VI.

437. The following Alterations woud supersede the Use of the Rake, and leathern Cases: the latter of which, by any accidental Crack or Flaw in the Leather, might admit a sufficient Quantity of common Air to produce an Explosion.

The cylindric Form of the Copper, or malleable Iron (to be used as a Lining for the Tube) is to be changed, into that of a half Cylinder, or inverted Muffle: and to be perforated with small Holes.

This Muffle is to be nearly filled with a Ton of Iron Borings: (the Ends to be made up, to prevent the Borings from falling out into the Tube;) the Muffle itself is to be supported by a Cradle⁠[139] of the same Form, made of strong Copper Wire,⁠[140] like the open Iron-Wire-Fenders: and the whole is to be thrust into the Tube.

The Length of the Muffle depends on the Quantity of Borings that are intended to be used.

The Ends of the Tube shoud not be made so strong as the Tube itself: that, if an Explosion happens, they may give way first, and prevent a Rupture of the Tube: not that any Danger is to be apprehended, that such an Event will take Place, so long as the Steam-Pipe is attended to, by a proper Person: the above Caution being only given, to prevent a Possibility of Rupture.

Each End shoud be cast, or forged with a hollow Handle; and shoud screw into the Tube.

The Length of the Tube shoud be such, that the Person who attends the Steam-Pipe, shoud feel no Inconvenience from the Heat of the Fire.

Nine Feet woud therefore be a proper Length: the conducting Tube the same.

Within six Inches from each End of the Tube which holds the Borings, a Hole, half an Inch in Diameter shoud be drilled across the Middle of the Tube, in an horizontal Direction.

Into these, an Iron Axis is to be fitted, (so as to take out occasionally) and pass throu’ the Tube: each End of the Axis is to project outwards a Couple of Inches, and to be made square, for the Socket of a strong Iron Winch or Handle.

Each Axis to be furnished with a strong Chain, of equal Length with the Tube; one End of which Chain is to be riveted, or otherwise fixed, to the Middle of the Axis; and the other, to be fastened occasionally to one Extremity of the Cradle and Muffle: the second Axis and Chain in like Manner, to the other Extremity.

The Muffle is to be placed in the Cradle: both are then to be thrust into the Tube, and fastened to the Chain at the farther Axis: in which Position the Muffle may be filled with Borings, and gradually drawn into the Tube; till the same End has reached the Center of the Fire. The nearer End is then to be hooked by the nearer Chain, already wrapped round the nearer Axis: and the light Iron Caps to be screwed on each End of the Tube.

438. The Boiler for Steam may be fixed on any Part of the Tube near the Fire, and near the opposite Axis; so that one Person may attend both the Steam-Pipe, and Axis. The Steam to be conveyed throu’ a small Orifice made in the Bottom of the Tube, between the same Axis and the Fire.

439. As soon as the Materials, above the Center of the Fire, are supposed to be red hot, the Steam-Pipe is to be opened for a Moment and shut again. The extricated Gass will be instantly heard, rushing throu’ the Vessel of cold Water; and as instantly seen to swell the varnished Linen-Trunk as it passes into the Balloon.

The Steam-Pipe is to be regulated by these infallible Signals: and the Process continued, till that Quantity of Borings, that was in the Center of the Fire, and consequently red hot, is supposed to be calcined.

At which Time, the Handles are to be applied to the Axis, and the Cradle and Muffle drawn 5 or 6 Inches forward into the Fire.

When drawn too far; Recourse must be had to the second Axis.

440. If great Expedition is required, two or three Conductors from the same Tube may be used: and, at the Distance of six or seven Feet from the Fire, Tin-Conductors may be added; taking Care that they are made, applied, and continued Air-tight.

THE END.

An alphabetical index of the contents:

Referring to the sections and notes, but not to the Pages.

FOOTNOTES:

[1] Ποιησον δ᾽ Αιθρην, δος δ᾽ Οφθαλμοῖσιν ιδεσθαι·
Ἐν δε Φαει και ολεσσον, επει νυ τοι ευαδεν οὑτως.
Homer’s Iliad, Book 17, Line 646.

[2] Phil. Trans. Vol. LXVII, for 1777, Part II, Page 513, containing Sir G. Shuckburgh’s Rules for the Mensuration of Heights with the Barometer. Also Vol. LXVIII, for 1778, Part II, Page 681:

[3] And Page 688.

[4] It were to be wished that the Divisions of the Thermometer by Farenheit were become general throughout Europe, in preference to those by Reaumur yet retained abroad; which Divisions of Reaumur are not sufficiently minute to mark the least sensible Change in the Temperature, are subject to frequent Mistakes, and the Inconvenience of adding in the Notation, the Words above or below the Cypher, zero, or Point of Congelation: besides their being in Conversation not easily compared with those of Farenheit; each Degree of the latter having to that of the former nearly the Proportion of 18 to 11: since Farenheit from the freezing Point upwards to boiling Water has 212 − 32 = 180°, and Reaumur to the same Height, 110° Divisions: Mr. Saussure says as 4 to 9; in which there is an evident Oversight: see his curious and philosophic Investigation of the Atmosphere in “Essais fur L’Hygrometrie.” 4to. A Neuchatel, 1783.

Frequent Mention being made of the Thermometer graduated according to Farenheit’s Scale, in different Parts of the following Account; it may not be amiss to shew the corresponding Points according to Reaumur, taken from “Thermometre universel de Comparaison, extrait du Journal de Physique de M. L’Abbé Rozier.”

Farenheit.Reaumur.
5413 & 4-9ths above the Cypher.
5514 ditto, nearly.
5715 2-9ths ditto, nearly.
5916 4-9ths ditto, nearly.
6017 1-9th ditto.
6520 1-9th ditto, nearly.

[5] The Strength of the Rope, or Cable, if its Length does not exceed 10 or 12 Yards, ought to be such as to support a weight, greater than the Weight of the Balloon and it’s Appendages, for the Resistance made by the Grapple against the Balloon acted on by the Wind is immediate: The Rope ought therefore to be made of Indian-Gut, as most elastic, or Silk, as lightest. But if the Rope be half a Mile, or a Mile long; the Resistance is gradual: the Balloon descending for some Minutes; and having an open Space to move in through the Air: the Rope or Cable acting as a Radius, and the Levity of the Balloon and Opposition of the circumambient Air preventing it from falling with any Violence.

The shorter Cable may be used at the Height of 10 Yards; in aid of the longer, to prevent it from rising; or to moor it, by winding the Reel, and hauling down the Balloon close to the Ground.

[6] The Resistance being as the Square of the Velocity; therefore if the Velocity be increased 3 Times, the Resistance will be as 3 × 3 = 9, i. e. will be increased 9 Times.

[7]

Pounds
Averdupois.
Weight of the Aironaut160
Provisions and Articles calculated at20
Sand-Ballast prepared in Bags44
Levity for Ascent10
——
Sum total,234

[8] Ancient Warriors among the Arabs, Spaniards, Romans, Gauls, and Germans, being frequently obliged to pass deep Rivers, never undertook a Campaign without them. For the above Anecdote, and many curious Experiments on Air, see Sam. Reyheri, Dissertatio de Aëre, tertium edita. Kiliæ. 1673.

[9] Equal Time with a Regulator corrected by an Observation.

[10] Being a Dial-Compass, the Dipping of the Needle was frequently checked by the Glass at the Top. A Mariner’s Compass is the best.

[11]

The Defect of the Reel remedied

[12] Slate (according to Cronstedt) is the Whetstone of fine Particles, composed of Glimmer, Quartz; and, in some Species, of a martial argillaceous Earth, See “Essay on Mineralogy” by Mendes Da Costa, Sect. 264.

[13]

Method of discovering Haze round the Sun, in bright Weather.

To know whether the Air is hazy, tho’ the Sun continues shining.

The Method taken for that Purpose was by placing the Hand so as to cover his Disk or Body, and then observe the Glory blazing round him; which may, in general, be seen to issue in great Abundance, in Rays of a golden Colour: occasioned by a Haziness or Vapour which pervades the lower Regions of the Air, most frequently in the hottest and calmest Weather, and in the hottest Climates. The Accumulation of these Vapours, before they are formed into Clouds, are often so great as to intercept the Sun’s Rays, or dye them the Colour of Blood: an Appearance frequent in Virginia, and also throughout the torrid Zone.

In the Campania of Rome, for Instance, the Italians have a peculiar Name for such Kind of Weather, when the Sun is neither visible nor invisible: Il Sole si vede, e’ non si vede.

By Degrees the Hand is to be removed so as just to have a Glance of the Sun’s Limb. And it frequently happens that the Air is exceedingly hazy; tho’ not a Cloud appears above the Horizon.

[14] Esse in Imaginibus quâpropter Causa videtur Cernendi, neque posse sine his Res ulla videri.
Lucretius de Rerum Natura. L. 4. V. 238.

[15] Notwithstanding what has been said; this, to the great and to the sordid Vulgar, woud still appear a solitary, helpless, and deplorable Situation. But such are not captivated with the golden Lines of Epictetus, (Chap. 13. Line 3. see Mrs. Carter’s Translation.)

“ΠΑΝΤΑ ΘΕΩΝ μεστα και ΔΑΙΜΟΝΩΝ·—Βλεπων τον ΗΛΙΟΝ και Σεληνην, και Ἀστρα, και ΓΗΣ απολαυων και ΘΑΛΑΣΣΗΣ, ἐρημος εστιν ου μαλλον ἠ και ἀβοηθητος·” Nor are they practically influenced by the better Words of a much finer Writer: “The Earth is full,” &c. &c. And “If I take the Wings of the Morning,” &c. &c.

[16] There being, at first, no Clouds, as usual, to occupy the Place of the lowest Stratum.

[17] It has been said that the apparent Height from the Balloon to the Ground was 7 Miles, viz. 4 to the Summit of the Clouds, and 3 below: and the barometric Height was about a Mile and half, viz. 2332 Yards, a Calculation of which will be given.

If then we divide that Height or Distance into 2 such Parts, that the greater shall be to the less as 4 to 3; we obtain the Length of each Part; i. e. the barometric Height from the Balloon to the Summit of the Clouds, and thence to the Earth; which is done thus:

Suppose the whole Distance to be any Line, as A. B. to be divided in C. Then, as 7 is the whole Line, and 4 the greater Part; say, as the whole 7 is to the greater Part 4, so is the whole Distance to a fourth Term proportional, which will be equal to the greater Distance sought:

Whole Distance
in Yards.		 Greater Distance in Yards.
Thus 7, : 4 ::

2332

: 1332⁠4⁄7 Ans.

4

———

7)9328
2332 the whole.

1332⁠4⁄7

1332⁠4⁄7 being the greater Distance found; take the greater from the whole, and then will remain the lesser Distance wanted, viz. 999⁠3⁄7: the 1332⁠4⁄7 = the greater Distance, and 999⁠3⁄7 = the lesser Distance: and adding the Fractions 4⁄7 3⁄7 = 1 to the 999; we have 1332 Yards for the greater Distance, or Height of the Balloon above the Summit of the superior Clouds: and 1000 Yards for the less Distance, or Height from the Earth to the Summit of the superior Clouds.

Note. The Line A. B. here selected is the famous Measure of (half) a mathematical Rhinland and Roman Foot, according to Snellius. (See Geographia Generalis of Varenius, published by Newton. Lib. 1. Cap. 2. De variis Mensuris.)

[18]

PROBLEM.

To find the circular Boundary of the celestial Prospect over the Tops of the superior Clouds, from the Balloon at the Height of near a Mile and half above the Surface of the Earth, viz. 2332 Yards. The Height from the Earth to the upper Surface or Floor of Clouds being 1000 Yards; and the Height above the Floor to the Balloon being 1332 Yards.

On the Curvature of the Earth and Clouds, and Elevation of the Eye above their circular Horizon.

Rule. To the Earth’s Diameter, equal to 7940 geographical Miles, add the Height of the Eye above its Surface: multiply the Sum by that Height: then the square Root of the Product gives the Distance at which an Object on the Surface of the Earth can be seen by an Eye so elevated. Note the Diameter of the Earth, in Feet, is 41798117, according to Newton. (See Practical Navigator, by J. Moore, 7th Ed. Page 251.)

FIRST.

Double 1000 Yards, the Height from the Earth to the Clouds for an Addition to the Diameter of the Earth, whose Surface is now considered, as extended to the concentric Floor of Cloud.

1000
1000
——
2000

SECOND.

13932702(1⁄3)

 Diameter of the Earth in Yards.

2000

 Addition to the Diameter.

————

13934702

 Sum, to which add

1332

 the Height of the Eye or of the

————

 Balloon above the Floor of Cloud.

13936034

 Sum, which multiply into

1332

 the Height of the Eye above the

————

 Floor.

27872068

41808102

41808102

13936034

——————
Extract the

. . . . .

1760) Yards in a Mile.
Square Root

18562797288

 (136245 (77 Miles.

1

12320

—

———

23) 85

13045

69

12320

——

———

266) 1662

Yards 440) 725

 (1 Quarter of a Mile.

1596

440

——

——

2722) 6679

285

 Yards.

5444

———

Ans. 77

 Miles, 1 Qu. 285 Yards.

27244) 123572

108976

———

272485) 1459688

1362425

————

97263

Circular Boundary of the terrestrial Prospect from the Balloon on a clear Day.

PROBLEM.

To find the circular Boundary of the terrestrial Prospect, on a clear Day, from the Balloon at the Height of near a Mile and half, viz. 2332 Yards: the Earth’s Diameter being

equal to13932705⁠2⁄3Yards,
add 2332the Height of the Eye or Balloon.
————
13935037he Sum, multiply into
2332the Height of the Eye, &c.
————
27870074
41805111
41805111
27870074
——————
Extract the. . . . . 1760) Yards in a Mile.
square Root32496506284(180267(102,
11760 say 102​1⁄2 Miles, Ans.
———
28)2244267
2243520
————
3602) 9650747 Yards, Remainder.
7204
———
36046) 244662
216276
————
360527) 2838684
2523689
————
314995Remainder.

[19] See his “Minute Philosopher.”

[20] Ullòa in his voyage to South-America relates, that in passing over the Deserts, Írides are frequently seen by Travellers round their own Heads as the Center of the Iris; and visible only to themselves. But what Analogy the Balloon Iris bears to them, Time and future Experiments may discover. See his “Voyage to South America, Vol. 1. Pa. 442.”

[21]

As Sound travels1142Feet in a
Second, it must have moved in30Seconds
———
Feet in a Yard3)34260= Feet
Yards in a Mile1760)11420(6 Miles
10560
——
Yards in a Quarter of a Mile440)860(1 Quarter
440
——
Answer 6 Miles, 1 Quarter, and420Yards.

[22] Equal to 2085 Yards; or 1 Mile, 325 Yards.

[23] Long’s Astronomy. Pages 227, 229.

[24] Also called the Horsham Stone, from a Place so named, in Surrey, where great Quantities are found.

[25]

PROBLEM.

To find the Length of the Shadow from a Person of middle Stature, (five Feet and a half High) viz. at XII o’Clock, on the 8th Day of September, 1785, at Chester, whose North Latitude is 53° 12′; (and 3° 11′ West Longitude from London.)

FIRST,

To find the Sun’s Altitude at XII.

From

90°. 00′′

 Subtract

The Latitude

53. 12

———

The Remain.

36. 48

 is the Complement of Latitude,
to which add (from the Tables)

Sun’s N. Decl.

5. 29

———

The Remain.

42. 17

 is the Sun’s Altitude (viz. at XII.)

SECOND,

For the Shadow say,
As the Sine of the Sun’s Altitude 42° 17′
To the Person’s Height, viz. 66 Inches,
So is the Co-Sine of the Sun’s Altitude,
To the Length of the Shadow.

For the Sine of the Sun’s Altitude 42° 17′ in the Table of artificial Sines, is the Logarithm 9.82788, which, subtracted from the arithmetic Complement, viz. 9.99999 (supposing the last Figure a 10) becomes,

.17212
Then for the Person’s Height, viz. 66 Inches: in the Table of Logarithms is the corresponding Number,

1.81254
And for the Co-Sine (had by subtracting the Altitude 42.17 from 90.00) viz. 47.43: among the artificial Sines is the Logarithm,

9.86913

————
The above Sums added, are

11.86079
which logarithmic Number (deducting the Initial 1 as useless) viz. 1.86079, in the Table of Logarithms, corresponds to 72.57, equal to 72 Inches, for the Length of the Shadow at XII.

Reducing then the Numbers 66 and 72, to the lowest Denomination, thus 6)66⁄72 = 11⁄12 the Proportion which the Length of the Shadow bears to the Height of the Object is thereby obtained: that is

[26] If the Length of the Shadow be divided into 12 Parts, the Height of the Object would be 11 of those Parts. See Moore’s Practical Navigator.

PROBLEM.

An easy Way to find the Proportion which the Length of the Shadow bears to the Height of an Object is, at any time when the sun shines, to fix a Plummet Line and frame upright in the Ground; measure the Length of its Shadow, and compare it with the Height of the frame.

[27] Equal to 3 Quarters of a Mile and 121 Yards.

[28] i. e. When the Barometer below is at 30 Inches, and Thermometer below at 60° viz. about 1000 Yards high in fine Weather, and 500 in changeable.

[29] Being 1083 Yards, i. e. half a Mile, and 203 Yards.

[30] It was High Water at Chester and Frodsham-Bridge, at 38 Minutes past I.

[31] Articles parted with, to check the first Descent at Bellair, near Frodsham: and to ascend the second Time.

To check the first Descent. Pounds. Ounces.
Ballast, at twice:

24

0
To clear Trees and Hedges, and re-ascend:
Barometer and Frame,

0

12​1⁄2
Basket with Tunning Dish and Bottles (except the Flask with Brandy and Water)

4

10
Half Mile of Twine on the Reel

1

0
Speaking Trumpet

0

8​1⁄2
Woollen Gloves

0

1

—————

31

0

24

0

—————

Remains for Re-ascent

7

0

[32] The Sun’s Azimuth from the North Point Westward, being 118.26′: its Supplement to 180° is 61°.34′ South westerly: i. e. South West by West, half West nearly.

[33] The Length of the Shadows being more than double the Height of the Objects: see [34].

[34] To find the Length of the Shadow at half past III.

(See Section 84, [Note [25].)

Given Lat. of Chester,

53°

12′

 To find Sun’s Alt.
Sun’s Dec.

5

29
Hour III, 30M.

52

30

This is the Case of an oblique spheric Triangle, wherein are two Sides and one Angle between them given, to find the Sun’s Azimuth, and the Sun’s Co-Alt.

Side

84.

31

 Sum of Sides

121.

19
Side

36.

48

 Diff. of Sides

47.

43
(3​1⁄2 Hour) Angle contained

52.

30
Half ditto

26.

15

 Co.

63.

45
Half Sum of Sides

60.

39

29.

22
Half Difference ditto

23.

51

66.

9

THE FIRST PREPARATIVE PROPORTION.

As Sine of 1⁄2 Sum of Sides

60.

39

0.05966

 Co-Ar.
To Sine of 1⁄2 Difference of Sides

23.

51

9.60675
So Co-Tangent 1⁄2 contained Angle

63.

45

10.30703

———

————
To T. of 1⁄2 Diff. of the other two Angles

43.

15

9.97344

SECOND PREPARATIVE PROPORTION.

As Co-Sine 1⁄2 Sum of Sides

29.

21

0.30968

 Co-Ar.
To Co-Sine 1⁄2 Diff.

66.

9

9.96123
So Co-Tangent 1⁄2 contained Angle

63.

45

10.30703
————
To T. 1⁄2 Sum of other Angles

75.

11

10.57794
Half Diff. before found

43.

15
———
Sum, is greater Angle

118.

26

 = Sun’s Azim.
Diff. is lesser Angle

31.

56

 = S’s right Asc.

Then by first Axiom in Trigonometry, to know the Sun’s Altitude say,

As Sine Sun’s right Asc.

31.

56

0.27659
To Sine Co-Lat.

36.

48

9.77744
So Sine of the contained Angle

52.

30

9.89947

————
To Co-Sine of the Sun’s Alt.

63.

57

9.95350

from

90.

———
Sun’s Alt.

26.

3

Having Sun’s Alt. to find the Shadow,

As Sine Sun’s Alt.

26.

3

0.35738

 Co-Ar.
To Person’s Height,

66

Inches,

1.81954
So Co-Sine of the Sun’s Alt.

63.

57

9.95350

————
To Length of Shadow,

135

Inches,

2.13042

Then 6(66⁄135 = 11⁄22 − | − 3⁄6 or 1⁄2, i. e. as 22 to 45: supposing the Length of the Shadow divided into 45 Parts; the Height of the Object woud be 22 of those Parts; or not quite half the Length of the Shadow, at half past III.

[35] See “Priestley on Electricity.”

[36] Εὔροια.

[37]

An Account of the Breath being visible at Sea, when the Thermometer was at 61.

[38] This Assertion may seem to contradict what was said in Section 44: When—“every Thing, that coud be seen at all, was seen distinct:” but it only proves that the Balloon had attained a greater Altitude during the Re-ascent, and that the shadows were much lengthened, as the Evening advanced.

[39] Angelica Kauffman.

[40] It consists of a Frame, made by placing two strong Posts, moveable at Pleasure, each nine or ten Feet high, upright in the Ground, at the Distance of two Yards: the Posts being well secured by broad Pedestals, to keep them firm: a strong horizontal Iron Axis goes throu’ the Top of the Posts; and throu’ the Centers of four Arms or Levers at their Junction.

Between the four corresponding Ends of each two Arms, (which Arms are also strengthened by Beams from one to the other), are fixed four Seats or Boxes, well secured, each holding three or four Persons, and moving on Iron Pivots, near the Top of the Boxes, so as always to preserve the vertical Equilibrium.

[41]

Recommended to Invalids.

[42] Particularly the Stomach and Diaphragm. See “Berdoe’s Enquiry.”

[43] Talis Aër qualis Spiritus. See “Health’s Improvement,” by Dr. Moffet, Chapter 3, Of Air, Page 79.

[44] Or Solid of least resistance, see Chambers’s Dictionary, with the Supplement.

[45] It will be found, that, on comparing the two Calculations in Section 52, Note [Note [18], corrected; the circular Distance from the Eye, above the Clouds, was 102 Miles, 1 Quarter, 320 Yards: while that above the Earth, seen from the same elevated Situation, (supposing the Day to have been clear for such a View,) was 102 Miles, 1 Quarter, 307 Yards: whose Difference is only 13 Yards: that is, the Distance above the Clouds to the nebulous Horizon, was rather more extensive, than that above the Earth to the terrestrial Horizon.

It may not, to some Readers, be deemed either unentertaining, or foreign to the Subject; if the Distance of the Prospect from the Balloon at its greatest barometric Altitude, viz. 2332 Yards, or a Mile and Half within 33 Yards, be compared with the Distance which may be seen from the Summit of the principal Mountains in different Parts of the Globe.

1. Cotopàzy, a Mountain in the Province of Quito, in America, and under the equinoctial Line, is said by Ullòa (Vol. 1. Page 422) to be 3126 Toizes or Fathom, i. e. 6252 Yards, or 3 Miles and a Half and 92 Yards in Height.

2. White Mountain, called by the French Mount Blanc, near Geneva, is considered by Sir G. Shuckburgh (Phil. Trans. Vol. 67, Part 2d, Page 598, for the Year 1777) as the highest Land in Europe, Asia, or Africa (known to Europeans) and calculated by him at 5220 Yards, or 3 Miles within 60 Yards above the Level of the Mediterranean Sea.

Mons. Bourit just returned from his last Tour, see his “Description de Glacieres” in 1773, makes the White Mountain but 5102 Yards in Height, (which is 30 Yards lower than Teneriffe) including the 410 Yards for the Level of the Lake of Geneva above the Mediterranean.

3. The Peak of Teneriffe in the Canary Islands, which, in approaching towards it, Authors agree, may be seen at the Distance of 120 Miles at Sea, if the Weather is clear; (Modern History, Vol. 14th, Page 451;) and, in returning from it, is discoverable at the Distance of 150 Miles, according to Glas’s History of the Canaries (Page 234);—has been estimated by Dr. Heberden in Madeira (Guide to the Lakes, Page 187) at 5132 Yards, or 3 Miles within 148 Yards.

Glas remarks farther, that in sailing from Teneriffe, the Peak, at the Distance of 150 Miles is very little darker than the azure Sky, on Account of the great Quantity of Vapour intercepted between the Eye and the Mountain: and not because it ceased to be an Object too small for the Sight; or was in Fact, below the Horizon, and only raised by Refraction of the Vapour.

With Respect to the Peak of St. George, situated in the Island called Pico, one of the Azòres; the Writer of this Account asserts, from the Mouth of an able and experienced Officer in his em some Weeks off those Islands; that the latter has frequently observed the Peak, at the Distance of 120 Miles, and coud then distinguish a third Part of its Height down the Mountain. Section 126, [Note [37]), see also [46] below.

4. Etna is 3877 Yards above the Mediterranean: (according to Brydone’s Tour throu’ Sicily and Malta, Vol. 1. Page 211) or 2 Miles and 357 Yards.

5. Blue Ridge, the highest Mountain in the Island of Jamaica, is, according to Dr. Clark, who measured it in November last, 3080 Yards, or 1 Mile and three Quarters, above the Level of the Ocean.

The distance to be seen is considered as terminating the Radius of a Circle, whose Center is the eye of the Observer, on each Mountain.

Height of the Mountains.distance to be seen from them in Miles.
Cotopàzy 3 Miles and a Half and 92 Yards, (for the Process, see Section 52, [Note [18]167​1⁄2 and 405 Yards.
White Mountain 3 Miles within 60 Yards.153​1⁄4 and 13 Yards.
Peak of Teneriffe 3 Miles within 148 Yards.152 within 72 Yards.
Mount Etna 2 Miles and 357 Yards.132 and 127 Yards.
Blue Ridge 1 Mile and 3 Quarters.117​3⁄4 and 30 Yards.
Balloon 1 Mile and half within 33 Yards.102​1⁄4 and 307

As it is well known that Objects of the greatest Magnitude appear but as blue air at even a less Distance than 100 Miles; to which add the Difficulty of Journies, and Ascent to the Summit of these astonishing Mounds of Earth; and all this for the Sake, not of a complete down prospect, subject to a perpetual Variety, but merely an imperfect Side-View: the pleasure and ease of attaining still more stupendous Heights at any Place and Time, by Means of the balloon, are strikingly in Favor of that Invention. And, notwithstanding the confessed Merit of Dr. Black’s Project with the Farciminàlis of a Calf, and Mr. Cavallo’s Soap Bubbles with inflammable Air; (see his History of Aerostation, Page 34;) if the Emperor had been alive who offered a Reward for the Invention of a NEW PLEASURE; the first Prize had been due to the Brothers Montgolfier, and a second to the Brothers Roberts.

[46] As therefore it may be supposed that the Peak of St. George, in receding from it, woud vanish at the Distance of 150 Miles; its Height may easily be ascertained geometrically thus:

See the Figure annexed.

Let M be the Summit of the Mountain: and let the Line M T drawn to the Circumference of the Circle at T, be the evanescent Distance of the Mountain in the Horizon, viz. 150 Miles.

Join T C, viz. a Line drawn from the Tangent to the Center of the Circle, which Line will therefore represent the Semidiameter of the Earth, viz. 3958 Miles, according to Newton.

Draw a Line from C to M, which will pass throu’ some Point of the Circumference as H, the Base of the Mountain.

Then, in the Triangle M T C, as the Angle at T is a right Angle (Euclid’s Elements, Book 3, Proposition 18;) and the Sides M T, and T C, containing the right Angle, are known; the third Side C M is readily found: (being a Corollary to the 47th Prop. 1st Book Euclid:) viz. having the two Sides of a right Angle Triangle given to find the third. Therefore

RULE.

Multiply the Sides containing the right Angle, each into itself: viz. 150 and 3958: add the Products into one Sum: from which extract the square Root; equal to the Length in Miles, of the third Side required.

From the third Side, subtract that Part, viz. C H, which is equal to the Semidiameter T C already found: and the Remainder H M is the Height of the Mountain.

Thus:

150

 Miles.

3958

 Miles in the Semidiameter of

150

3958

 the Earth

——

———

7500

31664

15

19790

———

35622

22500

11874
Square of the

————
greatest visible

15665764

 Square of the Semidiameter
Distance.

add 22500

 of the Earth.

————
Extract the sq. Root,

15688264

 (3960.84 Square Root.

9

 3958 subtract.

—

 ——

69) 668

 Rem. 2.84 Answer in Miles.

621

——

786) 478.2

471 6

———

79208) 6664.00

 continued to 2 Decimals.

6336 64

————

792164) 32736.00

 ditto.

31686 56

————

104944

To find the .84 Part of a Mile; multiply

1760Yards in a Mile,
Decimal Parts of a Mile to be reduced.84into Yards.
——
7040
14080
———
1760)1478.40(0
Subtract1478
——
282

Answer: the Height of the Mountain is 2 Miles 282 Yards.

[47] Rays flowing from the Sun seem to be red orange or yellow, according to the Quantity of Vapours floating in the Atmosphere, which absorbs the most refrangible ones: and the fewer the Vapours the more does the Sun’s Light approach to a perfect and intense white, according to the Doctrine of Newton: which seems to receive Confirmation from the Purity of the Solar Light, when seen above Clouds and Vapours, in the Balloon: where the Sun shines not so much with a golden as with a sparkling silver Light.

[48] Sounds immediately under the Balloon, seemed, as if originated near the Ear, and louder than they would have been heard, at the Distance of some Yards only, when on a Level with themselves: augmenting rather than decreasing, during the Ascent of the Balloon, till it arrived to a Height indicated by the Barometer at 27 Inches. Presently afterwards, the Balloon still rising; the Sounds died away: much sooner indeed than was expected.

The like was observed in descending from a State of perfect Tranquillity and Silence: Sounds from below, when about the same Height, suddenly rushing on the Ear.

It must be considered that by this Time, the shadows were much encreased; tho’ at half past II, they were more than double in Length to the Height of each Object.

The Trees woud therefore spread a shade across the Road.

The tops of the Houses likewise, being Part of them in the Shade; and either thatched with Straw, or covered with Slates of a dusky Hue; woud prevent their throwing off any striking Colour.

Possibly the Encrease of Shade alone, might give the Face of the Country below, a dark-green Cast.

It is certain that the Height of the Balloon must have been very great, to prevent the Sight of public and Turnpike-Roads, above which it frequently passed, and which had been plainly seen before the Re-ascent.

For suppose the Road but 5 Yards wide, which is less than the Truth; if it be allowed that an Object may be distinguished by a sharp-sighted Person, when its Distance from the Eye does not exceed 5156 Times the Diameter of the Object; i. e. when the Object does not subtend a less Angle at the Eye than 30 Seconds of a Circle, (Smith’s Optics, Article 97) which is the smallest visible Point, and equal to the 8000th Part of an Inch on the Retina;—by multiplying 5 Yards, viz. the Diameter of the public Road, into 5156 (or, in round Numbers, into 5000) Times its Distance from the Eye in the Balloon; the Product is 25000 Yards: which Product being divided by 1760, the Number of Yards in a Mile, amounts to 14 Miles, and 360 Yards.

Supposing farther, that a common Eye can only see an Object at half that Distance; the Height woud then be 7 Miles.

The Improbability, therefore, (on Account of the Warmth of the Air at that Height, viz. 60°;) of having soared to so great an Altitude, seems to point out, that the shadows must have contributed a principal Share, in preventing a Sight of the public and Turnpike Roads.

[49] The magnitude of an Object decreases, as the squares of its Distance from the Eye increase.

At whatever Distance, for Example, the Eye can see any Object clearly; as at the Distance of a Foot, or a Yard, if the Object be removed to twice that Distance; it will appear 4 Times smaller than it did before: 2 multiplied into 2, equals 4, which is the Square of 2: in the same Manner, if the Object be removed to thrice the Distance from the Eye, it will appear 9 Times as small, as at the first Distance: for 3 into 3 gives 9, the Square of 3: and so of any farther Distance.

[50] See “Berkeley’s New Theory of Vision, Section 67.”

[51] Dr. Smith having Recourse to intervening Objects; the Writer cannot assent to the Validity of his Argument, illustrated by a well-known Figure, to solve the Appearance of the horizontal Moon. See “Priestley’s History of Light and Colours, Page 712.”

[52]Phil. Trans. for 1785, Part 1, Page 287.

[53]Cavallo’s Treatise on Air, Page 576. Vitriolic Acid Air, Alkaline Air, and other elastic Fluids, are instantly absorbed by Water; (Page 673.) Inflammable Air, and fixed Air, are likewise absorbed by water. (Page 434).

[54] Nam fit, ut interdum tanquam demissâ Columnâ In Mare de Cœlo descendat.—Lucr. L. 6. V. 425.
Una Eurus Notusque ruunt, creberque Procellis Africus. Also
Omnia Ventorum concurrere Prælia vidi. Virgil.

[55]Franklin’s Account of Whirlwinds and Waterspouts, in his Miscellaneous Tracts. Lowthorp’s Abridgement of Phil. Trans. Vol. 2. Page 103. Varenius Geogr. Gen. C. 21, Pag. 265. A clear Account of the Effects of a depression is to be met with in “the History of Jamaica, in 3 vols. vol. 3. Page 800, on Trade and Land Winds.”

[56] Mons. Maupertius has found, that the extreme Cold at Tornea, in the northern Regions beyond the Artic Circle, came directly from above: see “La Figure de la Terre,” Page 59. Il semble que le vent souffle—de tous Côtés à la Fois; et il lance la Neige avec une telle Impetuosité, qu’en un Moment tous les Chemins font perdus. “It seems that the Wind blows from all Points of the Compass at once,” &c.

[57] The Doctrine of smokey Chimnies distinctly treated of under the Article smoke, in the Encyclopædia Britannica, may receive some Improvement, from Circumstances which ascertain the sudden Descent, Elevation, and quick Depression of Columns or rather Torrents of Air, viz. by widening the Tubes, and covering their Tops.

[58]It is thought more candid, and will to many be more satisfactory; to make occasional References to different Authors who have treated distinctly on a Subject, and leave the Reader to draw his own Conclusions by applying to their express Words;—than, either to insert abundant Quotations; or weave their Thoughts into the Texture of the Work: which must encrease its Bulk, without producing any Thing either new or instructive.

[59]Once, particularly, in the Month of January, at Lausanne: Farenheit’s Thermometer at 7 only: the Country covered with Snow; and a North Wind beating violently on the Lake, which continued liquid without Ice: owing, perhaps, in Part, to subterranean Heat, and Exhalations.

[60]The Depression and Reverberation of the Wind near Rivers, and its Descent from Mountains, a Point to be discussed, may furnish a Hint and Reason, why Rain falls more in one Place, than in another not far distant: and why in the same Place it falls in different Quantities, at different Heights, irregularly.

[61] Cavallo’s Treatise on Air, Page 446.—

[62] 442.—

[63] 441.—

[64] 442.

[65] It is light in Consequence of its Warmth, when compared with the cooler condensed Air above it.

[66] In the same Manner that Curls and Streams of Air descended into the Bason over the rising Steam, and interrupted the Regularity of its Elevation; in the larger Towns, during Winter (the Weather being moderate) the Pressure of Air on all Sides, from without, produces a constant Breeze towards the Center of the Town: as may be discovered, not only by the Smoke in its Deviation from the Perpendicular, as it issues from the Chimneys; but by all who are inclined to make the Trial; for, on leaving the Town, they will meet the Breeze.

In calm Weather, during Summer, the contrary Event happens: but more particularly in hot Climates. For the Country being hotter than the Town; a Depression of the Atmosphere takes Place, and scatters the Smoke on all Sides round the Town.

The Cities in Italy, and other hot Climates, on Account of the Buildings, and desirable Narrowness of the Streets, form one contiguous Shelter, Arbor, or grand Parasol: For which Reason, the Nobility leave the Country, and reside in the Towns during Summer: there finding a Coolness and Refreshment unknown on the scorching Plains.

A Reception and Dispersion of Air takes Place; as will presently be mentioned.

The same ocular Proof and Process in the Evaporation of Steam, accounts at once, for a curious Phenomenon constantly observable on all Waters; viz. a narrow smooth irregular Surface of considerable Length, nearly in the Direction of the Wind, yet unaffected by it: all which is probably nothing more than rising Volumes of elastic invisible Steam; resisting the two nearest descending Waves of air; and preventing them from approaching the Surface of Water, over which the Steam is compressed; and there producing a temporary calm.

[67]Phil. Trans. for 1777, Page 470. Thibet in Lat. 31, cold with Snow and Frost.

See Ullòa’s Voyage to South-America, Book 6, Chapter 7; where he describes the snowy Mountains, under the Equator.

As the Weather, near the Equinoctial, is more regular, its Changes closely following those of the Moon; and also the Winds and Hurricanes more violent; the Truth of the foregoing Theory will receive the strongest Confirmation by tracing the Effects of depressing torrents of air, in the Island of Jamaica, extracted from the Author already mentioned.

“The cool Vapour rushes from the Mountains towards the hot dry Air, which hovers over the Savannahs or Vallies.

The Rain falls heaviest in the Mountains. Vol. 3, Page 600.

The Land-Wind after Rain, proceeds from that Quarter whence the Rain has fallen heaviest; and seems to rush from above.

In Spain and North-America, the Wind rushes down. Page 601.

When the Land is most heated, the Sea-Breeze blows almost all Night. Page 602.

The Barometer subsides from 1 Inch to 1​1⁄2 at the full Moon, or just after it.

Wind blows from the Mountains all round the Island: and still a Sea-Breeze over the Mountains: to the Low-Lands, none, 604.

(In Jamaica likewise the Wind blows off the Island every way at once, so that no Ship can any where come in by Night, or go out but early in the Morning, before the Sea-Breeze sets in. See Abr. Phil. Tr. Vol. 3, P. 548.)

Mountain Air rushes down in a continual Current to every Part of the Coast, the Stream descending incessantly throu’ the Night: while heavy cold Air descends to the Mountain Tops, 604.

With a West Wind below there is an East Scud above, 605.

Mountains cloudy, low Lands sunny. 606.

In all the River-Courses of Jamaica, there is a sensible Current of Air. Rain never comes without some Wind: and the Showers almost invariably follow the very Meanders of the larger Rivers, 608.

Rain always cools: the Thermometer falling, after a Shower, from 6 to 8 Degrees, 610.

(And Iron rusts least in rainy Weather: [the Air being then driest,] descending from the upper Regions. Abr. Ph. Tr. V. 3, P. 546.)”

It is said also that “in Jamaica the Clouds gather, and shape according to the Mountains: so that old Seamen will tell you each Island towards Evening, by the Shape of the Cloud over it.”

The Sea-Breeze, being counterpoised by Descent of the etherial Air, produces a calm.

The same Author likewise says, that “the Clouds begin to gather about 2 or 3 o’Clock in the Afternoon at the Mountains, and do not embody first in the Air, and after settle there, but settle first and embody there: the rest of the Sky being clear till Sun-set. So that they do not pass near the Earth in a Body, and only stop where they meet with Parts of the Earth elevated above the rest; but precipitate from a very great Height, and in Particles of an exceeding rarified Nature; so as not to obscure the Air or Sky at all: that great Variety of beautiful Colours in the Canopy of Heaven being raised to a much greater Distance [he means Height] in Jamaica than it is here.” Abr. Ph. Tr. V. 3, P. 557.

(Prognostics of Weather, at certain Periods of the Moon, are mentioned by Captain Langford. Lowthorp’s Abr. Phil. Trans. Vol. 2, Page 105.)

[68]The Depression of a Torrent of Air in the Form of an hyperbolic Solid, contracting as it descends to the Earth, in Proportion as its Density encreases; may furnish a Hint towards the Solution of a Difficulty how to account for the Augmentation of vesiculous Vapours into large solid Drops, frequent during Summer-Showers.

[69]Mons. Saussure’s valuable “Essais sur L’Hygrometrie,” throw new Light on the Doctrine of Rarefaction and Condensation not unfavourable to the Hypothesis here advanced. Page 260.

[70]Ice, when exposed to marine acid Air, is dissolved by it, as fast as if it touched a red hot Iron. See Cavallo’s Treatise on Air, Page 727. Also Priestley’s Experiments and Observations, Vol. 1, Page 148.

[71]“The water remains transparent or colourless, tho’ saturated with marine acid Air, and by a very gentle Degree of Heat, the Gass may be again expelled from it, as it is expelled from Spirit of Salt.”

This Observation is applicable to the Transparency of Vapours, in the Air, tho’ mixed with the marine Acid exhaled from the Sea: for when the acid or Sea Air is mixed with Alkaline or Land Air, they instantly combine; lose their Elasticity, and form a white visible Substance or Cloud. Cavallo, Page 728. Priestley’s Exp. and Obs. Vol. 2, Page 293.

[72]On the Descent of Air in Thunder-Gusts, see “Chalmer’s Account of the Weather in South-Carolina, Vol. 1, Page 1, to 39.”

[73]“Historia Ventorum, Pag. 54, Art. 34.”

[74]Book V. Chapter 2d.

[75]Vol. 1. Page 184.

[76]Page 195.

[77]History of the Canary Isles, Page 252.

[78]As the superior Clouds, during the Balloon Excursion, did not much exceed the Height of 1000 Yards; supposing then the Clouds at an equal Height above the Sea, near Teneriffe; one ought to conclude, either, that the Peak was not so high as Glas represents it; or, that the Level of the Clouds was less than half the Height of the Mountain.

[79]See “Royal Astronomer, by R. Heath, Page 321, on Trade Winds and Monsoons.”

[80]One Pound of Nitre only, producing by mere Heat, 6 cubic Feet of Air. “Cavallo, Page 332, and 811, Experiments on Gun-Powder.”

[81] “See Recherches surles Modifications de l’Atmosphere. No. 715.” Ph. Trans. Part 2, for 1777. Col. Roy’s Experiments, Sect. 2d, Page 689, 744, 753, 764.

[82]The different Phenomena of the Aurora Borealis may be owing to the Ascent and Motion of the Apogay, in the middle Region, over the Stratum of Eknèfiai or Ground-Winds.

The Effects of Tides in the Air yet to be mentioned, must not, however, be wholly excluded.

The Aurora Borealis is seen in Spring, Autumn, and Winter: sometimes culminating, sometimes moving in Streams and Waves in the superior Regions of the Atmosphere: when culminating; as if rising out of Clouds in the North.

This Appearance may be owing to warm moist Air perpetually generating between the Tropics, and rolling over the cold dry Stratum of Eknèfiai Winds, which cut off its Communication with the Earth: till accumulating over the Poles, it enlightens the Atmosphere, converting a six Month’s Night into Day; and returns to the Surface silently: or in Lightning, whenever it is communicated to the Earth, throu’ Vapour descending by its own specific Gravity; or along with depressing Torrents of Air, known to be accompanied by frequent flashes.

When the Vapour is condensed in its Descent, by passing throu’ a Stratum of the Eknèfiai Winds; it becomes overcharged with the electric Matter, surrounding and adhering to it; and deposits the Overplus in Lightning, on its Approach to other Clouds, or to the Earth.

It is visible in the Form of a Vapour, when the Vapour to which it adheres, becomes overcharged with electric Matter, by Descent into a cool Eknèfiai Stratum below: there forming a luminous and transparent Atmosphere: the Particles of Light and Vapour being repelled to great Distances from each other at so rare a Height.

It culminates above the Vapour, because less heavy than the circumambient Air: and may be subject to the Attraction of other Planets.

The Aurora Borealis is also seen to issue in Streams and Waves of Light, with inexpressible Velocity, on its Return to the South, in a lower Stratum, as it passes throu’ Interstices, between the Vesicles of warm Vapour, raised and dispersed by the turbulent Apogay Winds, in the middle Region.

During Summer, the middle Region becomes blended with the lower, throu’ Defect of Cold: and the electric Matter is supposed to be communicated to the Earth, silently, and continually; but by Lightning, when a lower and colder Atmosphere condenses and overcharges the Vapour, and cuts off the Communication.

It cannot be seen but in escaping from Vesicle to Vesicle: nor, during Summer, after Sunset, on Account of the Twilight.

[83]Air is not unfit for Respiration, by having lost its vital Principle, but because it has imbibed Floguiston, which cannot easily be separated from it, but by Agitation in Water. Cavallo, on Air, Pages 479, 670.

[84] For if Moisture be one Cause, which keeps the Particles of Air at greater Distances from each other; this Cause decreases at great Altitudes.

If also the Elasticity decreases in Proportion, not only to the Height, but the Driness; its Particles must, on both Accounts, approach each other, at great Altitudes: tho’, from the Altitude only; they woud separate according to the Rule, viz. that the Rarity of the Air is proportionable to the Relaxation of the Force compressing it.

So that at the Height of 8 or 10 Miles, a Quantity of Air taken from the Surface of the Earth, woud occupy 6 Times its former Space: supposing the Air both below and above to be of the same Kind, as well as of the same mean Temperature of 55, on the Thermometer. See “Martin’s Philosophical Grammar, Page 178.”

[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]

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 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]

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. 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 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.21.87with one Degree of Heat, and
———
2187.00is 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°​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.

Transcriber’s Notes: