewis’s Commerce of the Arts.”[110]SeePriestley’s numerous Experiments: and that Library ofcurious Investigation, the Philosophical Transactions.[111]AndMagnitudeof distant Objects.Bacon says that Objects are morevisiblein an East Wind, and Sounds moreaudiblein a West Wind; being heard at agreaterDistance. “Historia Ventorum, P. 37, Art. 31.”[112]See Le Roi’s Uses of the airostatic Globeat Sea, in his“Navires des Anciens, Page 225.”[113]Thenatural Figureof theDìodon-Globe-Fish, a coloured Print of which is given in “Martyn’s new and elegant Dictionary of natural History:” where it is described as follows: “The Form of the Body is usually oblong: but when the Creature is alarmed, it possesses the Power ofinflatingits Belly to a globular Shape of great Size;”—seems to furnish a Hint for the proper Figure of a Balloon, when the Art is more improved.The Balloon, as far as it is meant to resemble the upper Part of the Fish, is to be made stiff, with Pasteboard orPapier-mâchèvarnished; for, being strong, and in a permanent Form, it is more capable of continuing Air-tight: the lower Parts beingflaccid, will be inflated, as the Balloon rises, and deflated during the Descent.Rowers, and propulsive Machinery, are to be fixed within the Fish, in Place of the Fins: and Goods ofgreaterWeight placed in a covered Car below: the Air-Bottle-Balloon being fixed between both.[114]And byKunckel’sorCanton’sPhosphorus, See“Priestley’s History oflight. Pages 585, 370.”[115]This was owing to the cool Air rushing in to supply the Tendency to a Vacuum by the Expansion of hot Steam, with the extricated Gass.The Accident proves that no Danger is to be dreaded fromexpansionof the Gass.[116]FromBersham-ForgenearWrexham, where there is always a sufficient Quantity.[117]ThedetachedThermometer might be protected from theSun, by being swung a few Inchesbelowthe Car of the Balloon by means of anOpeningmade purposely throu’ the Center of the Car.[118]Foundation of the first Table.(Ph. Tr. for 1777, Part 2d, Page 567.)—It was found byExperiment that the Decimal.000262was the Expansionon30 Inches of Quicksilver,witheach Degree of Temperature from freezing to boiling Water: also, the Decimal.000042was the Expansionon30 Inches of the Glass Tube (containing the Quicksilver),witheach Degree of———Temperature: therefore by Addition,.000304or by taking only 4 Decimals,.0003is the Expansionon30 Inches of Quicksilver, and the Glass Tube containing it,witheach Degree of Temperature.Construction of the first Table.Thus any vertical Number, shewing the Expansion, may be readilyformed, bydoubling,first, the Number immediately under each Inch for the Expansion below it: andafterwards, by adding the Number immediately under each Inch, to the Expansion last found.Note: The vertical Columns, below each Inch of Quicksilver shew the Expansiononthat Inch,withcorresponding Degrees of Temperature indicated by the Thermometer in the Column to the left Hand. Example: to find the Expansionon30 Inches of Quicksilverwith1 Degree of Temperature: the Answer in the Table is .003: i. e. such Expansion raises the Quicksilver the 3000th Part of an Inch.[119]There is seldom Occasion to take more than the four first Decimals out of the Table, the Remainder being oflittle value.[120]The Foundation of the second Table.This Table is calculated from Briggs’s Logarithms: each Number, in the second Column, being nothing more than the Logarithm—corresponding to the Point, (in thefirstColumn,) at which the Quicksilver stands in the barometric Tube,—subtracted from the Logarithm of 32 Inches multiplied by 6.Construction of the second Table.This Table consists of threeverticalColumns only: tho’here tripled, for the greater Convenience of Inspection.The first or left Hand Column shews, in Inches and Tenths (from ten Inches) the Gradations of the Quicksilver in the barometric Tube, beginning as low as one Inch above the Surface in the Cistern, and proceeding throu’ all the intermediate Points, to the unusual Extent of 32 Inches:[121]supposing likewise that the Tube is elevated in the Atmosphere, so that the contained Quicksilver, when exposed to the Temperature of 31°.24 of Farenheit, rests at each Point in the Table.The second vertical Column gives the different Heights in Feet and Tenths, to which the barometric Tube must be raised above its Level at 32 Inches, in order that the contained Quicksilver, if exposed to the Temperature of 31°.24 of Farenheit, may stand at each Point indicated in the first Column.The third vertical Column, gives, likewise in Feet and Tenths, thedifferencebetween each two adjoining Heights in the second Column, corresponding to a single Tenth (of Quicksilver): which single Tenth is the Difference between each two adjoining Tenths of an Inch in the first Column.For Example: Suppose the Quicksilver in the barometric Tube, in the first Column, stands atInches16.1answering to19570.4}Height in Feet in the Atmosphere.And again at16.2answering to19398.4———Differenceof .1 in Feet: remaining= 172.0which sixteen Inches two Tenths, is a single Tenth more than sixteen Inches one Tenth, and will therefore answer to alessHeight in the Atmosphere by that single Tenth; considering that the lower the Quicksilver falls in the Tube, the higher must the Barometer itself be raised in the Atmosphere, in order that the Quicksilver may rest at the lower Points of the Tube. If therefore alessHeight in the Atmosphere be required which shall answer to one Tenth more than 16 Inches two Tenths; subtract the Height answering to 16.2 from the Height answering to 16.1, i. e. subtract thelessHeight from thegreater, and the Remainder gives thatlessHeight in the third Column, answering to the Height of one Tenth more than 16 Inches 2 Tenths, of the Barometer.[121]The Barometer, (to which the Scale of Heights is applied, in the 2d Column of the 2d Table) is supposed to be sunk within the Surface of the Earth, till the Quicksilver rests at 32 Inches, as appears from the last Article in the table, viz. 32 Inches, 0.00 Feet. 32 Inches is therefore the Foundation of the Table, and corresponds, according to Shuckburgh, to 1647 Feet, under the Surface of the Sea, at low Water.This Depththen beingthe imaginary Levelpointed out by the Quicksilver, at theunusualExtent of 32 Inches;eachinteriorInch and Tenth of Quicksilver will correspond to asuperiorElevation of the Instrument, in Feet and Tenths above that Level, and will include the Mensuration of the deepest Mines.For themeanPressure of the Barometer, at low Water, from 132 Observations in Italy and England, is 30.04 Inches: the Temperature of the Barometer being at 55°, i. e. Temperate, and that of the Air at 62°.[122]Foundation of the Table for Tenths.The Height, inFeet, corresponding to the Expansion on the Tenth of an inch of Quicksilver with the Temperature of 31°.24 (as in the 3d Column of the 2d Table) are reduced by this Table into a ten Times less Number of Feet; and the Tenth of an Inch (of Quicksilver) is also again divided intotenmore Parts: in order to shew, in a ten Times less Number ofsuchFeet, the Expansion corresponding to any of those Parts into which theTenthof an Inch (of Quicksilver) has been divided.Construction and Use of the Table for Tenths.1. The Figures in the left vertical Column shew the Height inFeet, (from 81 to 130) corresponding to a single Tenth of an Inch of Quicksilver, viz. to the higher of two adjoining Tenths, as in the 3d Column of the 2d Table.2. The Figures, along the upper horizontal Line, shew the Number of Parts into which the Tenth of an Inch has been divided.3. The Figures, at the Point of Meeting, express, in a ten Times less Number, ofthe Feetin the left vertical Column, the Expansion corresponding to any of those Parts, into which the Tenth of an Inch (of Quicksilver) has been divided.Thus: 90 is aNumber of Feetcalled 9 Tenths of 100: but theTenthsareFeet, and not Tenths of a Foot.[123]The Standard Temperature was 31°.24, which not being exactly 1 Quarter, another Decimal is added, (for Ease in Computation,) by which 31.24 becomes 31.25, i. e. by dividing one Degree of Heat into 100 Parts, and taking 25 of those Parts, or dividing the 100 by 25, the Answer is 4, i. e. 1⁄4 of the whole 100: or (31)1⁄4.[124]The Foundation of the fourth Table.(Ph. Tr. for 1777, Part 2d, Pages 564, and 566,)—From theMeanof a Series of Experiments with a Manòmeter, or Instrument to measure theRarityand Density of the Atmosphere, depending on the Action ofHeatand Cold, it was found, that when thePortion of a Tubecontaining Air (at the Temperature of freezing by Farenheit, and Pressure of 301⁄2 Inches[125]by a common Barometer) was divided into 1000 Parts; the Volume ofAirwithin it, encreasednearlyin a certain Proportion, as each Degree of Temperature encreased; viz. at a Mean, 2.43, or simply (by rejecting the 2d Decimal as too minute) 2.4: that is, a 1000 Parts of Air became by Expansion with one Degree of the Thermometer, equal to 1002.43: i. e. the Portion of Air occupying 1000 Parts, did, with the Addition of one Degree of Heat, occupy 1002.43 Parts: that is (by rejecting the 2d Decimal 3 as too minute) occupied two Parts and 4 Tenths more than the thousand.Construction of the fourth Table.Supposing therefore that the Portion of the Tube containing Air, was one Foot in Length of Height, divided also into a thousand Parts; one Degree of Heat would encrease or expand it two Parts and four Tenths more than the thousand Parts into which the Foot was divided.CAUTION.The fourth Table properly consists of only nine horizontal Columns of thousands, in Breadth; which Columns are extended in Length to one hundred Lines, corresponding to 100 Degrees of Heat.The Table is here divided, in order that it may conform to the Size of the Pages: by which Means the Formation of each vertical Number by the following Rule, (which renders the Tableself-evident) might without this Caution, have been attended with some Difficulty.The vertical Columnsbelowthe Figures expressing each thousand, shew the Expansion of Aironeach respective thousand,withthe corresponding Degrees of Temperature indicated by the Thermometer in the vertical Column to the left Hand.Example the first: to find the Expansion of Aironone thousand Feet,withone Degree of Temperature; the Answer in the Table is 2.4, or 2.43: i. e. 2 Feet and 4 Tenths of a Foot, rejecting the 2d Decimal as too minute.Example the second: to find the Expansionon8 thousand Feet,with99 Degrees of Heat: the Answer is 1924.56: and so of the Rest.Thusanyof thevertical Numbersshewing the Expansion, may be readilyformed, bydoubling,first, the Number immediately under each thousand in the horizontal Line, for the nine first thousands, (of which the Breadth of the Table properly consists, exclusive of the thermometric Column) for the Expansion below it: and,afterwards, for each Expansion immediately below the former, by adding, to the Expansionlastfound, the Number immediately under its respective thousand.First Example: to find the vertical Number for the Expansion under the first thousand, viz. 1000,with2 Degrees of Heat: the Number under 1000 is 2.43: double this: and the Answer is 4.86.Second Example: suppose the Expansionlastfound be thatonone thousand Feetwith24 Degrees of Heat; viz. 58.32: and the Expansiononthe same thousand,withone Degree of Heat more, viz. on 25 Degrees, be required; add the Expansiononone thousand Feet,with24 Degrees, viz.58.32to the Expansiononthe same 1000,with1 Degree, viz.2.43———and the Answer is, by Addition,60.75Third Example: supposing the Expansionlastfound to be the Expansionon9000 Feetwith99 Degrees of Heat, which in the Table is 2165.1.It is required to find the Expansiononthe same 9000 Feet, with 100 Degrees of Heat; add to the Expansion last found,viz.2165.13,the Expansion on the same 9000 Feet,viz.21.87with one Degree of Heat, and———2187.00is the Answer by Addition.Any vertical Number shewing the Expansion maylikewisebefound, first,by multiplying the first Figure, or Number, of thegiventhousand Feet (in the horizontal Line,) into the Answer or Expansion on thefirstthousand Feet, with one Degree of Heat: for Example;To find the Expansion on 9000 Feet with one Degree of Heat.The Expansion on 1000 Feet, with 1 Degree of Heat (from whence, all the other Expansions are derived) being 2.43; multiply that Number by 9, the first Figure of the given thousand Feet, and the Answer or Expansion with 1 Degree of Heat, is 21.87: hence all the Answers or Expansions, immediatelyunder the horizontal Line of thousands, areformed.Then 2dly, any other vertical Number or Expansion may beformedby multiplying the Expansionimmediatelyunder thegiventhousand Feet in the horizontal Line, into thegivenNumber of Degrees: for Example;To find the Expansion on 9000 Feet, with 50 Degrees.The Expansion with one Degree on 9000, is 21.87: therefore the Expansion with 50°, is 50 Times more, viz. 1093.50, and so of the Rest.These different Methods serve to prove the Answers, and to elucidate the Table.[125]These Experiments were made with the Manòmeter when the Atmosphere was half an Inch heavier than in the Experiments to prove the Expansion of Quicksilver, the Barometerthenstanding at 30 Inches only.[126]There isseldomOccasion to take more than the first Decimal out of the Table.[127]“RULE.“Precept the 1st. With the Difference of the two Thermometers that give the Heat of the Barometer (and which for Distinction sake, are called the attached Thermometers) enter Table I, with the Degrees of Heat in the Column on the left Hand, and with the Height of the Barometer in Inches, in the horizontal Line at the Top; in the common Point of Meeting of the two Lines will be found the Correction for the Expansion of the Quicksilver by Heat, expressed in decimal Parts of an English Inch; which added to the coldest Barometer, or subtracted from the hottest, will give the Height of the two Barometers, such as would have obtained, had both Instruments been exposed to the same Temperature.“Precept the 2d. With these corrected Heights of the Barometers enter Table II, and take out respectively the Numbers corresponding to the nearest Tenth of an Inch; and if the Barometers, corrected as in the first Precept, are found to stand at an even Tenth, without any further Fraction, the Difference of these two tabular Numbers (found by subtracting the less from the greater) will give the approximate Height in English Feet. But if, as will commonly happen, the correct Height of the Barometers should not be at an even Tenth, write out the Difference for one entire Tenth, found in the Column adjoining, intitledDifferences;and with this Number enter Table III, of proportional Parts in the first vertical Column to the left Hand, or in the 11th Column; and, with the next Decimal, following the Tenths of an Inch in the Height of the Barometer (viz. the hundredths) enter the horizontal Line at the Top, the Point of meeting will give a certain Number of Feet, which write down by itself; do the same by the next decimal Figure in the Height of theBarometer (viz. the thousandths of an Inch,) with this Difference, striking off the last Cypher to the right Hand for a Fraction; add together the two Numbers thus found in the Table of proportional Parts, and their Sum subduct from the tabular Numbers, just found in Table II; the Differences of the tabular Numbers, so diminished, will give the approximate Height in English Feet.“Precept the 3d. Add together the Degrees of the two detached or Air Thermometers, and divide their Sum by 2, the Quotient will be an intermediate Heat, and must be taken for the mean Temperature of the vertical Column of Air intercepted between the two Places of Observation: if this Temperature should be 31°1⁄4 on the Thermometer, then will the approximate Height before found be the true Height; but if not, take its Difference from 31°1⁄4, and with this Difference seek the Correction in Table IV, for the Expansion of Air, with the Number of Degrees in the vertical Column on the left Hand, and the approximate Height to the nearest thousand Feet in the horizontal Line at the Top; for the hundred Feet strike off one Cypher to the right Hand; for the Tens strike off two; for the Units three: the Sum of these several Numbers added to the approximate Height, if the Temperature be greater than 31°1⁄4, subtracted if less, will give the correct Height in English Feet. An Example or two will make this quite plain.”[128]There is no Occasion to take more than four Decimals out of the Table.[129]See Section 368,Note [120].[130]Section 368,Note [121]on Note [120].[131]Taking one Decimalonlyout of the Table.[132]The question: In the upper Gallery of the Dome of St. Peter’s Church at Rome, and 50 Feet below the Top of the Cross, the Barometer, from a Mean of several Observations, stood at Inches 29.5218 Tenths: the attached Thermometer being at Degrees 56.6 Tenths; and the Air-Thermometer at 57 Degrees: at the same Time that another, placed on the Banks of the River Tyber, one Foot above the Surface of the Water, stood at 30.0168, the attached Thermometer at 60°.6, and the Air-Thermometer at 60°.2: what, was the Height of the Building above the Level of the River?[133]SeeSection 375. 2dly. If the Moiety,Half-Heat, or mean Temperature of the Air,is equalto the Standard-Temperature, to which the two Barometers are brought, by the 2d Table; the fourth Table, forExpansion of Air, is needless: the Height already found, in the 2d Table, being thetrueHeight of theupper Station.3dly. If the Moiety,Half-Heat, or mean Temperature of the Air, isless thanthe Standard-Temperature of 31°.24; subtract the mean Temperature from 31.24; and with the Remainder find the Expansion, as usual, by the 4th Table: subtract the Sum, (which is a corresponding Height in Feet and Tenths) from the Height in Feet and Tenths of theupperBarometer, at theStandard-Temperature, in the 2d Table: and the Remainder will be thetrueHeight of theMountainorupper Station. Section 384, Notea.[134]The question: Near the Convent of St. Clare, in a Street calledLa Strada dei Specchi, at Rome, thelowerBarometer stood at 30.082, its attached Thermometer 71 Degrees, and detached ditto at 68 Degrees: on the Tarpeian Rock, or West-End of the famous Hill called The Capitol, theupperBarometer was at 29.985, its attached Thermometer 70°.5, and detached ditto 76°: what was the Height of the Eminence?[135]Sadler’sPractical Arithmetic, Page 293.[136]The Writer has not hitherto been so fortunate as to meet with the original Memoir, containing the Particulars of this curious Experiment by Mons. Lavoisier.[137]Dr. Priestley’s Experiments and Observations relating to Air and Water. Ph. Tr. for 1785, Vol. 75, Part 1, Page 279.[138]The Diameter may be enlarged.[139]By Means of the Cradle,bothare more easily moved: the Muffle is prevented from adhering to the Tube; and Steam is admitted to the Borings.[140]Copper sustaining aredHeat, better than Iron; the latter of which,calcineswith Steam, or, in cooling.
[85]Chalmer describing a Whirlwind, which is aStormofcollectionandAscentofhotAir, &c. by Rarefaction, says, “as the Wind ceased, presently after the Whirlwind passed, thebranchesand Leaves of various Sorts of Trees, which had been carried into the Air, continued tofallforhalf an hour; and, in their Descent, appeared like Flocks of Birds of different Sizes.”This Circumstance proves that Columns ofhotAir must have been raised in a Body, in Succession, to so considerable a Height, thatBranchesof Trees carried up by them, tookhalf an Hourin falling.
This Circumstance proves that Columns ofhotAir must have been raised in a Body, in Succession, to so considerable a Height, thatBranchesof Trees carried up by them, tookhalf an Hourin falling.
[86]It may be from this Principle, that in the East, Liquids are keptcoolby being hung in the Shade, in theopenAir, suspended inwet Cloths: there being a continual Breeze and Succession ofcool drySpunges(as it were) of Air, in Contact with thewettedCloths, whose Moisture will thus be more quickly evaporated.
[87]Historia Ventorum, Pag. 48, Art. 33.
[88]“Cum enim (Venti) Choreas ducant, Ordinem Saltationis nosse jucundum fuerit. Art. 18.”
[89]On the Action of the Sun and Moon over Animal Bodies, by Dr. Mead, Miscell. Cur. Vol. 1.P. 372, 373.
[90]For these Observations seeGassendus’s Natural Philosophy.De Chales’s Navigator. AndAstro-Meteoro-Logica, per J. Goad.
[91]SeeMaclaurin’s Newton, Page 376.
[92]Air at a Medium is 800 Timesrarerthan Water: so that if 800 Times the Quantity of Airnaturallycontained in a Vessel whose Dimensions are those of a cubic Foot, were pressed into it by a Syringe orCondenser, the Air woud differ nothing from Water in Density.
[93]SeeWilson on Climate, Chap. 15. Pages 46, 54.
[94]55.
[95]By reducing 10 Feet 6 Inches, and 6 Feet 7 Inches, into Inches, and dividing by common Divisors, as 3 and 2; it is found that 10 Feet 6 Inches, will be to 6 Feet 7 Inches, as 3 to 2 nearly: that is, as 15 Miles to 10 Miles.
[96]White’s Ephèmeris, Page 38, for the Speculum Phenomenorum, or Mirror of the Heavens.
[97]See the Book which gives an Account of Walker’s Eidouranion.TheintelligentReader will easily distinguish the Effects, attributed to the Planets, viz. their mutual Attractions, owing to natural Causes only;—from the futile Ravings of judicial Astrology.
TheintelligentReader will easily distinguish the Effects, attributed to the Planets, viz. their mutual Attractions, owing to natural Causes only;—from the futile Ravings of judicial Astrology.
[98]SeeLondon Chronicle, 26th July, 1785.
[99]To find the Direction of an upper Current, without the Inconvenience of rising above the Level which the Aironaut has fixed on.This the Abbé Bertholon has hinted at, by Means of a smaller Balloon.The Dimensions of which, must however be so large; that, allowing for the Evaporation of Gass, it willjustrise with the Weight of a Quantity of Cord, a Mile and half, for Instance, in Length: and have sufficient Room left within, to admit of the Expansion of Gass without Rupture.The Pioneer-Balloon may be taken up,empty, and filled with Gass necessarily escaping fromthe mouthof thegreat Balloon, when stationary: and may be sent up with a Cord, fastened to the Center above the Car of thegreat Balloon, to reconnoitre thesuperiorCurrents: or it may be only filledin Part; and made todescend, anddiscoverthelowerCurrents.See“Des Avantages de Ballons, &c. Page 72.”
This the Abbé Bertholon has hinted at, by Means of a smaller Balloon.
The Dimensions of which, must however be so large; that, allowing for the Evaporation of Gass, it willjustrise with the Weight of a Quantity of Cord, a Mile and half, for Instance, in Length: and have sufficient Room left within, to admit of the Expansion of Gass without Rupture.
The Pioneer-Balloon may be taken up,empty, and filled with Gass necessarily escaping fromthe mouthof thegreat Balloon, when stationary: and may be sent up with a Cord, fastened to the Center above the Car of thegreat Balloon, to reconnoitre thesuperiorCurrents: or it may be only filledin Part; and made todescend, anddiscoverthelowerCurrents.
See“Des Avantages de Ballons, &c. Page 72.”
[100]As theHeightsof the Atmosphere encrease in anarithmeticalProgression; the Densities are said to encrease in ageometricalProgression: which is a mathematical and pedantic Mode of Expression.ForarithmeticalProgressionheremeans no more than the Height of 1, 2, 3, 4, 5, 6, &c. &c. Yards, Fathoms, Roods, or any other equal Interval.If then at the Height of one Yard, the Balloon has acquired (suppose) the Levity of 1 Pound; then, if this Levity encreases in geometrical Progression; (as twice 1 is 2,) it will, at the Height of 2 Yards, have encreased to 2 Pounds: and, as twice 2 is 4;) it will, at the Height of 3 Yards, have encreased to 4 Pounds: and, as (as twice 4 is 8;) it will, at the Height of 4 Yards, have encreased to 8 Pounds: and, (as twice 8 is 16;) it will, at the Height of 5 Yards, have encreased to 16: and, (as twice 16 is 32;) the Levity will, at the Height of 6 Yards, have encreased to 32 Pounds; and so on,doublingthe preceding Number; at the Height of each Yard, Fathom, Rood, Mile, &c. &c.
ForarithmeticalProgressionheremeans no more than the Height of 1, 2, 3, 4, 5, 6, &c. &c. Yards, Fathoms, Roods, or any other equal Interval.
If then at the Height of one Yard, the Balloon has acquired (suppose) the Levity of 1 Pound; then, if this Levity encreases in geometrical Progression; (as twice 1 is 2,) it will, at the Height of 2 Yards, have encreased to 2 Pounds: and, as twice 2 is 4;) it will, at the Height of 3 Yards, have encreased to 4 Pounds: and, as (as twice 4 is 8;) it will, at the Height of 4 Yards, have encreased to 8 Pounds: and, (as twice 8 is 16;) it will, at the Height of 5 Yards, have encreased to 16: and, (as twice 16 is 32;) the Levity will, at the Height of 6 Yards, have encreased to 32 Pounds; and so on,doublingthe preceding Number; at the Height of each Yard, Fathom, Rood, Mile, &c. &c.
[101]Whiston’sTacquet’s Euclid, Book XI. Definition of arightCylinder, Art. 3, Page 166.
[102]Archimedes’s Theorems. Proposition 33, 34; at the End ofWhiston’sEuclid, Page 42.
[103]Inferred in theChester Chronicle, Sept. 30, 1785.
[104]The Writer not having yet been able to procure it from the London Booksellers.
[105]SeeChambers’s Dictionaryunder the Articleresistence.
[106]See his“Navires des Anciens.”
[107]See“Gordon’s Principles of Naval Architecture.”Also the Balzaes and Guaraes, inUllòa’s Voyage to America, Book 4, Chapter 9, Vol. 1, Page 183.
Also the Balzaes and Guaraes, inUllòa’s Voyage to America, Book 4, Chapter 9, Vol. 1, Page 183.
[108]Mons. Carra proposed to ascend with two Balloons. One, a seventh Part less than the other, is to be connected by a Rope, throu’ a Pulley fixed in the equatorial Hoop of the great Balloon, to a Reel in the Center of the Car: in descending, the Reel is to be unwound: the great Balloon and Car will therefore descend, while the small Balloon remains in the Air. The Scheme is certainly practicable. See the Cut in theLondon Magazinefor June, 1784.
[109]See“Lewis’s Commerce of the Arts.”
[110]SeePriestley’s numerous Experiments: and that Library ofcurious Investigation, the Philosophical Transactions.
[111]AndMagnitudeof distant Objects.Bacon says that Objects are morevisiblein an East Wind, and Sounds moreaudiblein a West Wind; being heard at agreaterDistance. “Historia Ventorum, P. 37, Art. 31.”
Bacon says that Objects are morevisiblein an East Wind, and Sounds moreaudiblein a West Wind; being heard at agreaterDistance. “Historia Ventorum, P. 37, Art. 31.”
[112]See Le Roi’s Uses of the airostatic Globeat Sea, in his“Navires des Anciens, Page 225.”
[113]Thenatural Figureof theDìodon-Globe-Fish, a coloured Print of which is given in “Martyn’s new and elegant Dictionary of natural History:” where it is described as follows: “The Form of the Body is usually oblong: but when the Creature is alarmed, it possesses the Power ofinflatingits Belly to a globular Shape of great Size;”—seems to furnish a Hint for the proper Figure of a Balloon, when the Art is more improved.The Balloon, as far as it is meant to resemble the upper Part of the Fish, is to be made stiff, with Pasteboard orPapier-mâchèvarnished; for, being strong, and in a permanent Form, it is more capable of continuing Air-tight: the lower Parts beingflaccid, will be inflated, as the Balloon rises, and deflated during the Descent.Rowers, and propulsive Machinery, are to be fixed within the Fish, in Place of the Fins: and Goods ofgreaterWeight placed in a covered Car below: the Air-Bottle-Balloon being fixed between both.
The Balloon, as far as it is meant to resemble the upper Part of the Fish, is to be made stiff, with Pasteboard orPapier-mâchèvarnished; for, being strong, and in a permanent Form, it is more capable of continuing Air-tight: the lower Parts beingflaccid, will be inflated, as the Balloon rises, and deflated during the Descent.
Rowers, and propulsive Machinery, are to be fixed within the Fish, in Place of the Fins: and Goods ofgreaterWeight placed in a covered Car below: the Air-Bottle-Balloon being fixed between both.
[114]And byKunckel’sorCanton’sPhosphorus, See“Priestley’s History oflight. Pages 585, 370.”
[115]This was owing to the cool Air rushing in to supply the Tendency to a Vacuum by the Expansion of hot Steam, with the extricated Gass.The Accident proves that no Danger is to be dreaded fromexpansionof the Gass.
The Accident proves that no Danger is to be dreaded fromexpansionof the Gass.
[116]FromBersham-ForgenearWrexham, where there is always a sufficient Quantity.
[117]ThedetachedThermometer might be protected from theSun, by being swung a few Inchesbelowthe Car of the Balloon by means of anOpeningmade purposely throu’ the Center of the Car.
[118]Foundation of the first Table.(Ph. Tr. for 1777, Part 2d, Page 567.)—It was found byExperiment that the Decimal.000262was the Expansionon30 Inches of Quicksilver,witheach Degree of Temperature from freezing to boiling Water: also, the Decimal.000042was the Expansionon30 Inches of the Glass Tube (containing the Quicksilver),witheach Degree of———Temperature: therefore by Addition,.000304or by taking only 4 Decimals,.0003is the Expansionon30 Inches of Quicksilver, and the Glass Tube containing it,witheach Degree of Temperature.Construction of the first Table.Thus any vertical Number, shewing the Expansion, may be readilyformed, bydoubling,first, the Number immediately under each Inch for the Expansion below it: andafterwards, by adding the Number immediately under each Inch, to the Expansion last found.Note: The vertical Columns, below each Inch of Quicksilver shew the Expansiononthat Inch,withcorresponding Degrees of Temperature indicated by the Thermometer in the Column to the left Hand. Example: to find the Expansionon30 Inches of Quicksilverwith1 Degree of Temperature: the Answer in the Table is .003: i. e. such Expansion raises the Quicksilver the 3000th Part of an Inch.
Foundation of the first Table.
.000262
.000042
———
.000304
.0003
is the Expansionon30 Inches of Quicksilver, and the Glass Tube containing it,witheach Degree of Temperature.
Construction of the first Table.
Thus any vertical Number, shewing the Expansion, may be readilyformed, bydoubling,first, the Number immediately under each Inch for the Expansion below it: andafterwards, by adding the Number immediately under each Inch, to the Expansion last found.
Note: The vertical Columns, below each Inch of Quicksilver shew the Expansiononthat Inch,withcorresponding Degrees of Temperature indicated by the Thermometer in the Column to the left Hand. Example: to find the Expansionon30 Inches of Quicksilverwith1 Degree of Temperature: the Answer in the Table is .003: i. e. such Expansion raises the Quicksilver the 3000th Part of an Inch.
[119]There is seldom Occasion to take more than the four first Decimals out of the Table, the Remainder being oflittle value.
[120]The Foundation of the second Table.This Table is calculated from Briggs’s Logarithms: each Number, in the second Column, being nothing more than the Logarithm—corresponding to the Point, (in thefirstColumn,) at which the Quicksilver stands in the barometric Tube,—subtracted from the Logarithm of 32 Inches multiplied by 6.Construction of the second Table.This Table consists of threeverticalColumns only: tho’here tripled, for the greater Convenience of Inspection.The first or left Hand Column shews, in Inches and Tenths (from ten Inches) the Gradations of the Quicksilver in the barometric Tube, beginning as low as one Inch above the Surface in the Cistern, and proceeding throu’ all the intermediate Points, to the unusual Extent of 32 Inches:[121]supposing likewise that the Tube is elevated in the Atmosphere, so that the contained Quicksilver, when exposed to the Temperature of 31°.24 of Farenheit, rests at each Point in the Table.The second vertical Column gives the different Heights in Feet and Tenths, to which the barometric Tube must be raised above its Level at 32 Inches, in order that the contained Quicksilver, if exposed to the Temperature of 31°.24 of Farenheit, may stand at each Point indicated in the first Column.The third vertical Column, gives, likewise in Feet and Tenths, thedifferencebetween each two adjoining Heights in the second Column, corresponding to a single Tenth (of Quicksilver): which single Tenth is the Difference between each two adjoining Tenths of an Inch in the first Column.For Example: Suppose the Quicksilver in the barometric Tube, in the first Column, stands atInches16.1answering to19570.4}Height in Feet in the Atmosphere.And again at16.2answering to19398.4———Differenceof .1 in Feet: remaining= 172.0which sixteen Inches two Tenths, is a single Tenth more than sixteen Inches one Tenth, and will therefore answer to alessHeight in the Atmosphere by that single Tenth; considering that the lower the Quicksilver falls in the Tube, the higher must the Barometer itself be raised in the Atmosphere, in order that the Quicksilver may rest at the lower Points of the Tube. If therefore alessHeight in the Atmosphere be required which shall answer to one Tenth more than 16 Inches two Tenths; subtract the Height answering to 16.2 from the Height answering to 16.1, i. e. subtract thelessHeight from thegreater, and the Remainder gives thatlessHeight in the third Column, answering to the Height of one Tenth more than 16 Inches 2 Tenths, of the Barometer.
The Foundation of the second Table.
This Table is calculated from Briggs’s Logarithms: each Number, in the second Column, being nothing more than the Logarithm—corresponding to the Point, (in thefirstColumn,) at which the Quicksilver stands in the barometric Tube,—subtracted from the Logarithm of 32 Inches multiplied by 6.
Construction of the second Table.
This Table consists of threeverticalColumns only: tho’here tripled, for the greater Convenience of Inspection.
The first or left Hand Column shews, in Inches and Tenths (from ten Inches) the Gradations of the Quicksilver in the barometric Tube, beginning as low as one Inch above the Surface in the Cistern, and proceeding throu’ all the intermediate Points, to the unusual Extent of 32 Inches:[121]supposing likewise that the Tube is elevated in the Atmosphere, so that the contained Quicksilver, when exposed to the Temperature of 31°.24 of Farenheit, rests at each Point in the Table.
The second vertical Column gives the different Heights in Feet and Tenths, to which the barometric Tube must be raised above its Level at 32 Inches, in order that the contained Quicksilver, if exposed to the Temperature of 31°.24 of Farenheit, may stand at each Point indicated in the first Column.
The third vertical Column, gives, likewise in Feet and Tenths, thedifferencebetween each two adjoining Heights in the second Column, corresponding to a single Tenth (of Quicksilver): which single Tenth is the Difference between each two adjoining Tenths of an Inch in the first Column.
For Example: Suppose the Quicksilver in the barometric Tube, in the first Column, stands at
16.1
19570.4
16.2
19398.4
———
= 172.0
which sixteen Inches two Tenths, is a single Tenth more than sixteen Inches one Tenth, and will therefore answer to alessHeight in the Atmosphere by that single Tenth; considering that the lower the Quicksilver falls in the Tube, the higher must the Barometer itself be raised in the Atmosphere, in order that the Quicksilver may rest at the lower Points of the Tube. If therefore alessHeight in the Atmosphere be required which shall answer to one Tenth more than 16 Inches two Tenths; subtract the Height answering to 16.2 from the Height answering to 16.1, i. e. subtract thelessHeight from thegreater, and the Remainder gives thatlessHeight in the third Column, answering to the Height of one Tenth more than 16 Inches 2 Tenths, of the Barometer.
[121]The Barometer, (to which the Scale of Heights is applied, in the 2d Column of the 2d Table) is supposed to be sunk within the Surface of the Earth, till the Quicksilver rests at 32 Inches, as appears from the last Article in the table, viz. 32 Inches, 0.00 Feet. 32 Inches is therefore the Foundation of the Table, and corresponds, according to Shuckburgh, to 1647 Feet, under the Surface of the Sea, at low Water.This Depththen beingthe imaginary Levelpointed out by the Quicksilver, at theunusualExtent of 32 Inches;eachinteriorInch and Tenth of Quicksilver will correspond to asuperiorElevation of the Instrument, in Feet and Tenths above that Level, and will include the Mensuration of the deepest Mines.For themeanPressure of the Barometer, at low Water, from 132 Observations in Italy and England, is 30.04 Inches: the Temperature of the Barometer being at 55°, i. e. Temperate, and that of the Air at 62°.
This Depththen beingthe imaginary Levelpointed out by the Quicksilver, at theunusualExtent of 32 Inches;eachinteriorInch and Tenth of Quicksilver will correspond to asuperiorElevation of the Instrument, in Feet and Tenths above that Level, and will include the Mensuration of the deepest Mines.
For themeanPressure of the Barometer, at low Water, from 132 Observations in Italy and England, is 30.04 Inches: the Temperature of the Barometer being at 55°, i. e. Temperate, and that of the Air at 62°.
[122]Foundation of the Table for Tenths.The Height, inFeet, corresponding to the Expansion on the Tenth of an inch of Quicksilver with the Temperature of 31°.24 (as in the 3d Column of the 2d Table) are reduced by this Table into a ten Times less Number of Feet; and the Tenth of an Inch (of Quicksilver) is also again divided intotenmore Parts: in order to shew, in a ten Times less Number ofsuchFeet, the Expansion corresponding to any of those Parts into which theTenthof an Inch (of Quicksilver) has been divided.Construction and Use of the Table for Tenths.1. The Figures in the left vertical Column shew the Height inFeet, (from 81 to 130) corresponding to a single Tenth of an Inch of Quicksilver, viz. to the higher of two adjoining Tenths, as in the 3d Column of the 2d Table.2. The Figures, along the upper horizontal Line, shew the Number of Parts into which the Tenth of an Inch has been divided.3. The Figures, at the Point of Meeting, express, in a ten Times less Number, ofthe Feetin the left vertical Column, the Expansion corresponding to any of those Parts, into which the Tenth of an Inch (of Quicksilver) has been divided.Thus: 90 is aNumber of Feetcalled 9 Tenths of 100: but theTenthsareFeet, and not Tenths of a Foot.
Foundation of the Table for Tenths.
The Height, inFeet, corresponding to the Expansion on the Tenth of an inch of Quicksilver with the Temperature of 31°.24 (as in the 3d Column of the 2d Table) are reduced by this Table into a ten Times less Number of Feet; and the Tenth of an Inch (of Quicksilver) is also again divided intotenmore Parts: in order to shew, in a ten Times less Number ofsuchFeet, the Expansion corresponding to any of those Parts into which theTenthof an Inch (of Quicksilver) has been divided.
Construction and Use of the Table for Tenths.
1. The Figures in the left vertical Column shew the Height inFeet, (from 81 to 130) corresponding to a single Tenth of an Inch of Quicksilver, viz. to the higher of two adjoining Tenths, as in the 3d Column of the 2d Table.
2. The Figures, along the upper horizontal Line, shew the Number of Parts into which the Tenth of an Inch has been divided.
3. The Figures, at the Point of Meeting, express, in a ten Times less Number, ofthe Feetin the left vertical Column, the Expansion corresponding to any of those Parts, into which the Tenth of an Inch (of Quicksilver) has been divided.
Thus: 90 is aNumber of Feetcalled 9 Tenths of 100: but theTenthsareFeet, and not Tenths of a Foot.
[123]The Standard Temperature was 31°.24, which not being exactly 1 Quarter, another Decimal is added, (for Ease in Computation,) by which 31.24 becomes 31.25, i. e. by dividing one Degree of Heat into 100 Parts, and taking 25 of those Parts, or dividing the 100 by 25, the Answer is 4, i. e. 1⁄4 of the whole 100: or (31)1⁄4.
[124]The Foundation of the fourth Table.(Ph. Tr. for 1777, Part 2d, Pages 564, and 566,)—From theMeanof a Series of Experiments with a Manòmeter, or Instrument to measure theRarityand Density of the Atmosphere, depending on the Action ofHeatand Cold, it was found, that when thePortion of a Tubecontaining Air (at the Temperature of freezing by Farenheit, and Pressure of 301⁄2 Inches[125]by a common Barometer) was divided into 1000 Parts; the Volume ofAirwithin it, encreasednearlyin a certain Proportion, as each Degree of Temperature encreased; viz. at a Mean, 2.43, or simply (by rejecting the 2d Decimal as too minute) 2.4: that is, a 1000 Parts of Air became by Expansion with one Degree of the Thermometer, equal to 1002.43: i. e. the Portion of Air occupying 1000 Parts, did, with the Addition of one Degree of Heat, occupy 1002.43 Parts: that is (by rejecting the 2d Decimal 3 as too minute) occupied two Parts and 4 Tenths more than the thousand.Construction of the fourth Table.Supposing therefore that the Portion of the Tube containing Air, was one Foot in Length of Height, divided also into a thousand Parts; one Degree of Heat would encrease or expand it two Parts and four Tenths more than the thousand Parts into which the Foot was divided.CAUTION.The fourth Table properly consists of only nine horizontal Columns of thousands, in Breadth; which Columns are extended in Length to one hundred Lines, corresponding to 100 Degrees of Heat.The Table is here divided, in order that it may conform to the Size of the Pages: by which Means the Formation of each vertical Number by the following Rule, (which renders the Tableself-evident) might without this Caution, have been attended with some Difficulty.The vertical Columnsbelowthe Figures expressing each thousand, shew the Expansion of Aironeach respective thousand,withthe corresponding Degrees of Temperature indicated by the Thermometer in the vertical Column to the left Hand.Example the first: to find the Expansion of Aironone thousand Feet,withone Degree of Temperature; the Answer in the Table is 2.4, or 2.43: i. e. 2 Feet and 4 Tenths of a Foot, rejecting the 2d Decimal as too minute.Example the second: to find the Expansionon8 thousand Feet,with99 Degrees of Heat: the Answer is 1924.56: and so of the Rest.Thusanyof thevertical Numbersshewing the Expansion, may be readilyformed, bydoubling,first, the Number immediately under each thousand in the horizontal Line, for the nine first thousands, (of which the Breadth of the Table properly consists, exclusive of the thermometric Column) for the Expansion below it: and,afterwards, for each Expansion immediately below the former, by adding, to the Expansionlastfound, the Number immediately under its respective thousand.First Example: to find the vertical Number for the Expansion under the first thousand, viz. 1000,with2 Degrees of Heat: the Number under 1000 is 2.43: double this: and the Answer is 4.86.Second Example: suppose the Expansionlastfound be thatonone thousand Feetwith24 Degrees of Heat; viz. 58.32: and the Expansiononthe same thousand,withone Degree of Heat more, viz. on 25 Degrees, be required; add the Expansiononone thousand Feet,with24 Degrees, viz.58.32to the Expansiononthe same 1000,with1 Degree, viz.2.43———and the Answer is, by Addition,60.75Third Example: supposing the Expansionlastfound to be the Expansionon9000 Feetwith99 Degrees of Heat, which in the Table is 2165.1.It is required to find the Expansiononthe same 9000 Feet, with 100 Degrees of Heat; add to the Expansion last found,viz.2165.13,the Expansion on the same 9000 Feet,viz.21.87with one Degree of Heat, and———2187.00is the Answer by Addition.Any vertical Number shewing the Expansion maylikewisebefound, first,by multiplying the first Figure, or Number, of thegiventhousand Feet (in the horizontal Line,) into the Answer or Expansion on thefirstthousand Feet, with one Degree of Heat: for Example;To find the Expansion on 9000 Feet with one Degree of Heat.The Expansion on 1000 Feet, with 1 Degree of Heat (from whence, all the other Expansions are derived) being 2.43; multiply that Number by 9, the first Figure of the given thousand Feet, and the Answer or Expansion with 1 Degree of Heat, is 21.87: hence all the Answers or Expansions, immediatelyunder the horizontal Line of thousands, areformed.Then 2dly, any other vertical Number or Expansion may beformedby multiplying the Expansionimmediatelyunder thegiventhousand Feet in the horizontal Line, into thegivenNumber of Degrees: for Example;To find the Expansion on 9000 Feet, with 50 Degrees.The Expansion with one Degree on 9000, is 21.87: therefore the Expansion with 50°, is 50 Times more, viz. 1093.50, and so of the Rest.These different Methods serve to prove the Answers, and to elucidate the Table.
The Foundation of the fourth Table.
(Ph. Tr. for 1777, Part 2d, Pages 564, and 566,)—From theMeanof a Series of Experiments with a Manòmeter, or Instrument to measure theRarityand Density of the Atmosphere, depending on the Action ofHeatand Cold, it was found, that when thePortion of a Tubecontaining Air (at the Temperature of freezing by Farenheit, and Pressure of 301⁄2 Inches[125]by a common Barometer) was divided into 1000 Parts; the Volume ofAirwithin it, encreasednearlyin a certain Proportion, as each Degree of Temperature encreased; viz. at a Mean, 2.43, or simply (by rejecting the 2d Decimal as too minute) 2.4: that is, a 1000 Parts of Air became by Expansion with one Degree of the Thermometer, equal to 1002.43: i. e. the Portion of Air occupying 1000 Parts, did, with the Addition of one Degree of Heat, occupy 1002.43 Parts: that is (by rejecting the 2d Decimal 3 as too minute) occupied two Parts and 4 Tenths more than the thousand.
Construction of the fourth Table.
Supposing therefore that the Portion of the Tube containing Air, was one Foot in Length of Height, divided also into a thousand Parts; one Degree of Heat would encrease or expand it two Parts and four Tenths more than the thousand Parts into which the Foot was divided.
CAUTION.
The fourth Table properly consists of only nine horizontal Columns of thousands, in Breadth; which Columns are extended in Length to one hundred Lines, corresponding to 100 Degrees of Heat.
The Table is here divided, in order that it may conform to the Size of the Pages: by which Means the Formation of each vertical Number by the following Rule, (which renders the Tableself-evident) might without this Caution, have been attended with some Difficulty.
The vertical Columnsbelowthe Figures expressing each thousand, shew the Expansion of Aironeach respective thousand,withthe corresponding Degrees of Temperature indicated by the Thermometer in the vertical Column to the left Hand.
Example the first: to find the Expansion of Aironone thousand Feet,withone Degree of Temperature; the Answer in the Table is 2.4, or 2.43: i. e. 2 Feet and 4 Tenths of a Foot, rejecting the 2d Decimal as too minute.
Example the second: to find the Expansionon8 thousand Feet,with99 Degrees of Heat: the Answer is 1924.56: and so of the Rest.
Thusanyof thevertical Numbersshewing the Expansion, may be readilyformed, bydoubling,first, the Number immediately under each thousand in the horizontal Line, for the nine first thousands, (of which the Breadth of the Table properly consists, exclusive of the thermometric Column) for the Expansion below it: and,afterwards, for each Expansion immediately below the former, by adding, to the Expansionlastfound, the Number immediately under its respective thousand.
First Example: to find the vertical Number for the Expansion under the first thousand, viz. 1000,with2 Degrees of Heat: the Number under 1000 is 2.43: double this: and the Answer is 4.86.
Second Example: suppose the Expansionlastfound be thatonone thousand Feetwith24 Degrees of Heat; viz. 58.32: and the Expansiononthe same thousand,withone Degree of Heat more, viz. on 25 Degrees, be required; add the Expansion
58.32
2.43
———
60.75
Third Example: supposing the Expansionlastfound to be the Expansionon9000 Feetwith99 Degrees of Heat, which in the Table is 2165.1.
It is required to find the Expansiononthe same 9000 Feet, with 100 Degrees of Heat; add to the Expansion last found,
2165.13,
21.87
———
2187.00
Any vertical Number shewing the Expansion maylikewisebefound, first,by multiplying the first Figure, or Number, of thegiventhousand Feet (in the horizontal Line,) into the Answer or Expansion on thefirstthousand Feet, with one Degree of Heat: for Example;
To find the Expansion on 9000 Feet with one Degree of Heat.
The Expansion on 1000 Feet, with 1 Degree of Heat (from whence, all the other Expansions are derived) being 2.43; multiply that Number by 9, the first Figure of the given thousand Feet, and the Answer or Expansion with 1 Degree of Heat, is 21.87: hence all the Answers or Expansions, immediatelyunder the horizontal Line of thousands, areformed.
Then 2dly, any other vertical Number or Expansion may beformedby multiplying the Expansionimmediatelyunder thegiventhousand Feet in the horizontal Line, into thegivenNumber of Degrees: for Example;
To find the Expansion on 9000 Feet, with 50 Degrees.
The Expansion with one Degree on 9000, is 21.87: therefore the Expansion with 50°, is 50 Times more, viz. 1093.50, and so of the Rest.
These different Methods serve to prove the Answers, and to elucidate the Table.
[125]These Experiments were made with the Manòmeter when the Atmosphere was half an Inch heavier than in the Experiments to prove the Expansion of Quicksilver, the Barometerthenstanding at 30 Inches only.
[126]There isseldomOccasion to take more than the first Decimal out of the Table.
[127]“RULE.“Precept the 1st. With the Difference of the two Thermometers that give the Heat of the Barometer (and which for Distinction sake, are called the attached Thermometers) enter Table I, with the Degrees of Heat in the Column on the left Hand, and with the Height of the Barometer in Inches, in the horizontal Line at the Top; in the common Point of Meeting of the two Lines will be found the Correction for the Expansion of the Quicksilver by Heat, expressed in decimal Parts of an English Inch; which added to the coldest Barometer, or subtracted from the hottest, will give the Height of the two Barometers, such as would have obtained, had both Instruments been exposed to the same Temperature.“Precept the 2d. With these corrected Heights of the Barometers enter Table II, and take out respectively the Numbers corresponding to the nearest Tenth of an Inch; and if the Barometers, corrected as in the first Precept, are found to stand at an even Tenth, without any further Fraction, the Difference of these two tabular Numbers (found by subtracting the less from the greater) will give the approximate Height in English Feet. But if, as will commonly happen, the correct Height of the Barometers should not be at an even Tenth, write out the Difference for one entire Tenth, found in the Column adjoining, intitledDifferences;and with this Number enter Table III, of proportional Parts in the first vertical Column to the left Hand, or in the 11th Column; and, with the next Decimal, following the Tenths of an Inch in the Height of the Barometer (viz. the hundredths) enter the horizontal Line at the Top, the Point of meeting will give a certain Number of Feet, which write down by itself; do the same by the next decimal Figure in the Height of theBarometer (viz. the thousandths of an Inch,) with this Difference, striking off the last Cypher to the right Hand for a Fraction; add together the two Numbers thus found in the Table of proportional Parts, and their Sum subduct from the tabular Numbers, just found in Table II; the Differences of the tabular Numbers, so diminished, will give the approximate Height in English Feet.“Precept the 3d. Add together the Degrees of the two detached or Air Thermometers, and divide their Sum by 2, the Quotient will be an intermediate Heat, and must be taken for the mean Temperature of the vertical Column of Air intercepted between the two Places of Observation: if this Temperature should be 31°1⁄4 on the Thermometer, then will the approximate Height before found be the true Height; but if not, take its Difference from 31°1⁄4, and with this Difference seek the Correction in Table IV, for the Expansion of Air, with the Number of Degrees in the vertical Column on the left Hand, and the approximate Height to the nearest thousand Feet in the horizontal Line at the Top; for the hundred Feet strike off one Cypher to the right Hand; for the Tens strike off two; for the Units three: the Sum of these several Numbers added to the approximate Height, if the Temperature be greater than 31°1⁄4, subtracted if less, will give the correct Height in English Feet. An Example or two will make this quite plain.”
“RULE.
“Precept the 1st. With the Difference of the two Thermometers that give the Heat of the Barometer (and which for Distinction sake, are called the attached Thermometers) enter Table I, with the Degrees of Heat in the Column on the left Hand, and with the Height of the Barometer in Inches, in the horizontal Line at the Top; in the common Point of Meeting of the two Lines will be found the Correction for the Expansion of the Quicksilver by Heat, expressed in decimal Parts of an English Inch; which added to the coldest Barometer, or subtracted from the hottest, will give the Height of the two Barometers, such as would have obtained, had both Instruments been exposed to the same Temperature.
“Precept the 2d. With these corrected Heights of the Barometers enter Table II, and take out respectively the Numbers corresponding to the nearest Tenth of an Inch; and if the Barometers, corrected as in the first Precept, are found to stand at an even Tenth, without any further Fraction, the Difference of these two tabular Numbers (found by subtracting the less from the greater) will give the approximate Height in English Feet. But if, as will commonly happen, the correct Height of the Barometers should not be at an even Tenth, write out the Difference for one entire Tenth, found in the Column adjoining, intitledDifferences;and with this Number enter Table III, of proportional Parts in the first vertical Column to the left Hand, or in the 11th Column; and, with the next Decimal, following the Tenths of an Inch in the Height of the Barometer (viz. the hundredths) enter the horizontal Line at the Top, the Point of meeting will give a certain Number of Feet, which write down by itself; do the same by the next decimal Figure in the Height of theBarometer (viz. the thousandths of an Inch,) with this Difference, striking off the last Cypher to the right Hand for a Fraction; add together the two Numbers thus found in the Table of proportional Parts, and their Sum subduct from the tabular Numbers, just found in Table II; the Differences of the tabular Numbers, so diminished, will give the approximate Height in English Feet.
“Precept the 3d. Add together the Degrees of the two detached or Air Thermometers, and divide their Sum by 2, the Quotient will be an intermediate Heat, and must be taken for the mean Temperature of the vertical Column of Air intercepted between the two Places of Observation: if this Temperature should be 31°1⁄4 on the Thermometer, then will the approximate Height before found be the true Height; but if not, take its Difference from 31°1⁄4, and with this Difference seek the Correction in Table IV, for the Expansion of Air, with the Number of Degrees in the vertical Column on the left Hand, and the approximate Height to the nearest thousand Feet in the horizontal Line at the Top; for the hundred Feet strike off one Cypher to the right Hand; for the Tens strike off two; for the Units three: the Sum of these several Numbers added to the approximate Height, if the Temperature be greater than 31°1⁄4, subtracted if less, will give the correct Height in English Feet. An Example or two will make this quite plain.”
[128]There is no Occasion to take more than four Decimals out of the Table.
[129]See Section 368,Note [120].
[130]Section 368,Note [121]on Note [120].
[131]Taking one Decimalonlyout of the Table.
[132]The question: In the upper Gallery of the Dome of St. Peter’s Church at Rome, and 50 Feet below the Top of the Cross, the Barometer, from a Mean of several Observations, stood at Inches 29.5218 Tenths: the attached Thermometer being at Degrees 56.6 Tenths; and the Air-Thermometer at 57 Degrees: at the same Time that another, placed on the Banks of the River Tyber, one Foot above the Surface of the Water, stood at 30.0168, the attached Thermometer at 60°.6, and the Air-Thermometer at 60°.2: what, was the Height of the Building above the Level of the River?
[133]SeeSection 375. 2dly. If the Moiety,Half-Heat, or mean Temperature of the Air,is equalto the Standard-Temperature, to which the two Barometers are brought, by the 2d Table; the fourth Table, forExpansion of Air, is needless: the Height already found, in the 2d Table, being thetrueHeight of theupper Station.3dly. If the Moiety,Half-Heat, or mean Temperature of the Air, isless thanthe Standard-Temperature of 31°.24; subtract the mean Temperature from 31.24; and with the Remainder find the Expansion, as usual, by the 4th Table: subtract the Sum, (which is a corresponding Height in Feet and Tenths) from the Height in Feet and Tenths of theupperBarometer, at theStandard-Temperature, in the 2d Table: and the Remainder will be thetrueHeight of theMountainorupper Station. Section 384, Notea.
3dly. If the Moiety,Half-Heat, or mean Temperature of the Air, isless thanthe Standard-Temperature of 31°.24; subtract the mean Temperature from 31.24; and with the Remainder find the Expansion, as usual, by the 4th Table: subtract the Sum, (which is a corresponding Height in Feet and Tenths) from the Height in Feet and Tenths of theupperBarometer, at theStandard-Temperature, in the 2d Table: and the Remainder will be thetrueHeight of theMountainorupper Station. Section 384, Notea.
[134]The question: Near the Convent of St. Clare, in a Street calledLa Strada dei Specchi, at Rome, thelowerBarometer stood at 30.082, its attached Thermometer 71 Degrees, and detached ditto at 68 Degrees: on the Tarpeian Rock, or West-End of the famous Hill called The Capitol, theupperBarometer was at 29.985, its attached Thermometer 70°.5, and detached ditto 76°: what was the Height of the Eminence?
[135]Sadler’sPractical Arithmetic, Page 293.
[136]The Writer has not hitherto been so fortunate as to meet with the original Memoir, containing the Particulars of this curious Experiment by Mons. Lavoisier.
[137]Dr. Priestley’s Experiments and Observations relating to Air and Water. Ph. Tr. for 1785, Vol. 75, Part 1, Page 279.
[138]The Diameter may be enlarged.
[139]By Means of the Cradle,bothare more easily moved: the Muffle is prevented from adhering to the Tube; and Steam is admitted to the Borings.
[140]Copper sustaining aredHeat, better than Iron; the latter of which,calcineswith Steam, or, in cooling.