[85]Chalmer describing a Whirlwind, which is a Storm of collection and Ascent of hot Air, &c. by Rarefaction, says, “as the Wind ceased, presently after the Whirlwind passed, the branches and Leaves of various Sorts of Trees, which had been carried into the Air, continued to fall for half an hour; and, in their Descent, appeared like Flocks of Birds of different Sizes.”

This Circumstance proves that Columns of hot Air must have been raised in a Body, in Succession, to so considerable a Height, that Branches of Trees carried up by them, took half an Hour in falling.

[86] It may be from this Principle, that in the East, Liquids are kept cool by being hung in the Shade, in the open Air, suspended in wet Cloths: there being a continual Breeze and Succession of cool dry Spunges (as it were) of Air, in Contact with the wetted Cloths, 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 see Gassendus’s Natural Philosophy. De Chales’s Navigator. And Astro-Meteoro-Logica, per J. Goad.

[91]See Maclaurin’s Newton, Page 376.

[92]Air at a Medium is 800 Times rarer than Water: so that if 800 Times the Quantity of Air naturally contained in a Vessel whose Dimensions are those of a cubic Foot, were pressed into it by a Syringe or Condenser, the Air woud differ nothing from Water in Density.

[93] See Wilson 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.

The intelligent Reader 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]See London 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 will just rise 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 from the mouth of the great Balloon, when stationary: and may be sent up with a Cord, fastened to the Center above the Car of the great Balloon, to reconnoitre the superior Currents: or it may be only filled in Part; and made to descend, and discover the lower Currents.

See “Des Avantages de Ballons, &c. Page 72.”

[100] As the Heights of the Atmosphere encrease in an arithmetical Progression; the Densities are said to encrease in a geometrical Progression: which is a mathematical and pedantic Mode of Expression.

For arithmetical Progression here means 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, doubling the preceding Number; at the Height of each Yard, Fathom, Rood, Mile, &c. &c.

[101]Whiston’s Tacquet’s Euclid, Book XI. Definition of a right Cylinder, Art. 3, Page 166.

[102]Archimedes’s Theorems. Proposition 33, 34; at the End of Whiston’s Euclid, Page 42.

[103]Inferred in the Chester Chronicle, Sept. 30, 1785.

[104]The Writer not having yet been able to procure it from the London Booksellers.

[105]See Chambers’s Dictionary under the Article resistence.

[106]See his “Navires des Anciens.”

[107]See “Gordon’s Principles of Naval Architecture.”

Also the Balzaes and Guaraes, in Ullòa’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 the London Magazine for June, 1784.

[109]See “Lewis’s Commerce of the Arts.”

[110]See Priestley’s numerous Experiments: and that Library of curious Investigation, the Philosophical Transactions.

[111]And Magnitude of distant Objects.

Bacon says that Objects are more visible in an East Wind, and Sounds more audible in a West Wind; being heard at a greater Distance. “Historia Ventorum, P. 37, Art. 31.”

[112]See Le Roi’s Uses of the airostatic Globe at Sea, in his “Navires des Anciens, Page 225.”

[113]The natural Figure of the Dìodon-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 of inflating its 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 or Papier-mâchè varnished; for, being strong, and in a permanent Form, it is more capable of continuing Air-tight: the lower Parts being flaccid, 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 of greater Weight placed in a covered Car below: the Air-Bottle-Balloon being fixed between both.

[114]And by Kunckel’s or Canton’s Phosphorus, See “Priestley’s History of light. 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 from expansion of the Gass.

[116]From Bersham-Forge near Wrexham, where there is always a sufficient Quantity.

[117]The detached Thermometer might be protected from the Sun, by being swung a few Inches below the Car of the Balloon by means of an Opening made purposely throu’ the Center of the Car.

[118]

(Ph. Tr. for 1777, Part 2d, Page 567.)—It was found by
Experiment that the Decimal	.000262
was the Expansion on 30 Inches of Quicksilver, with each Degree of Temperature from freezing to boiling Water: also, the Decimal	.000042
was the Expansion on 30 Inches of the Glass Tube (containing the Quicksilver), with each Degree of	———
Temperature: therefore by Addition,	.000304
or by taking only 4 Decimals,	.0003

is the Expansion on 30 Inches of Quicksilver, and the Glass Tube containing it, with each Degree of Temperature.

Construction of the first Table.

Thus any vertical Number, shewing the Expansion, may be readily formed, by doubling, first, the Number immediately under each Inch for the Expansion below it: and afterwards, by adding the Number immediately under each Inch, to the Expansion last found.

Note: The vertical Columns, below each Inch of Quicksilver shew the Expansion on that Inch, with corresponding Degrees of Temperature indicated by the Thermometer in the Column to the left Hand. Example: to find the Expansion on 30 Inches of Quicksilver with 1 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 of little value.

[120]

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 the first Column,) 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 three vertical Columns 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, the difference between 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

Inches	16.1	answering to	19570.4	}	Height in Feet in the Atmosphere.
And again at	16.2	answering to	19398.4
			———
Difference of .1 in Feet: remaining			= 172.0

which sixteen Inches two Tenths, is a single Tenth more than sixteen Inches one Tenth, and will therefore answer to a less Height 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 a less Height 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 the less Height from the greater, and the Remainder gives that less Height 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 Depth then being the imaginary Level pointed out by the Quicksilver, at the unusual Extent of 32 Inches; each interior Inch and Tenth of Quicksilver will correspond to a superior Elevation of the Instrument, in Feet and Tenths above that Level, and will include the Mensuration of the deepest Mines.

For the mean Pressure 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]

The Height, in Feet, 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 into ten more Parts: in order to shew, in a ten Times less Number of such Feet, the Expansion corresponding to any of those Parts into which the Tenth of 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 in Feet, (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, of the Feet in 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 a Number of Feet called 9 Tenths of 100: but the Tenths are Feet, 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]

(Ph. Tr. for 1777, Part 2d, Pages 564, and 566,)—From the Mean of a Series of Experiments with a Manòmeter, or Instrument to measure the Rarity and Density of the Atmosphere, depending on the Action of Heat and Cold, it was found, that when the Portion of a Tube containing Air (at the Temperature of freezing by Farenheit, and Pressure of 30​1⁄2 Inches[125] by a common Barometer) was divided into 1000 Parts; the Volume of Air within it, encreased nearly in 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 Table self-evident) might without this Caution, have been attended with some Difficulty.

The vertical Columns below the Figures expressing each thousand, shew the Expansion of Air on each respective thousand, with the corresponding Degrees of Temperature indicated by the Thermometer in the vertical Column to the left Hand.

Example the first: to find the Expansion of Air on one thousand Feet, with one 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 Expansion on 8 thousand Feet, with 99 Degrees of Heat: the Answer is 1924.56: and so of the Rest.

Thus any of the vertical Numbers shewing the Expansion, may be readily formed, by doubling, 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 Expansion last found, the Number immediately under its respective thousand.

First Example: to find the vertical Number for the Expansion under the first thousand, viz. 1000, with 2 Degrees of Heat: the Number under 1000 is 2.43: double this: and the Answer is 4.86.

Second Example: suppose the Expansion last found be that on one thousand Feet with 24 Degrees of Heat; viz. 58.32: and the Expansion on the same thousand, with one Degree of Heat more, viz. on 25 Degrees, be required; add the Expansion

on one thousand Feet, with 24 Degrees, viz.	58.32
to the Expansion on the same 1000, with 1 Degree, viz.	2.43
	———
and the Answer is, by Addition,	60.75

Third Example: supposing the Expansion last found to be the Expansion on 9000 Feet with 99 Degrees of Heat, which in the Table is 2165.1.

It is required to find the Expansion on the 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.	21.87	with one Degree of Heat, and
	———
	2187.00	is the Answer by Addition.

Any vertical Number shewing the Expansion may likewise be found, first, by multiplying the first Figure, or Number, of the given thousand Feet (in the horizontal Line,) into the Answer or Expansion on the first thousand 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, immediately under the horizontal Line of thousands, are formed.

Then 2dly, any other vertical Number or Expansion may be formed by multiplying the Expansion immediately under the given thousand Feet in the horizontal Line, into the given Number 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 Barometer then standing at 30 Inches only.

[126] There is seldom Occasion to take more than the first Decimal out of the Table.

[127]

“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, intitled Differences; 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 the Barometer (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 Decimal only out 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] See Section 375. 2dly. If the Moiety, Half-Heat, or mean Temperature of the Air, is equal to the Standard-Temperature, to which the two Barometers are brought, by the 2d Table; the fourth Table, for Expansion of Air, is needless: the Height already found, in the 2d Table, being the true Height of the upper Station.

3dly. If the Moiety, Half-Heat, or mean Temperature of the Air, is less than the 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 the upper Barometer, at the Standard-Temperature, in the 2d Table: and the Remainder will be the true Height of the Mountain or upper Station. Section 384, Note a.

[134] The question: Near the Convent of St. Clare, in a Street called La Strada dei Specchi, at Rome, the lower Barometer 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, the upper Barometer was at 29.985, its attached Thermometer 70°.5, and detached ditto 76°: what was the Height of the Eminence?

[135] Sadler’s Practical 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, both are more easily moved: the Muffle is prevented from adhering to the Tube; and Steam is admitted to the Borings.

[140]Copper sustaining a red Heat, better than Iron; the latter of which, calcines with Steam, or, in cooling.