The Expansions of the Air being reciprocally as the heights of the Mercury, it is evident, that by the help of the Curve of the Hyperbola and its Asymptotes, the said Expansions may be expounded to any given height of the Mercury: For by the 65th Prop. lib. 2. Conic. Mydorgii, the Rectangles, ABCE, AKGE, ALDE, &c. (in Plate 1. Fig. 4.) are always equal, and consequently the sides, CB, GK, LD, &c. are reciprocally as the sides AB, AK, AL, &c. If then the Lines AB, AK, AL, be supposed equal to the heights of the Mercury, or the pressures of the Atmosphere, the Lines CB, GK, LD, answering thereto, will be as the Expansions of the Air under those Pressures, or the Bulks that the same quantity of Air will occupy; which Expansions being taken infinitely many, and infinitely little, (according to the Method of Indivisibles) their Summ will give the Spaces of Air between the several heights of the Barometer; that is to say, the Summ of all the Lines between CB and KG, or the Area CBKG, will be proportioned to the Distance or Space intercepted between the Levels of two Places in the Air, where the Mercury would stand at the heights represented by the Lines AB, AK; so then the Spaces of Air answering to equal Parts of Mercury in the Barometer, are as the Area's CBKG, GKLD, DLFM, &c. These Area's again are, by the Demonstration of Gregory of St. Vincent, proportionate to the Logarithms of the Numbers expressing the Rationes of AK to AB, of AL to AK, of AM to AL, &c. So then by the common Table of Logarithms, the height of any Place in the Atmosphere, having any assign'd height of the Mercury, may most easily be found: For the Line CB in the Hyperbola, whereof the Area's design the Tabular Logarithms, being 0,0144765; 'twill be, as 0,0144765, to the difference of the Logarithms of 30, or any other lesser Number, for 900 Feet, or the Space answering to an Inch of Mercury, if the Air were equally prest with 30 Inches of Mercury, and every where alike, to the height of the Barometer in the Air, where it will stand at that lesser number of Inches: And by the Converse of this Proportion may the height of the Mercury be found, having the Altitude of the Place given. From these Rules I deriv'd the following Tables.
| A Table shewing the Altitude, to given heights of the Mercury. | |
| Inch. | Feet. |
| 30 | 0 |
| 29 | 915 |
| 28 | 1862 |
| 27 | 2844 |
| 26 | 3863 |
| 25 | 10947 |
| 15 | 18715 |
| 10 | 29662 |
| 5 | 48378 |
| 1 | 91831 |
| 0.5 | 110547 |
| 0.25 | 129262 |
| 0.1 | 29 m. or 154000 |
| 0.01 | 41 m. or 216169 |
| 0.001 | 53 m. or 278338 |
| A Table shewing the heights of the Mercury, at given Altitudes. | |
| Feet. | Inch. |
| 0 | 30 00 |
| 1000 | 28 91 |
| 2000 | 27 86 |
| 3000 | 26 85 |
| 4000 | 35 87 |
| 5000 feet | 24 93 |
| 1 mile | 24 67 |
| 2 | 20 29 |
| 3 | 16 68 |
| 4 | 13 72 |
| 5 | 11 28 |
| 10 | 4 24 |
| 15 | 1 60 |
| 20 | 0 95 |
| 25 | 0 23 |
| 30 | 0 08 |
| 40 | 0 012 |
UPON these Suppositions it appears, that at the height of 41 Miles the Air is so rarified, as to take up 3000 times the Space it occupies here, and at 53 Miles high it would be expanded above 30000 times; but it's probable that the utmost Power of its Spring cannot exert it self, to so great an Extension, and that no part of the Atmosphere reaches above 45 Miles from the Surface of the Earth.
This seems confirm'd from the Observations of the Crepusculum, which is observ'd commonly to begin and end when the Sun is about 18 Degrees below the Horizon; for supposing the Air to reflect light from its most rarified Parts, and that as long as the Sun illuminates any of its Atoms, they are visible to an Eye not intercepted by the Curvity of the Earth, it will follow from Fig. 5. Plate 1. that the proportion of the height of the whole Air, to the Semi-diameter of the Earth, is much about, as 1 to 90, or as the excess of the Secant of about 8½ Degrees to the Radius. For if E be the Eye of the Observer, S a Place where the Sun sets at the end of Twilight in E, and the Arch ECS, or TCA, be found 18 Degrees, the excess of the Secant of half thereof ECH, would be the height of the Air, viz. GH: But the Beam of the Sun ASH, and the Visual Ray EH, do each of them suffer a Refraction of about 32 or 33 Minutes, whereby being bent inwards from H towards G, the height of the Air need not be so great as if they went streight; and having from the Angle ECS taken the double Refraction of the Horizontal Ray, the half of the Remainder will be 8½ Degrees circiter, whose Secant being 10,111, it follows, that as 10000 to 111, so the Semi-diameter of the Earth supposed 4000 Miles, to 44,4 Miles; which will be the height of the whole Air, if the Places E, S, whose visible Portions of the Atmosphere ERZH, and SHKB, just touch one the other, be 18 Degrees asunder.
At this height the Air is expanded into above 3000 times the space it occupies here, and we have seen the Experience of condensing it into the 60th part of the same Space, so that it should seem, that the Air is a Substance capable of being compressed into the 180000th part of the Space it would naturally take up, when free from pressure. Now what Texture or Composition of Parts shall be capable of this great Expansion and Contraction, seems a very hard Question; and which, I suppose, is scarce sufficiently accounted for, by comparing it to Wool, Cotten, and the like springy Bodies.
Hitherto I have only consider'd the Air and Atmosphere, as one unalter'd Body, as having constantly at the Earth's Surface the 800th part of the weight of Water, and being capable of Rarifaction and Condensation in infinitum; neither of which Hypotheses are rigidly true: For here in England it is notoriously known, that the weight of the whole Atmosphere is various, being counterpoised sometimes by 28½ Inches of Mercury, and at other times by no less than 30½; so that the under parts being pressed by about a 15th part, less weight, the specifick Gravity of the Air upon that score will sometimes be a 15th part lighter than another; besides Heat and Cold, does very considerably dilate and contract the Air, and consequently alter its Gravity; to which add the mixture of Effluvia, or steams arising from almost all Bodies, which assimulating into the Form of Air, are kept suspended therein, as Salts dissolv'd in Liquors, or Metals in corroding Menstrua; which Bodies being all of them very much heavier than Air, their Particles by their Admixture must needs encrease the weight of that Air they lie incorporated withal, after the same manner as melted Salts do augment the specifick Gravity of Water. The other Consideration is, that the Rarifaction and Condensation of the Air is not precisely according to the proportion here laid down; for the Experiment very nearly agrees thereto, as may be seen in the 58th Chapter of Mr. Hook's Micrography; yet are the Condensations not possible beyond certain degrees: For being compressed into an 800th part of the Space it takes up here, its consistence would be equally dense with that of Water; which yields not to any force whatsoever, as hath been found by several Experiments tried here, and at Florence, by the Academia del Cimento. Nor can the Rarifaction proceed in infinitum; for supposing the Spring whereby it dilates it self, occasion'd by what Texture of Parts you please, yet must there be a determinate Magnitude of the natural State of each Particle, as we see it is in Wool, and the like, whose Bodies being compressable into a very small Space, have yet a determinate bulk which they cannot exceed, when free'd from all manner of Pressure.
These Objections being true, do disturb the Geometrical Accuracy of these Conclusions, drawn from the specifick Gravity of the Air observ'd at any time; but the Method here shewn will compute by a like Calculation, the heights of the Quick-silver, and the Rarifactions of the Air from any assign'd height of the Barometer at the Earth's Surface, and any specifick Gravity given. As to the Condensation and Rarifaction by Heat and Cold, and the various mixture of Aqueous and other Vapours, these two Objections seem generally to compensate each other; for when the Air is rarified by Heat, they are raised most copiously; so that though the Air properly so call'd, be expanded, and consequently lighter, yet the Interstices thereof being crouded full of Vapours of much heavier Matters, bulk for bulk, the weight of the Compositum may continue much the same, at least a most curious Experiment made by the Ingenious Mr. John Caswell, of Oxford, upon the top of Snowdon Hill, in Carnarvanshire, seems to prove, that the first Inches of Mercury have their Portions of Air near enough to what I now determine: For the height of the Hill being 1240 Yards, or very near it, he found the Mercury to have subsided to 25,6 Inches, or 4 inches below the mean Altitude thereof at the Level of the Sea, (which is a greater difference than has been found in any of our former Experiments,) and the Space answering to 4 Inches, by my Calculation, should be 1288 Yards; and it agrees as well with the Observations in the Appendix to Mr. Pascall's Book, del Equilibre des Liqueurs, made on the high Hill in Auvergne, call'd le puy de Domme. So that the Rarifaction and Vapours seem not to have alter'd considerably, the Gravity of the under Parts of the Air; and much above the height where these Experiments were made, do few Vapours ascend, and the Cold is such that the Snow lies continually, so that for the more elevated Parts of the Sphere of Air, there is much less Reason to doubt.
But now we have had occasion to mention the difference there is between the height of the Mercury at one time, from the height thereof at another, it may not be unacceptable to offer at some Reasons for the said difference; which, at least to my self, seem to have some appearance of Truth. First, Then it's undoubtedly demonstrable, that the height of the Cylinder of Mercury is equal to the weight of the whole incumbent Air, and consequently that that whole is sometimes a fifteenth more than at other times; which cannot otherwise be, but by the access of new Matter when 'tis heavy, and its diminution when 'tis light; that Hypothesis therefore that shews how the Air shall be encreased or diminished, in any particular place, will give a Reason for the greater and lesser height of the Mercury in the Baroscope: But to direct us in the choice of the several Causes, which may be assign'd for the Increase and Decrease of the Air, 'twill not be unnecessary to enumerate some of the principal Observations made upon the Barometer, most whereof are sufficiently known already to all those that are curious in these Matters.
The First is, That in calm Weather, when the Air is inclin'd to Rain, the Mercury is commonly low.
2. That in serene good settled Weather, the Mercury is generally high.