the same Number of Feet:
Detached Thermom. _above_ 76°.
Detached Thermom. _below_ 68.0
————
Whole Heat 144.0
Half Heat 72.0(0 adding a Cypher)
Standard-Heat 31.24
—————
which deduct, and there remains 40.76: with which, by the 4th Table,
find the Expansion of Air on Feet 81.73:
_First, with_ 40°, _on_ 81.73, thus:
_on_ 80. as 8000 – 777.6 = 7.776
1. as 1000 – 97.2 = .0972
.7 as 7000 – 680.4 = .06804
.03 as 3000 – 291.6 = .002916
————————
7.944156
_Second_, _with_ .76 _on_ 81.73, thus:
_on_ 80. as 8000 – 1477.4 = .14774
1. as 1000 – 184.6 = .001846
.7 as 7000 – 1292.7 = .0012927
.03 as 3000 – 554.0 = .0000554
————————
Expansion .1509341
add the former Expansion 7.944156
—————————
Sum of the Expansions, viz. }
Height in Feet } 8.0950901
from Excess of Heat above Standard,
_with_ 40°.76 _on_ 81.73,
+added+ to the Height at the Standard-Heat, }
in Feet } 81.73
gives, in Feet and Tenths, the true ——————
Height of the Tarpeian Rock 89.8|2.
CHAPTER LXXIX.
A CALCULATION TO ASCERTAIN THE HEIGHT OF THE BALLOON ON THE DAY OF
ASCENT: ONE BAROMETER AND ONE THERMOMETER ONLY, BEING TAKEN UP INTO
THE CAR.
Section 423. The Question is stated from Section 36: and the Mode
of Operation taken from the _Recapitulation_ of the second Example,
Section 409.
Observation before the Ascent:
Below: Barometer 29.8; attached Thermometer 0; detached Thermometer 65°.
Above: Barometer 23¼ = 23²⁵⁄₁₀₀ or 23.25;[135] attached Thermom. 0;
detached Thermom. 65°.
There being no attached Thermometers; the _first_ Table is useless: the
Barometer below is therefore supposed to be of the same Temperature as
when above; the detached Thermometer remaining at the same Degree, viz.
65°.
State the Barometer, thus: when _below_, at 29.8
when _above_, at 23.25.
_End of the first Stage._
424. Find the Height (at the Standard-Heat) corresponding to the Inches
and _nearest_ Tenth above and below 23.25: i.e. above 23.2, and below
23.3: by the 2d Table.
Now 23.2 corresponds to 8379.7: and the Difference of .1 above, i.e.
to 23.3, is in Feet = 112|.1: by the 3d Column of the same Table.
With this Difference, consult the 3d Table: i.e. with 112, (omitting
the .1 as too minute) on the remaining Decimals above 23.2, viz. on
05, as on 5, or ⁵⁄₁₀; and the Answer is 56 Feet: which Number being
subtracted from 8379.7, the Remainder 8323.7, is the Height in Feet of
the Barometer in the Car, at the Standard-Heat.
Repeat the last Process for the Barometer on the Ground.
Now 29.8, by the 2d Table, corresponds to 1856.0; and there being
no Parts or Decimals more minute than a Tenth, viz. .8, there is no
Occasion for the 3d Table.
Subtract the Barometer in the Car, from the same when on the Ground;
and, by the 2d Table,
upper Barom. 23.25, corresp. to 8323.7, and the
lower Barom. 29.8, to 1856.0: the
Remainder is the Height in Feet —————— of the
Barometer in the Car viz. 6467.7, with the
Standard-Heat.
_End of the second Stage._
425. Detached Therm. above, at 65°
Detached Therm. when below, at 65
———
Whole Heat 130
Half Heat 65.(00 adding Cyphers)
Standard-Heat 31.24
—————
which deduct, and there remains 33.76 Degrees
more than the Standard-Heat, for each Barometer.
Then for the Expansion of Air, with such Heat more than the Standard,
consult the 4th Table: viz. _with_ 33°.76 _on_ Inches 6467.7, the
Height of the Barometer in the Car with the Standard-Heat, thus:
426. _First_, _with_ 33°, _on_ 6467.7
_on_ 6000 as 6000 = 481.1, decimated 481.1
400 as 4000 = 320.7 32.07
60 as 6000 = 481.1 4.811
7 as 7000 = 561.3 .5613
.07 as 7000 = 561.3 .05613
—————————
Expansion = 518.59843
427. _Second_, _with_ .76 _on_ 6467.7:
_on_, as before, 6000 = 1108. decim. 11.08
4000 = 738.7 .7387
6000 = 1108. .1108
7000 = 1292.7 .012927
7000 = 1292.7 .0012927
——————————
Expansion = 11.9437197
Add the former 518.59843
————————————
Total Expansion = 530.5|542197
viz. Height _by Expansion_ in Feet,
with more than the Standard-Heat,
add to Height in Feet at
the Standard-Heat 6467.7
——————
428. The true Height, in Feet and
Tenths, of the Barometer in the
Car 6998.2
Feet in a Yard 3) ——————
Yards in a Mile 1760) 2332.2 Feet.
1760 (1 Mile.
——————
Yards in a Quarter of a Mile 440 ) 572 (1 Qr.
440
———
32 Yards.
The Height of the Balloon 1 Mile, 1 Quarter, 32 Yards, and 2 Feet.
_End of the last Stage,
and of the Mensuration of Heights._
N. B. A _thermometric_ sliding Rule, for the Expansion of Quicksilver,
and of Air, may possibly, from the foregoing Tables, be so contrived
and adapted to the Barometer, as to tell the Height by Inspection,
while in the Car of the Balloon.
CHAPTER LXXX.
HINTS, ON THE CHEAPEST METHOD OF INFLATING BALLOONS, WITH DESCRIPTIONS
OF DIFFERENT MODELS FOR A GASS-STEAM-ENGINE.
Section 429. The _Expence_ attending the Inflation of Balloons is a
solid Objection to their frequent Use.
A Check is thereby given to every Improvement that might otherwise be
expected from a Repetition of Experiments.
It is, in short, the chief Difficulty under which the +aironautic art+
at present labours.
This Difficulty, however, if once overcome, (and of which there is
little Doubt) will probably bring those extraordinary Machines, into
general Estimation.
What _now_ costs fifty Pounds, may _then_ be done for five: abating the
Expence of the preparatory Engine.
Mons. Lavoisier, by the Application of Steam to Iron Filings enclosed
in a Copper Retort, has generated inflammable Air, or light Gass:[136]
and Dr. Priestley, by converting a Gun-Barrel into a Steam-Engine, has
produced a Gass 13 Times lighter than common Air;[137] whereas by the
present expensive Method, with Metal and Acid, the Gass for Inflation
is seldom more than six Times lighter.
What has hitherto been atchieved on a small Scale, is here meant to be
extended.
As no Particulars are made public, or at least, have yet come to
the Author’s Knowledge, relative to the Construction of such a
Gass-Steam-Engine, as may, with Safety and Effect, be applied to the
Inflation of Balloons; the following Descriptions of different Models
may deserve some Notice:—may possibly excite the Attention of the
ingenious; and put them on contriving _easier_ Means to obtain the
_same_ End.
I.
430. Let there be an Iron _Hot-hearth_, one Yard square, and two Inches
thick. Let it be _set_ on a Common Brick Stove, built as near the
Ground as possible, (or even below it) in the open Air. Its Chimney
to consist of malleable Iron, flat at the Top, and strong enough to
support a Tea-Kettle or Boiler to produce Steam: and extending at least
one Yard from the End of the Hearth horizontally, before it turns up.
It may rise three or four Yards high, slanting farther from the Hearth:
the Form a hollow Cylinder: with a Turn-Cap at the Top, two Feet long,
set on at right Angles; for the Management of the Smoke.
Supposing then the Fire-Place to face the West; the Chimney may project
Eastward. The North Side is to be appropriated to the Iron-Borings or
Turnings; and on the South Side is to be deposited the Dross or Calx.
A Muffle or Mould of malleable Iron is to be screwed and luted over the
hot Hearth. The four Sides of the Muffle next the Hearth are to have
horizontal Lips or Rims projecting half an Inch: and Screws are to be
driven, throu’ Holes drilled at proper Distances, into the Hearth. The
Sides are to rise upright a Couple of Inches: closing, as they rise, in
the Form of a hollow Cylinder, one Foot in Diameter, and perhaps a Yard
above the Hearth: which is now converted into a _Gass-Steam-Engine_.
It is proposed to strew over the _Hot-hearth_ a thin Layer of Borings,
one Tenth of an Inch thick; to which Layer when _red_ hot, the boiling
Steam is to be applied. The extricated Gass is to be conveyed from
the Top of the Cylinder, by Means of an extended Trunk of Tin, and
varnished Linen, into a Tub of cold Water kept _continually_ flowing
over, into which a few Lumps of quick Lime are thrown: and from thence
the Gass is to rise into the Balloon.
431. The Iron, whether Filings or Turnings, proper for Inflation,
must be _bright_; wholly free from Chips, Bits of Wood, and all
heterogeneous Particles: but particularly RUST, and GREASE: _less_ than
a cubic Inch of the latter, woud spoil a Ton of the brightest, and
otherwise the best prepared Materials. (Section 339.)
A Day or two _only_, before a Balloon is inflated; the proper Quantity
of bright Iron shoud be heated +red hot+ in _Charcoal_, and suffered to
go cold.
For Want of this simple Preparation of the Iron, the Gass has proved
defective in Point of _LEVITY_: altho’ the Balloon appeared fully
inflated.
This Misfortune happened at Birmingham, and other Places.
432. The _Desideratum_ is, _quickly_ to apply, and _remove_ the
Borings, keeping the Machine _nearly_ Air-tight. For, it is now well
known, that the Gass will _explode_, if one-third Part of common Air be
introduced: or, if less; it may _unite_ with the _Gass_, and detract
from _its_ Levity.
433. The following _Particulars_ may likewise be considered as an
Improvement.
II.
1. To lay a Plate of Iron, Brass, or Copper, over the Hearth; which, if
made of _cast_ Iron, will be apt to crack, in Contact with the Steam;
and will also unite with and concrete the Iron Turnings or Gun-Borings
into a solid Mass, that woud be separated with Difficulty.
2. To make the Dross-Pit in the Form of a hollow Wedge, narrow at the
Top: screwing and luting it to the South Side of the Hearth. It shoud
hold the Dross arising from a Ton of Borings; which will be sufficient
for the Inflation of a Balloon, to carry one Person.
3. On the North Side is to be erected a Platform of Brick, a Yard
square, _floored_ with a Plate of Iron: the inside Surface to be even
with the Bottom of the Hearth.
4. The Ton of Borings is to be placed on the _Floor_, and covered with
another Muffle, secured and luted to the Side of the Hearth: having a
Communication of two Inches high, and one Yard wide, with the Bottom of
the Hearth: as the Dross-Pit has.
5. A Brass or Copper Rake is to remain within the two Muffles: to
press forward the Borings, spread them over the Hearth; stir them
frequently;—by turning the Instrument, scrape them into the Dross-Pit;
and apply fresh from the _Deposit_.
6. To perform these manual Operations within the Machine kept
Air-tight; it will be necessary, at the exterior End of the Muffle, to
fasten a strong leathern Case, made very wide and pliant, and two Yards
long: into which the End of the Rake-Handle is to be inserted.
III.
434. _The Mode of Operation._
The Borings being spread on the Hearth, and _red_ hot; the Steam Pipe
is to be opened, and _instantly_ shut. The Gass being _suddenly_
extricated; the Pipe is to be opened, and shut again as before: the
Borings pushed into the Dross-Pit, and a fresh Supply spread. This
Process to be renewed, till the Inflation is completed.
If it be thought necessary to prevent the Steam from communicating with
the whole Depôt of Borings, and so evolve too much Gass; a little Brass
Door with Hinges of the same, might be made to hang from the Top of
the Communication between the two Muffles: which Door opening inwards,
and hanging vertically, woud by the Pressure of the Gass, stop up the
Open: and yet, if made strong, _not_ prevent the Operations of the
Rake, at proper Times.
IIII.
435. The Machine woud be less complex, with one large Muffle, somewhat
longer North and South than the Hearth; furnished with leathern Case
and Rake. Put in the Borings at one End: keep the Steam-Pipe always
open; with a _Hand_ at the Rake; pushing away the Dross, and pressing
forwards fresh Borings.
V.
436. Further: it has since occurred, that a Machine in the Form of a
+gun-barrel+, _extended in all its Dimensions_, will probably answer
_every_ Intention.
And of this Kind are the hollow cylindrical Tubes, of _different_
Lengths, and about a Foot in Diameter,[138] which are _cast_, for the
Conveyance of Steam, from the Boiler of a Steam-Engine.
Such a one, (previously lined with a Cylinder of Copper, or malleable
Iron, to prevent the Adhesion of the Borings, when reduced to a Calx
by the Admission of Steam;) might be placed horizontally over a Stove,
(with or without a Chimney) and surrounded with _red_ hot Coals.
The Ton of Borings might be deposited at one End of the Tube; and, by
Means of the Air-tight flexible leathern Case, be pressed with a Rake,
_gradually_ into the Fire, and _beyond_ it when calcined.
Care must be taken to make the _Apparatus_ nearly Air-tight.
The Steam shoud pass into the Tube, from _below_: and the Gass be
conducted towards the Balloon throu’ another Iron Cylinder, nearly
equal in Diameter and at right Angles with the first; lying also in an
horizontal Direction; along the Ground.
The Tubes might be _forged_ or _cast_, so as to form but one
rectangular Piece.
The further End of the second Tube shoud communicate with a _third_,
made of Tin, and bent downwards about a Foot; thence at right Angles,
for six Inches: then to rise up, also at right Angles, the Length of
six Inches more.
The Tin Tube is to descend into a Cistern of cold Water, made to flow
over continually, by a fresh Supply; and into which, a few Lumps of
Quicklime shoud be thrown.
The Gass, which will press upwards throu’ the Water, is to be received
into an inverted Funnel, and thence (as in Section 339, Art. 2.)
conveyed to the Balloon.
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_.
A. Section.
Absorption of Water by Air, _Experiment to prove_ the, 247
Accumulation of Air, _mediocèanal_, 259, 260
Aërial Scenes _described_, 39, 47, 51, 56
Air gives +form+ to _Things_, 53
- _gentle_, its Effect on the _Surface_ of the Balloon, 201
- _calm_, its _Effect_ on the _Surface_ of the Balloon, 202
- _pure_, cool, defloguisticated, perpetually descending, 252
- _descending Torrents_ of, on Etna and Teneriffe, 265
- _Reception and Dispersion of_, what, 280
Air Bottle Balloon, _its Use_, 311
- - - _preferred_ to an _interior_ Balloon, 314
Aironaut _Employments_ of the, in the Balloon, 29
- - _Attitude_ of the, in the Balloon, 32, 33
- - _lost over a Country_ well-known when _below_, 177
- - to _try_ different Heights, to find a _favorable Wind_, 309
- - to _wait_, in the _Calm above_ the Clouds, for a _Wind_, 309
Airostat, a small one _first_ liberated, 8
Altitude _apparent_, from the Balloon when _stationary_, 49
- - _barometric_, 49, _b_.
Anchor and Cable, 13
Apogay Winds, what, 241
Apparent Height _proportioned_ to the _barometric_ Height, 49
Appearance of a Plain _below_, the Size of a moderate Carpet, what,
179, 189
Appearance of a Plain _below_, the Size of a Handkerchief, what,
181, 187
Appearances at _different_ Altitudes, _from the Balloon_, 213
Articles, _Weight_ and _Number_ of, 26
Ascent, to _check_ and _promote_, 14
- - _Preparations_ for, 22
- - of the Balloon at 40 Minutes past I. o’clock, 28
- - with _twenty Pounds_ of _Levity_, 28
- - of Balloons, Causes to _limit_ the, 279
- - _proper Times_ for, 285
- - _new_ Mode of, to _determine_ the _Height_, 299
Atmosphere _gross_, when seen throu’, _from below_, 55
- - Depression of the, 232
- - State of, _favorable_ to the _Direction_ of Balloons, 268
- - Conjectures concerning the _Warmth_ of the _superior_, 275
- - probably _respirable_ at _great Altitudes_, 277
- - _Height_ of, 290
- - _Weight_ of, in _England_, 290
Attention to the Balloon _necessary_, 35
Aurora Borealis, Conjectures concerning _Appearance_ of, 274
B.
Ballast of what it consisted, 27
- - when to be _first_ thrown out, 21
- - in Hand, ready to throw out, 91
- - thrown down, 67, 95
- - thrown over _nearly_ 32 Pounds, 103
- - poured down at once 20 Pounds, 183
Balloon going to Sea, 75, 87, 90
- - in a quiescent Bed of Air, 75
- - of rowing it to any Point, in a Calm, 75
- - drawn aside out of the Perpendicular, 103
- - shrunk to its former Shape, 123
- - alternately rising and falling, 125, 138
- - in the Air five Hours and a Quarter, 207
- - sustained above Water, how, 294, 295
- - best Form of, 307
- - Double, what, 314
Balloons their Defects, and further Improvements, 303
- - Air-tight Varnish for, 320, 325
Barometer, and Thermometer, when stationary, 36
- - Fluctuation of the Quicksilver in the, 37
- - Mensuration of Heights by the, 350
Beautiful preferred to the Sublime, in Prospects, 42
- - Appearance, 43
Bladders necessary, 26
- - began to _crackle_, 116
Bottles of Air thrown down, Caution, 74, 77, 84
Breath not affected, nor visible, during the Excursion, 126
Breeze Sea-, 88, 92, 257
C.
Cable, and Anchor or _Grapple_, 13
- - to be fastened to a _Center above_ the Car, 297
Calculations of the _Distance_ seen from the Balloon, 52, _a_.
- - of the Height of _Mountains_, 171, _a_.
Calm _above_, and Wind _below_, at the same Time, 168
Canal artificial, Duke of Bridgewater’s, Appearance of, 166
Cannon first discharged at IX. o’clock, 7
- - the second Time, at XII., 11
- - the third Time, at 40 Minutes and a half past I., 64
- - the last Time, at 10 Minutes and a half past II., 62
Car and Hoops, their _Dimensions_, 35
Caution to keep the Circle clear during the Inflation, 23
- - against the _Dropping_ of Water _out of_ the Balloon, 31
- - on Landing, 98
- - _not_ to open the upper Valve, 122
Charts Balloon, first suggested, 168
Chilliness _first_ perceived, 92; again, 109
- - _felt_ near moist Places, 283
Circularity of Prospect, 79, 221
Circumstance, _each_ to be recorded, 4
Circumstances _apparently superfluous_, mentioned and repeated,
why, 5
Clouds, an upper Tier _seen_ to move in a safe Direction, 7, 46
- - Perspective of the, 51
- - _appearing_ in rapid Motion, 163
- - View of the, taken from above them, 130, 171
- - Colouring of the, 172
- - _highest visible_, 213
Cochuc-Varnish, 320
Cold, its Effects on the Balloon, 94
Colour of the Rivers, _red_, 44
- - of the City of Chester, _blue_, 45
- - of Thunder-Clouds, 54
- - of upper Clouds, 57, 172,
Colours, _primary_, of Objects beneath, 129
Columns of Air, depressing, observed by the Ancients, 239
Compass, the properest Kind of, 38, _a_.
Conclusions, useful, 159
Conjunction of the Planets _preceding_ a Hurricane, 211
Contemplation of the Prospect, 113
Course of the Balloon traced, to shew the Manner in which it was
affected in passing over Water, 78
Curls and Streams of Air, Smoke and Vapour, 250, _b_.
Currents of Air, horizontal, 20
- - from _above_, to be guarded against, 21
Currents _under_, of Air, 87
- - of Air, blowing _to and from_ great Towns, 250
- - of Air, _contrary_, at different Heights, at the same Time,
267
- - the Balloon rising throu’ _different_, 106
D.
Defects in the Composition for Balloons, _remedied_, 320
Depressing Torrents of Air, 254
Depression of the Atmosphere, 232
- - over _moist_ Places in _fair_ Weather, 243
- - of the Atmosphere proved from History, 253
- - _nocturnal_, of the Atmosphere, 267
- - corroborating Proofs of a, 268
Depth below, conveys no Idea of Distance, 157
Depths, Mensuration of, with Barometers, &c. 348, 368, _a_, _a_.
Descent of the Balloon, to _retard_ the, 15
- - Signs of the, 17, 159, 181
- - at _first rapid_, with a rushing Noise, 96, 97
- - Proof of _gentle_, 100
- - Change in _visible_ Objects, during the, 182
- - of Balloons over Water, _enquired_ into, 229, 230
- - - - - - Means to prevent, 294, 295
Description of the Ascent, 47
Diameter of the Prospects _above_ and _below_, 52, 79
Diminution of Objects, _excessive_, when seen from the Balloon, 223
- - - - Laws respecting the, 224
Direction of the Balloon, Hints for the. 315
Distance seen from the Balloon, Calculations of the. 52, _a_.
- - of the Balloon from _Chester_, at the Report of the 4th
Cannon, 64
- - Idea of, from _Experience_, 158
- - what is the _greatest_, to be seen from the Summits of the
_highest_ Mountains, 171, _a_.
- - at which an Object can be distinguished by a _good_ Eye, 175,
_a_.
- - of the Balloon-_Course_, 191
- - at which, the Balloon was seen, 227
- - and Height of a Balloon, found by a Quadrant, 310
Dove turned out of the Car, 61
E.
Earth removed from _Sight_, 170
Echo none _above_, 39
Eknèfiai Winds, what, 241
- - a dry Wind, 267
Electricity of the Air, 65
Elliptic Solid, the Form of the Balloon an, 160
Employments of the Aironaut, 32
Engines _Steam_, Models of, for Inflation, described, 429
Equatorial Hoop, its Use, 161, 315
Evaporation of _Steam_, 249
Expansion of the Balloon, by what Manouvre, 132
Experiment to prove whether the _superior_ Atmosphere be _hazy_,
tho’ the Sun continue _shining_, 47, _a_.
Experiments necessary, in order to improve the Modes of
_Direction_, 296
Examples in the Mensuration of _Heights_ with Barometers. See Table.
Example 1st, Practice of the, 351
- - - Recapitulation of the, 385
- - 2d, Practice of the, 386
- - - Recapitulation of the, 409
- - 3d, Practice of the, 410
- - 4th, Practice of the, to determine _small_ Heights, 419
- - 5th, Practice of the, to determine the Height of the Balloon,
423
F.
Fish _Dìodon-Globe_, a _Model_ for Balloons, 377
Flag _white_, hung out a Quarter of a Mile in Length, 4
- - hung out half a Mile, in all, 66
- thrown _down_ at a Mile high, 59
- Descent of the, 60
- _white_, its Effect on the Balloon, 70
- - Progress of the Balloon marked by the. 91
- - _impeding_ the Balloon, 103
- - the remaining one unfolded, 105
- - shewed a Change in the _Direction_ of the _Wind_, 105
Flights with the Balloon, for three Hours longer, 193
Flying-Coach, 149
Foot Roman, the _Measure_ of a, 49, _b_.
Form of the Balloon at its _greatest_ Altitude, 14
- - - the _same_ at each Descent, 159
G.
Gass not offensive during the _Voyage_, why, 34
- procured by Means of _Acid_, 338
Gass procured by Means of _Steam_, 429
Geography Balloon, _first_ suggested, 167
Globe-Fish, a _Model_ for Balloons, 377
Grapple or Anchor, 13
Gums Copal, Sandarac, Mastic, &c., 326
H.
Heat of the _Sun_, _greatest_, while in the Car, 59
Height _apparent_, proportioned to the _barometric_ Height, 49
- - of the Balloon, when _stationary_, at the _first_ Ascent,
viz. 2332 Yards, 52, _a_.
- - in the Balloon, conveys no Apprehension of falling, 156
- - of _principal_ Mountains, noted, 171
- - of a Mountain, seen at a _Distance_, calculated, 171, _a_,
_a_.
- - to which Balloons will _probably_ ascend, 278
- - fixed, Method of ascending to any, 299
- - of the Balloon, to ascertain by a _Quadrant_, 310
- - _preparatory_ Instruments to observe the, 350
- - of the Balloon measured, 425
Heights to measure, Densities to estimate, 299
- - of the Atmosphere, while they encrease in an _arithmetical_
Progression, the Densities are said to encrease in
_geometrical_ Progression: the Meaning of such Terms, 301, _a_.
Hemisphere _upper only_, of a Balloon to be inflated, 315
Hoop equatorial, its Use, 161, 315
Horizontal Motion, Signs of, _deceitful_, 18
Hours proper for the Ascent of _Balloons over Water_, 254, 255, 261
Hygrometer _Horse-Hair_, the _best_ Kind, 217
I.
Illustration of the Scenery, 72
Improvement during the Process of Inflation, 24
Improvements how to be made in the propulsive Machinery, 319, 330
- - in the Process of Inflation by Acid, suggested, 339
- - suggested in the Process by Steam, 429
Incorrectness of Maps, 81
Inflation began at X. o’clock, with a small Balloon, 8
- - Degree of, to be limited, 278, 317
- - Process of, 339
- - by Means of Acid, Expence saved in the, 347
- - by Means of Steam, Expence saved in the, 429
Inflation by Means of Steam, Model and Mode of, 429
- - by Steam, preferred to the Process by Acid, 429
Information derived from the Shape of the Balloon, 159, 160
Inventory of the Voyage, 12
Iris 1st, round the Shadow of the Balloon, 56
- 2d, 73
- 3d, 136
Iron _bright_ and _fresh_, proper for inflation, 431
L.
Landing, Manouvres during the, 98
- - first, near _Frodsham_ in _Cheshire_, 100
- - second, near _Warrington_ in _Lancashire_, 188
- - Precautions to secure a safe, 297
- - in _windy_ Weather, Precautions to secure a safe, 298
- - _improved_ Mode of, 317
Latitudes variable, _light Airs_ playing in Eddies, common in the,
241
Level of the _lowest_ Stratum of Clouds in _fair_ Weather, 93
- all Inequalities of Surface reduced to the _same_, 111
Light of a _red_ Colour, Conjectures concerning the, 222
M.
Machinery _propulsive_, to be used in the _Calm_, _above Winds_, 319
Magnitude of Objects, Laws respecting the, 224
Manouvres seen at a _great_ Distance, 140
Map consulted, 174
Mast, a light _hollow_, 315
Meanders of the River _encreased_ to the _View_, 81
Mensuration of Heights and _Depths_ by Barometers, 348
Methods to ascertain the _true_ Height, 350
Method, the cheapest to inflate by Steam instead of Acid, 429
Mistakes to be noticed, to prevent Repetition, 2
Motion encreased, progressive not perceived, 165
Motion of Air, called _Reception and Dispersion of Air_, what, 280
Mountains, Names and Heights of principal, 171, _a_.
- - their Use, 265
Mouth of the Balloon, _closed_, 102
N.
Neck of the Balloon, how to place it, 31
- - _first_ tyed, 125
- - risen near _eight_ Feet upwards, 119
- - an _Attempt_ to reach it, 121
- - held _Air-tight_ in the _Hand_, 125
Notes made during the Voyage, 36
O.
Objects diminishing as the Balloon arises, Description of, 109
Objects, all _terrestrial_, disappearing, 163
Order preserved during the Inflation, 23
P.
Parashute or Umbrella, 15
- the Balloon formed a vast, 184
Perspective new, 39, 229
Place where the Balloon alighted, 100, 187
Points, the plainest generally most essential, frequently
overlooked, 4, 338
Preparations for Ascent, 22
Prospects _most beautiful_, at what Height, 93
- below noted, 128
Pulley or Reel, 13
R.
Rain _warm_ in Winter, accounted for from the Theory of
Accumulation, 270
Reception and Dispersion of Air, 280
Reel or Pulley, its Defects remedied, 41, _a._
Respiration easy during the Excursion, 114
Resistence of the Air, as the _Square_ of the Velocity of the
falling Body, 15, _a._
Rising, Signs of, 16, 30
Rivers, _no Appearance of_ Water in the, 110
Rule, general for measuring Heights, copied, 384
Rusty Iron, _improper_ for Inflation, 398
S.
Sail, three seen in the _Liverpool_ Channel, 108
- _triangular_ Latteen, _purposely to retard_ the Balloon, 315
- Anemòmeter, what, 315
- Weights to be added to the, 316
- Vane-, what, 318
Scenes aërial, described. See Sublime.
Sea-Breeze discovered, 88
- - its Duration, 256
- - its Extent, 257
Sensation of _rising_ described, 30
Sensations accompanying the Balloon, 141, 154
Shadow of the Balloon _traced_ on the Clouds, 56, 73, 136
Shadows, their Length, _at Noon_, calculated, 84
- - - - - _at half past III._ calculated, 100
- - encreased, seemed to raise the Objects, 127
Shape of the Balloon _altered_, 118
Sign of Descent, 181
Signs to be observed in the Management of Balloons, 14, 15, 17, 20
Situation novel, peculiar to the Balloon, 221
Sound of the Gass throu’ the upper Valve, 134
- in the Air, an _uncommon_, 162
Sounds immediately under the Balloon, their Effects, 175, _a._
Spirits raised by the Purity of the Air, 155
Spunges of Air, 247
Squalls of Wind, the Day preceding the Ascent, 6
Stationary, the Balloon, 36, 122
Steam, Mode of Inflation by Means of, 429
Storms of _Collection_ and _Dispersion_, 232, 263
Sublime and beautiful Scenes, 3, 39, 47, 48, 49, 51, 71, 84, 112
Sun, when hottest, 59
Sympathy of the Spectators, 46
T.
Table the 1st. See Mensuration.
- - for Expansion with Heat, from 1 to 40 Degrees, on Inches of
the Barometer, from 9 to 32 Inches, 363
- the 2nd, shewing the Variations of the Barometer, at each Inch
and Tenth of the Quicksilver, from 1 to 32 Inches, the Air
being at the freezing Point, 371
- the 3d, for easy Calculations, from the 2d Table, 373
- the 4th, shewing the Expansion with Heat, from 1 to 100
Degrees, on any Number of Feet in the Air, 381
Tastes not altered, on Account of the Height, 65
Thermometer warmer _above_ than _below_, 126
Thermometers compared, 12, _c._
Thunder-Clouds described, 52
- - under the Balloon, 172
Tide of Air in the Atmosphere, 291
Tides highest, 288, 289
Time, noted, 7, 8, 11, 22, 28, 36, 62, 63, 68, 73, 77, 85, 100,
101, 124, 162, 174, 186, 203, 206
- of Ascent, 28
Time, in which the Excursion was performed, viz. two Hours and a
Quarter, 191
- Noon, a dangerous one, for Balloons to pass an Arm of the Sea,
256
- the best, pointed out, 256
- Noon and full Tide, improper: Midnight and low Water, proper
Hours for Ascent, over Water, 287
Torrents of Air mediocèanal, depressing, 257, 258, 259
- - - - - accumulating, 260
Transparency circular, of Vapour, 222
Twine cut, lest it should prove a Conductor of Electricity between
the Balloon and Earth, 103
U.
Useful Conclusions, 159
Utility of Balloons, 332, 333
Utility _general_, of Balloons, 338
V.
Valve upper, emits the _lightest_ Gass, 124
- _first_ tried, 133
- -Swing, or Umbrella-Pendulum, as _propulsive_ Machinery,
communicates a _progressive_ Motion to the Balloon, 319
Vane-Sail, 318
Vapour, Observation of the _reddish_, 33
- _white_, _beautiful_ Effects of, 71
- - began to be accumulated at a _certain_ Height, 80
Vapours, their _Transparency_, 222
Varnishes, 320, 325
Velocity of the Balloon, 192
Vessels, the _four_ and the River Wever _disappeared_, 110
View _circular_, from the Balloon at its _greatest_ Elevation, 55
- of the Balloon over _Helsbye-Crag_,77
- of the Clouds, _from_ above _them_, 171
- _from_ the Balloon of the Country between Chester and
Rixton-Moss, 192
Vis Inertiæ, 70, 316
W.
Warmth of the superior Atmosphere, 275
- of the Air above Plains and cultivated Countries, 276
- of the Air over the _Sea_, at certain Times and Seasons, 276
- descending from _above_, 284
Water poured down, to observe the Effects of Air upon it, 74
- Balloon influenced on its Approach to, 76, 78
- Balloon above the Influence of, 131
- the Descent of Balloons over, 229
- the Causes of their Descent over, 230
- Absorption of, by Air, 247
- a curious Phenomenon seen on its Surface, 249, 250, _b._
- Means to prevent the Descent of Balloons over, and within its
Influence, 294, 295
Waves of Air, 21
- of the Sea, the Dashing of, heard; the Sea being invisible, 80
Weather, about the Time of the Excursion, 211
Weighing during the Inflation avoided, how, 24
Weight of Provisions and Articles, 24
- of the Balloon, and its Apparatus, 25
Wind heard below, 86
Winds, the Eknèfiai and Apogay, what, 241
- the Directions in which they blow, 253, _a._
- the Eknèfiai productive of Cold, 253, _a._
- _Land_- and _Sea_-, 253, _a._
- contrary, at different Heights, their Use to waft Balloons to a
given Point, 268
Wings, their Use, first to retard, second to direct, 315
Winter-Dress, preparatory, 26, 338
- -Prospect from the Balloon, 169
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.
54 13 & 4-9ths above the Cypher.
55 14 ditto, nearly.
57 15 2-9ths ditto, nearly.
59 16 4-9ths ditto, nearly.
60 17 1-9th ditto.
65 20 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 Aironaut 160
Provisions and Articles
calculated at 20
Sand-Ballast prepared in Bags 44
Levity for Ascent 10
———
_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] [Sidenote: The Defect of the Reel remedied]
The Loop shoud have been furnished with a +Swivel+: or the Lath or Reel
shoud have been a Kind of Pulley, a Foot in Diameter, and two Inches
wide. The Hook of which having also a Swivel might have been held in
the Hand: and thus the Twine woud have run off in a short Time with the
greatest Readiness; the Swivel conforming to the circular Motion of the
Balloon.
[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] [Sidenote: 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(⅓) 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 ———————————
Square . . . . . 1760) Yards in a Mile.
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
[Sidenote: 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 to 13932705⅔ Yards,
add 2332 the Height of the Eye or
———————— Balloon.
13935037 the Sum, multiply into
2332 the Height of the Eye, &c.
————————
27870074
41805111
41805111
27870074
———————————
Extract the . . . . . 1760) Yards in a Mile.
square Root 32496506284 (180267 (102,
1 1760 say 102½ Miles, Ans.
—— ————
28) 224 4267
224 3520
——— ————
3602) 9650 747 Yards, Remainder.
7204
————
36046) 244662
216276
——————
360527) 2838684
2523689
———————
314995 Remainder.
[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 travels 1142 Feet in a
Second, it must have moved in 30 Seconds
————
Feet in a Yard 3 )34260 = Feet
Yards in a Mile 1760 )11420( 6 Miles
10560
—————
Yards in a Quarter of a Mile 440)860( 1 Quarter
440
—————
Answer 6 Miles, 1 Quarter, and 420 Yards.
[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. See Page 98 [34].
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 12½
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 8½
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 _a_.)
{Lat. of Chester, 53° 12′}
Given {Sun’s Dec. 5 29 } To find Sun’s Alt.
{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
(3½ Hour) Angle contained 52. 30
Half ditto 26. 15 } 63. 45
Half Sum of Sides 60. 39 } Co. 29. 22
Half Difference ditto 23. 51 } 66. 9
THE FIRST PREPARATIVE PROPORTION.
As Sine of ½ Sum of Sides 60. 39 0.05966 Co-Ar.
To Sine of ½ Difference of Sides 23. 51 9.60675
So Co-Tangent ½ contained Angle 63. 45 10.30703
—————— ————————
To T. of ½ Diff. of the other two Angles 43. 15 9.97344
SECOND PREPARATIVE PROPORTION.
As Co-Sine ½ Sum of Sides 29. 21 0.30968 Co-Ar.
To Co-Sine ½ Diff. 66. 9 9.96123
So Co-Tangent ½ contained Angle 63. 45 10.30703
————————
To T. ½ 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 ½, 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.
See Section 84, Note [26].
[35] See “Priestley on Electricity.”
[36] Εὔροια.
[37] [Sidenote: An Account of the _Breath_ being visible at Sea, when
the Thermometer was at 61.]
The Breath is said to become _visible_ at Sea or Land at any
Temperature of the Thermometer not _exceeding_ 60°: tho’, in Latitude
41°, and Westward of the Azores Islands, being in Sight of the Peak of
+st. george+, (which probably equals, if not exceeds, the Height of
Teneriffe) the Observer has seen his _own Breath_, and _that_ of the
Sailors on Deck, when the Thermometer in the _Shade_ was at 61: the Air
(in January) being _then remarkably_ damp.
[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] [Sidenote: Recommended to _Invalids_.]
Why not recommend the Use of that Machine to Invalids? who woud
find Refreshment in the +open+ Air: as its Rotation communicates a
gentle Motion to the System,[42] without the least Fatigue; _rather_
encreasing the _Animal_ Spirits.
[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 (_a_), _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 +Majesty’s+ _Navy_,
who, during the last War, cruized 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 (_a_), 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, } 167½ and 405
see Section 52, Note (_a_)). } Yards.
_White Mountain_ 3 Miles within } 153¼ and 13
60 Yards. } Yards.
_Peak of Teneriffe_ 3 Miles within } 152 within 72
148 Yards. } Yards.
_Mount Etna_ 2 Miles and 357 } 132 and 127
Yards. } Yards.
_Blue Ridge_ 1 Mile and 3 Quarters. } 117¾ and 30
} Yards.
_Balloon_ 1 Mile and half within } 102¼ and 307
33 Yards. } Yards.
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:
[Illustration]
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
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.
[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 1½ _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
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.