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.
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] | 1671⁄2 and 405 Yards. |
| White Mountain 3 Miles within 60 Yards. | 1531⁄4 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. | 1173⁄4 and 30 Yards. |
| Balloon 1 Mile and half within 33 Yards. | 1021⁄4 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.
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
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
1760 |
Yards in a Mile, | |
| Decimal Parts of a Mile to be reduced | .84 |
into Yards. |
—— |
||
7040 |
||
14080 |
||
——— |
||
1760)1478.40 |
(0 | |
Subtract |
1478 |
|
—— |
||
282 |
Answer: the Height of the Mountain is 2 Miles 282 Yards.
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.
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.
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.
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 11⁄2 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.)
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.
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.
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.”