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thinner in every part of that space; at a treble dis. Plate II. tance, it will be nine times thinner; and at a quadruple distance, sixteen times thinner, than it was at first; and so on, according to the increase of the square surfaces B, C, D, E, described upon the distances AB, AC, AD, AE. Consequently, the quantities of this rarefied light received upon a surface of any given size and shape whatever, removed successively to these several distances, will be but one-fourth, one-ninth, one-sixteenth, respectively, of the whole quantity received by it at the first distance AB. Or, in general words, the densities and

quantities of light, received upon any given plane, are diminished in the same proportion, as the squares of the distances of that plane, from the luminous body, are increased : and on the contrary, are increased in the same proportion as these squares are diminished.

170. The more a telescope magnifies the discs of Why the the Moon and planets, so much the dimmer they planets appear than to the bare eye; because the telescope dimmer cannot magnify the quantity of light as it does the when surface; and, by spreading the same quantity of light through

viewed over a surface so much larger than the naked eye telescopes

than by beheld, just so much dimmer must it

appear when

the bare viewed by a telescope, than by the bare eye. eye.

171. When a ray of light passes out of one medium * into another, it is refracted, or turned out of its first course, more or less, as it falls more or less obliquely on the refracting surface which divides the two mediums. This may be proved by several experiments ; 'of which we shall only give three for example's sake. 1. In a bason, FGH, put a piece of Fig. VIII. money, as DB, and then retire from it to A ; that is, till the edge of the bason at E just hides the money from your sight; then keeping your head


* A medium, in this sense, is any transparent body, or that through which the rays of light can nass; as water, glass, diamond, air; and even a vacuum is sometimes called a medium.


rays of

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steady, let another person fill the bason gently with


water. As he fills it, you will see more and more Refrac. of the piece DB; which will be all in view when the tion of the bason is full, and appear as if lifted up to C.

For light. the ray AEB, which was straight while the bason

was empty, is now bent at the surface of the water in E, and turned out of its rectilineal course into the direction ED. Or, in other words, the ray DEK, that proceeded in a straight line from the edge D while the bason was empty, and went above the eye at A, is now bent at E; and instead of going on in the rectilineal direction DEK, goes in the angled direction DEA, and by entering the eye at A renders the object DB visible. Or, 2dly, Place the bason where the Sun shines obliquely, and observe where the shadow of the rim E falls on the bottom, as at B: then fill it with water, and the shadow will fall at D; which proves that the rays of light, falling obliquely on the surface of the water, are refracted, or bent downward into it.

172. The less obliquely the rays of light fall upon the surface of any medium, the less they are refract. ed; and if they fall perpendicularly on it, they are not refracted at all. For, in the last experiment, the higher the Sun rises, the less will be the difference between the places where the edge of the shadow falls in the empty and in the full bason. And, 3dly, if a stick be laid over the bason, and the Sun's rays be reflected perpendicularly into it from a lookingglass, the shadow of the stick will fall upon the same place of the bottom, whether the bason be full or empty.

173. The denser that any medium is, the more is

light refracted in passing through it. The at.

174. The Earth is surrounded by a thin fluid mosphere. mass of matter, called the air or atmosphere, which

gravitates to the Earth, revolves with it in its diurnal motion, and goes round the Sun with it every year.

This fluid is of an elastic or springy nature, and its lowest part, being pressed by the weight of all the air above it, is pressed the closest together; and therefore the atmosphere is densest of all at the Earth's surface, and higher up becomes gradually

" It is well known* that the air near the surface of our Earth possesses a space about 1200 times greater than water of the same weight. And therefore, a cylindric column of air 1200 feet high, is of equal weight with a cylinder of water of the same breadth, and but one foot high. But a cylinder of air reaching to the top of the atmosphere is of equal weight with a cylinder of water about 33 feet hight; and therefore, if from the whole cylinder of air, the lower part of 1200 feet high be taken away, the remaining upper part will be of equal weight with a cylinder of water 32 feet, high; wherefore, at the height of 1200 feet or two furlongs, the weight of the incumbent air is less, and consequently the rarity of the compressed air is greater, than near the Earth's surface, in the ratio of 33 to 32. And the air, at all heights whatever, supposing the expansion thereof to be reciprocally proportional to its compression (and this proportion has been proved by the experiments of Dr. Hooke and others) will be set down in the following table : in the first column of which you have the height of the air in miles, whereof 4000 make a semi-diameter of the Earth; in the second the compression of the air, or the incumbent weight; in the third its rarity or expansion, supposing gravity to decrease in the duplicate ratio of the distances from the Earth's centre: The small numeral figures being here used to shew what number of ciphers


NEWTON's system of the World, p. 120. + This is evident from common pumps.

must be joined to the numbers expressed by the larger figures, as 0.171224 for 0.000000000000000 00 1224, and 26956's for 26956000000000000000.

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From the above table it appears that the air in proceeding upward is rarified in such manner, that a sphere of that air which is nearest the Earth but of one inch diameter, if dilated to an equal rarefaction with that of the air at the height of ten semi-diameters of the Earth, would fill up more space than is contained in the whole heavens on this side the fixed stars, And it likewise appears that the Moon does not move in a perfectly free and unresisting medium; although the air, at a height equal to her distances, is at least 340019° times thinner than at the Earth's surface; and therefore cannot resist her

motion, so as to be sensible, in many ages. Its weight 175. The weight of the air, at the Earth's surhow

face, is found by experiments made with the air-pump; found.

and also by the quantity of mercury that the atmosphere balances in the barometer; in which, at a mean state, the mercury stands 294 inches high. And if the tube were a square inch wide, it would at that height contain 294 cubic inches of mercury, which

is just 15 pounds weight; and so much weight of air every square inch of the Earth's surface sustains ; and consequently every square foot 144 times as much. Now, as the Earth's surface contains, in round numbers, 200,000,000 square miles, it must contain no less than 5,575,680,000,000,000 square feet; which being multiplied by 2160, the number of pounds on each square foot, amounts to 12,043, 468,800,000,000,000 pounds, for the weight of the whole atmosphere. At this rate, a middle-sized man, whose surface is about 15 square feet, is pressed by 32,400 pounds weight of air all around; for fluids press equally up and down, and on all sides. But, because this enormous weight is equal on all sides, and counterbalanced by the spring of the air diffused through all parts of our bodies, it is not in the least degree felt by us.

176. Oftentimes the state of the air is such, that A common we feel ourselves languid and dull; which is commonly thought to be occasioned by the air's being weight of foggy and heavy about us. But that the air is then the air. too light, is evident from the mercury's sinking in the barometer, at which time it is generally found that the air has not sufficient strength to bear up the vapours which compose the clouds, for when it is otherwise, the clouds mount high, and the air is more elastic and weighty above us, by which means it balances the internal spring of the air within us, braces up our blood vessels and nerves, and makes us brisk and lively.

177. According to * Dr. Krill, and other astro-Without nomical writers, it is entirely owing to the atmos.

phere the phere that the heavens appear bright in the day-heavens time. For, without an atmosphere, only that part

would al. of the heavens would shine in which the Sun was pear dark,

ways applaced: and if we could live without air, and should and we

should turn our backs toward the Sun, the whole heavens have no

twilight. * See his Astror.omy, p. 232.

mistake about the

an atmos

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