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] _Foundation of the first Table._

(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] _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 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
And again at 16.2 answering to 19398.4 } in the Atmosphere.
———————
_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] _Foundation of the Table for Tenths._

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. ¼ of the whole 100: or (31)¼.

[124] _The Foundation of the fourth Table._

(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 30½ 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] “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, 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°¼ on the Thermometer, then will the approximate Height before found be the true Height; but if not, take its Difference from 31°¼, 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°¼, 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 (_a_).

[130] Section 368, Note (_a_) on Note (_a_).

[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.

Transcriber’s Notes:

• Text enclosed by underscores is in italics (_italics_).
• Text enclosed by pluses is in small caps (+small caps+).
• Obvious typographical errors have been silently corrected.
• Archaic language and spelling is left as-is, except “AERIAL” was
printed with dots above the ‘A’ and ‘E’, this was assumed to be a
typesetter's limitation and replaced with “AËRIAL", to match the
lower case usage.
• Errata have been applied, as much as I understood them.
• Numbers for sections 259–261 are repeated.