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between them, and if we suppose a Db to be the sphere of the earth, and C its centre in the figure CD 6B, we
know Db, the length of the arch of the circle between D and b, – viz. half the measured interval, and b B, the excess of its secant above its radius — which is the height of B, — data which, by the solution of an easy geometrical problem, enable us to find the length of the radius DC. If, as is really the case, we suppose both the heights and distance of the stations inconsiderable in comparison with the size of the earth, the solution alluded to is contained in the following proposition:
The earth's diameter bears the same proportion to the distance of the visible horizon from the eye as that distance does to the height of the eye above the sea level.
When the stations are unequal in height the problem is a little more complicated. .
(28.) Although, as we have observed, the effect of refraction prevents this from being an exact method of ascertaining the dimensions of the earth, yet it will suffice to afford such an approximation to it as shall be of use in the present stage of the reader's knowledge, and help him to many just conceptions, on which account we shall exemplify its application in numbers. Now, it appears by observation, that two points, each ten feet above the surface, cease to be visible from each other over still water, and in average atmospheric circumstances, at a distance of about 8 miles. But 10 feet is the 528th part of a mile, so that half their distance, or 4 miles, is to the height of each as 4 x 528 or 2112:1, and therefore in the same proportion to 4 miles is the length of the earth’s diameter. It must, therefore, be? equal to 4 x 2112=8448, or, in round numbers, about 8000 miles, which is not very far from the truth.
(29.) Such is the first rough result of an attempt to ascertain the earth's magnitude; and it will not be amiss if we take advantage of it to compare it with objects we have been accustomed to consider as of vast size, so as to interpose a few steps between it and our ordinary ideas of dimension. We have before likened the inequalities on the earth's surface, arising from moun. tains, valleys, buildings, &c. to the roughnesses on the rind of an orange, compared with its general mass. The comparison is quite free from exaggeration. The highest mountain known does not exceed five miles in perpen. dicular elevation: this is only one 1600th part of the earth's diameter; consequently, on a globe of sixteen inches in diameter, such a mountain would be represented by a protuberance of no more than one hundredth part of an inch, which is about the thickness of ordi. nary drawing-paper. Now as there is no entire con. tinent, or even any very extensive tract of land, known, whose general elevation above the sea is any thing like half this quantity, it follows, that if we would construct a correct model of our earth, with its seas, continents, and mountains, on a globe sixteen inches in diameter, the whole of the land, with the exception of a few prominent points and ridges, must be comprised on it within the thickness of thin writing-paper; and the highest hills would be represented by the smallest visible grains of sand.
(30.) The deepest mine existing does not penetrate half a mile below the surface : a scratch, or pin-hole, duly representing it, on the surface of such a globe as our model, would be imperceptible without a magnifier.
(31.) The greatest depth of sea, probably, does not much exceed the greatest elevation of the continents; and would, of course, be represented by an excavation, in about the same proportion, into the substance of the globe; so that the ocean comes to be conceived
as a mere film of liquid, such as, on our model, would be left by a brush dipped in colour and drawn over those parts intended to represent the sea : only, in so conceiv. ing it, we must bear in mind that the resemblance ex. tends no farther than to proportion in point of quantity. The mechanical laws which would regulate the distri. bution and movements of such a film, and its adhesion to the surface, are altogether different from those which govern the phenomena of the sea.
(32.) Lastly, the greatest extent of the earth's sur. face which has ever been seen at once by man, was that exposed to the view of MM. Biot and Gay-Lussac, in their celebrated aeronautic expedition to the enormous height of 25,000 feet, or rather less than five miles. To estimate the proportion of the area visible from this elevation to the whole earth's surface, we must have recourse to the geometry of the sphere, which informs us that the convex surface of a spherical segment is to the whole surface of the sphere to which it belongs as the versed sine, or thickness of the segment, is to the diameter of the sphere; and further, that this thickness, in the case we are considering, is almost ex. actly equal to the perpendicular elevation of the point of sight above the surface. The proportion, therefore, of the visible area, in this case, to the whole earth's surface, is that of five miles to 8000, or 1 to 1600. The portion visible from Ætna, the Peak of Teneriffe, or Mowna Roa, is about one 4000th.
(33.) When we ascend to any very considerable elevation above the surface of the earth, either in a balloon, or on mountains, we are made aware, by many uneasy sensations, of an insufficient supply of air. The barometer, an instrument which informs us of the weight of air incumbent on a given horizontal surface, confirms this impression, and affords a direct measure of the rate of diminution of the quantity of air which a given space includes as we recede from the surface. From its indications we learn, that when we have ascended to the height of 1000 feet, we have left below us about one thirtieth of the whole mass of the atmosphere: - that at 10,600 feet of perpendicular elevation (which is rather less than that of the summit of Ætna*) we have as. cended through about one third; and at 18,000 feet (which is nearly that of Cotopaxi) through one half the material, or, at least, the ponderable, body of air incum. bent on the earth's surface. From the progression of these numbers, as well as, ,à priori, from the nature of the air itself, which is compressible, i. e. capable of being condensed, or crowded into a smaller space in proportion to the incumbent pressure, it is easy to see that, although by rising still higher we should continually get above more and more of the air, and so relieve ourselves more and more from the pressure with which it weighs upon us, yet the amount of this additional relief, or the ponderable quantity of air surmounted, would be by no means in proportion to the additional height ascended, but in a constantly decreasing ratio. An easy calculation, how. ever, founded on our experimental knowledge of the properties of air, and the mechanical laws which regulate its dilatation and compression, is sufficient to show that, at an altitude above the surface of the earth not exceeding the hundredth part of its diameter, the tenuity, or rarefaction, of the air must be so excessive, that not only animal life could not subsist, or combustion be maintained in it, but that the most delicate means we possess of ascertaining the existence of any air at all would fail to afford the slightest perceptible indications of its presence.
(34.) Laying out of consideration, therefore, at present, all nice questions as to the probable existence of a definite limit to the atmosphere, beyond which there is, absolutely and rigorously speaking, no air, it is clear, that, for all practical purposes, we may speak of those regions which are more distant above the earth's surface than the hundredth part of its diameter as void of air, and of course of clouds (which are nothing but visible vapours, diffused and floating in the air, sustained by it, and rendering it turbid as mud does water). It seems probable, from many indications, that the greatest height at which visible clouds ever exist does not exceed ten miles ; at which height the density of the air is about an eighth part of what it is at the level of the sea.
* The height of Ætna above the Mediterranean (as it results from a barometrical measurement of my own, made in July, 1824, under very favour. able circunistances) is 10,872 English feet, Author.
(35.) We are thus led to regard the atmosphere of air, with the clouds it supports, as constituting a coating of equable or nearly equable thickness, enveloping our globe on all sides; or rather as an aërial ocean, of which the surface of the sea and land constitutes the bed, and whose inferior portions or strata, within a few miles of the earth, contain by far the greater part of the whole mass, the density diminishing with extreme rapidity as we recede upwards, till, within a very moderate distance (such as would be represented by the sixth of an inch on the model we have before spoken of, and which is not more in proportion to the globe on which it rests, than the downy skin of a peach in comparison with the fruit within it), all sensible trace of the existence of air disappears.
(36.) Arguments, however, are not wanting to render it, if not absolutely certain, at least in the highest degree probable, that the surface of the aërial, like that of the aqueous ocean, has a real and definite limit, as above hinted at; beyond which there is positively no air, and above which a fresh quantity of air, could it be added from without, or carried aloft from below, instead of dilating itself indefinitely upwards, would, after a certain very enormous but still finite enlargement of volume, sink and merge, as water poured into the sea, and distribute itself among the mass beneath. With the truth of this conclusion, however, astronomy has little concern ; all the effects of the atmosphere in mo. difying astronomical phenomena being the same, whether it be supposed of definite extent or not.
(37.) Moreover, whichever idea we adopt, it is equally certain that, within those limits in which it possesses any appreciable density, its constitution is the same over