Chapter IV: Part 4

147. As Mercury and Venus, seen from the Earth, have their respective Elongations from the Sun, and Stationary places; so has the Earth, seen from Mars; and Mars, seen from Jupiter; and Jupiter, seen from Saturn. That is, to every superiour Planet, all the inferiour ones have their Stations and Elongations; as Venus and Mercury have to the Earth. As seen from Saturn, Mercury never goes above 2-1/2 degrees from the Sun; Venus 4-1/3; the Earth 6; Mars 9-1/2; and Jupiter 33-1/4: so that Mercury, as seen from the Earth, has almost as great a Digression or Elongation from the Sun, as Jupiter seen from Saturn.

[Sidenote: A proof of the Earth’s annual motion.]

148. Because the Earth’s Orbit is included within the Orbits of Mars, Jupiter, and Saturn, they are seen on all sides of the Heavens; and are as often in Opposition to the Sun as in Conjunction with him. If the Earth stood still, they would always appear direct in their motions, never retrograde nor stationary. But they seem to go just as often backward as forward; which, if gravity be allowed to exist, affords a sufficient proof of the Earth’s annual motion.

[Sidenote: Fig. III.

PLATE II.

General Phenomena of a superiour Planet to an inferiour.]

149. As Venus and the Earth are superiour Planets to Mercury, they shew much the same Appearances to him that Mars and Jupiter do to us. Let Mercury _m_ be at _f_, Venus _v_ at _F_, and the Earth at _E_; in which situation Venus hides the Earth from Mercury; but, being in opposition to the Sun, she shines on Mercury with a full illumined Orb; though, with respect to the Earth, she is in conjunction with the Sun and invisible. When Mercury is at _f_, and Venus at _G_, her enlightened side not being directly towards him, she appears a little gibbous; as Mars does in a like situation to us: but, when Venus is at _I_, her enlightened side is so much towards Mercury at _f_, that she appears to him almost of a round figure. At _K_, Venus disappears to Mercury at _f_, being then hid by the Sun; as all our superiour Planets are to us, when in conjunction with the Sun. When Venus has, as it were, emerged out of the Sun beams, as at _L_, she appears almost full to Mercury at _f_; at _M_ and _N_, a little gibbous; quite full at _F_, and largest of all; being then in opposition to the Sun, and consequently nearest to Mercury at _f_; shining strongly on him in the night, because her distance from him then is somewhat less than a fifth part of her distance from the Earth, when she appears roundest to it between _I_ and _K_, or between _K_ and _L_, as seen from the Earth _E_. Consequently, when Venus is opposite to the Sun as seen from Mercury, she appears more than 25 times as large to him as she does to us when at the fullest. Our case is almost similar with respect to Mars, when he is opposite to the Sun; because he is then so near the Earth, and has his whole enlightened side towards it. But, because the Orbits of Jupiter and Saturn are very large in proportion to the Earth’s, these two Planets appear much less magnified at their Oppositions or diminished at their Conjunctions than Mars does, in proportion to their mean apparent Diameters.

CHAP. VII.

_The physical Causes of the Motions of the Planets. The Excentricities of their Orbits. The Times in which the Action of Gravity would bring them to the Sun._ ARCHIMEDES_’s ideal Problem for moving the Earth. The World not eternal._

[Sidenote: Gravitation and Projection.

Fig. IV.

PLATE II.

Circular Orbits.

Fig. IV.]

150. From the uniform projectile motion of bodies in straight lines, and the universal power of attraction, arises the curvilineal motions of all the Heavenly bodies. If the body _A_ be projected along the right line _ABX_, in open Space, where it meets with no resistance, and is not drawn aside by any other power, it will for ever go on with the same velocity, and in the same direction. For, the force which moves it from _A_ to _B_ in any given time, will carry it from _B_ to _X_ in as much more time; and so on, there being nothing to obstruct or alter it’s motion. But if, when this projectile force has carried it, suppose to _B_, the body _S_ begins to attract it, with a power duly adjusted, and perpendicular to it’s motion at _B_, it will then be drawn from the straight line _ABX_, and forced to revolve about _S_ in the Circle _BYTU_. When the body _A_ comes to _U_, or any other part of it’s Orbit, if the small body _u_, within the sphere of _U_’s attraction, be projected as in the right line _Z_, with a force perpendicular to the attraction of _U_, then _u_ will go round _U_ in the Orbit _W_, and accompany it in it’s whole course round the body _S_. Here, _S_ may represent the Sun, _U_ the Earth, and _u_ the Moon.

151. If a Planet at _B_ gravitates, or is attracted, toward the Sun, so as to fall from _B_ to _y_ in the time that the projectile force would have carried it from _B_ to _X_, it will describe the curve _BY_ by the combined action of these two forces, in the same time that the projectile force singly would have carried it from _B_ to _X_, or the gravitating power singly have caused it to descend from _B_ to _y_; and these two forces being duly proportioned, and perpendicular to one another, the Planet obeying them both, will move in the circle _BYTU_[30].

[Sidenote: Elliptical Orbits.

PLATE II.]

152. But if, whilst the projectile force carries the Planet from _B_ to _b_, the Sun’s attraction (which constitutes the Planet’s gravitation) should bring it down from _B_ to I, the gravitating power would then be too strong for the projectile force; and would cause the Planet to describe the curve _BC_. When the Planet comes to _C_, the gravitating power (which always increases as the square of the distance from the Sun _S_ diminishes) will be yet stronger for the projectile force; and by conspiring in some degree therewith, will accelerate the Planet’s motion all the way from _C_ to _K_; causing it to describe the arcs _BC_, _CD_, _DE_, _EF_, &c. all in equal times. Having it’s motion thus accelerated, it gains so much centrifugal force, or tendency to fly off at _K_ in the line _Kk_, as overcomes the Sun’s attraction: and the centrifugal force being too great to allow the Planet to be brought nearer the Sun, or even to move round him in the Circle _Klmn_, &c. it goes off, and ascends in the curve _KLMN_, &c. it’s motion decreasing as gradually from _K_ to _B_ as it increased from _B_ to _K_, because the Sun’s attraction acts now against the Planet’s projectile motion just as much as it acted with it before. When the Planet has got round to _B_, it’s projectile force is as much diminished from it’s mean state about _G_ or _N_, as it was augmented at _K_; and so, the Sun’s attraction being more than sufficient to keep the Planet from going off at _B_, it describes the same Orbit over again, by virtue of the same forces or laws.

[Sidenote: Fig. IV.

The Planets describe equal Areas in equal times.]

153. A double projectile force will always balance a quadruple power of gravity. Let the Planet at _B_ have twice as great an impulse from thence towards _X_, as it had before: that is, in the same length of time that it was projected from _B_ to _b_, as in the last example, let it now be projected from _B_ to _c_; and it will require four times as much gravity to retain it in it’s Orbit: that is, it must fall as far as from _B_ to 4 in the time that the projectile force would carry it from _B_ to _c_; otherwise it could not describe the curve _BD_, as is evident by the Figure. But, in as much time as the Planet moves from _B_ to _C_ in the higher part of it’s Orbit, it moves from _I_ to _K_ or from _K_ to _L_ in the lower part thereof; because, from the joint action of these two forces, it must always describe equal areas in equal times, throughout it’s annual course. These Areas are represented by the triangles _BSC_, _CSD_, _DSE_, _ESF_, &c. whose contents are equal to one another, quite round the Figure.

[Sidenote: A difficulty removed.]

154. As the Planets approach nearer the Sun, and recede farther from him, in every Revolution; there may be some difficulty in conceiving the reason why the power of gravity, when it once gets the better of the projectile force, does not bring the Planets nearer and nearer the Sun in every Revolution, till they fall upon and unite with him. Or why the projectile force, when it once gets the better of gravity, does not carry the Planets farther and farther from the Sun, till it removes them quite out of the sphere of his attraction, and causes them to go on in straight lines for ever afterward. But by considering the effects of these powers as described in the two last Articles, this difficulty will be removed. Suppose a Planet at _B_ to be carried by the projectile force as far as from _B_ to _b_, in the time that gravity would have brought it down from _B_ to 1: by these two forces it will describe the curve _BC_. When the Planet comes down to _K_, it will be but half as far from the Sun _S_ as it was at _B_; and therefore, by gravitating four times as strongly towards him, it would fall from _K_ to _V_ in the same length of time that it would have fallen from _B_ to 1 in the higher part of it’s Orbit, that is, through four times as much space; but it’s projectile force is then so much increased at _K_, as would carry it from _K_ to _k_ in the same time; being double of what it was at _B_, and is therefore too strong for the tendency of the gravitating power, either to draw the Planet to the Sun, or cause it to go round him in the circle _Klmn_, &c. which would require it’s falling from _K_ to _w_, through a greater space than gravity can draw it whilst the projectile force is such as would carry it from _K_ to _k_: and therefore the Planet ascends in it’s Orbit _KLMN_, decreasing in it’s velocity for the cause already assigned in § 152.

[Sidenote: The Planetary Orbits elliptical.

Their Excentricities.]

155. The Orbits of all the Planets are Ellipses, very little different from Circles: but the Orbits of the Comets are very long Ellipses; the lower focus of them all being in the Sun. If we suppose the mean distance (or middle between the greatest and least) of every Planet and Comet from the Sun to be divided into 1000 equal parts, the Excentricities of their Orbits, both in such parts and in _English_ miles, will be as follows. Mercury’s, 210 parts, or 6,720,000 miles; Venus’s, 7 parts, or 413,000 miles; the Earth’s, 17 parts, or 1,377,000 miles; Mars’s, 93 parts, or 11,439,000 miles; Jupiter’s, 48 parts, or 20,352,000 miles; Saturn’s, 55 parts, or 42,735,000 miles. Of the nearest of the three forementioned Comets, 1,458,000 miles; of the middlemost, 2,025,000,000 miles; and of the outermost, 6,600,000,000.

[Sidenote: The above laws sufficient for motions both in circular and
elliptic Orbits.]

156. By the above-mentioned laws § 150 _& seq._ bodies will move in all kinds of Ellipses, whether long or short, if the spaces they move in be void of resistance. Only, those which move in the longer Ellipses, have so much the less projectile force impressed upon them in the higher parts of their Orbits; and their velocities, in coming down towards the Sun, are so prodigiously increased by his attraction, that their centrifugal forces in the lower parts of their Orbits are so great as to overcome the Sun’s attraction there, and cause them to ascend again towards the higher parts of their Orbits; during which time, the Sun’s attraction acting so contrary to the motions of those bodies, causes them to move slower and slower, until their projectile forces are diminished almost to nothing; and then they are brought back again by the Sun’s attraction, as before.

[Sidenote: In what times the Planets would fall to the Sun by the power
of gravity.]

157. If the projectile forces of all the Planets and Comets were destroyed at their mean distances from the Sun, their gravities would bring them down so, as that Mercury would fall to the Sun in 15 days 13 hours; Venus in 39 days 17 hours; the Earth or Moon in 64 days 10 hours; Mars in 121 days; Jupiter in 290; and Saturn in 767. The nearest Comet in 13 thousand days; the middlemost in 23 thousand days; and the outermost in 66 thousand days. The Moon would fall to the Earth in 4 days 20 hours; Jupiter’s first Moon would fall to him in 7 hours, his second in 15, his third in 30, and his fourth in 71 hours. Saturn’s first Moon would fall to him in 8 hours; his second in 12, his third in 19, his fourth in 68 hours, and the fifth in 336. A stone would fall to the Earth’s center, if there were an hollow passage, in 21 minutes 9 seconds. Mr. WHISTON gives the following Rule for such Computations. “[31]It is demonstrable, that half the Period of any Planet, when it is diminished in the sesquialteral proportion of the number 1 to the number 2, or nearly in the proportion of 1000 to 2828, is the time that it would fall to the Center of it’s Orbit.” This proportion is, when a quantity or number contains another once and a half as much more.

[Sidenote: The prodigious attraction of the Sun and Planets.]

158. The quick motions of the Moons of Jupiter and Saturn round their Primaries, demonstrate that these two Planets have stronger attractive powers than the Earth has. For, the stronger that one body attracts another, the greater must be the projectile force, and consequently the quicker must be the motion of that other body, to keep it from falling to it’s primary or central Planet. Jupiter’s second Moon is 124 thousand miles farther from Jupiter than our Moon is from us; and yet this second Moon goes almost eight times round Jupiter whilst our Moon goes only once round the Earth. What a prodigious attractive power must the Sun then have, to draw all the Planets and Satellites of the System towards him; and what an amazing power must it have required to put all these Planets and Moons into such rapid motions at first! Amazing indeed to us, because impossible to be effected by the strength of all the living Creatures in an unlimited number of Worlds, but no ways hard for the Almighty, whose Planetarium takes in the whole Universe!

[Sidenote: ARCHIMEDES’s Problem for raising the Earth.]

159. The celebrated ARCHIMEDES affirmed he could move the Earth if he had a place to stand on to manage his machinery[32]. This assertion is true in Theory, but, upon examination, will be found absolutely impossible in fact, even though a proper place and materials of sufficient strength could be had.

The simplest and easiest method of moving a heavy body a little way is by a lever or crow, where a small weight or power applied to the long arm will raise a great weight on the short one. But then, the small weight must move as much quicker than the great weight as the latter is heavier than the former; and the length of the long arm of the lever to the length of the short arm must be in the same proportion. Now, suppose a man pulls or presses the end of the long arm with the force of 200 pound weight, and that the Earth contains in round Numbers 4,000,000,000,000,000,000,000 or 4000 Trillions of cubic feet, each at a mean rate weighing 100 pound; and that the prop or center of motion of the lever is 6000 miles from the Earth’s center: in this case, the length of the lever from the _Fulcrum_ or center of motion to the moving power or weight ought to be 12,000,000,000,000,000,000,000,000 or 12 Quadrillions of miles; and so many miles must the power move, in order to raise the Earth but one mile, whence ’tis easy to compute, that if ARCHIMEDES or the power applied could move as swift as a cannon bullet, it would take 27,000,000,000,000 or 27 Billions of years to raise the Earth one inch.

If any other machine, such as a combination of wheels and screws, was proposed to move the Earth, the time it would require, and the space gone through by the hand that turned the machine, would be the same as before. Hence we may learn, that however boundless our Imagination and Theory may be, the actual operations of man are confined within narrow bounds; and more suited to our real wants than to our desires.

[Sidenote: Hard to determine what Gravity is.]

160. The Sun and Planets mutually attract each other: the power by which they do so we call _Gravity_. But whether this power be mechanical or no, is very much disputed. We are certain that the Planets disturb one another’s motions by it, and that it decreases according to the squares of the distances of the Sun and Planets; as light, which is known to be material, likewise does. Hence Gravity should seem to arise from the agency of some subtile matter pressing towards the Sun and Planets, and acting, like all mechanical causes, by contact. But on the other hand, when we consider that the degree or force of Gravity is exactly in proportion to the quantities of matter in those bodies, without any regard to their bulks or quantity of surface, acting as freely on their internal as external parts, it seems to surpass the power of mechanism; and to be either the immediate agency of the Deity, or effected by a law originally established and imprest on all matter by him. But some affirm that matter, being altogether inert, cannot be impressed with any Law, even by almighty Power: and that the Deity must therefore be constantly impelling the Planets toward the Sun, and moving them with the same irregularities and disturbances which Gravity would cause, if it could be supposed to exist. But, if a man may venture to publish his own thoughts, (and why should not one as well as another?) it seems to me no greater absurdity, to suppose the Deity capable of superadding a Law, or what Laws he pleases, to matter, than to suppose him capable of giving it existence at first. The manner of both is equally inconceivable to us; but neither of them imply a contradiction in our ideas: and what implies no contradiction is within the power of Omnipotence. Do we not see that a human creature can prepare a bar of steel so as to make it attract needles and filings of iron; and that he can put a stop to that power or virtue, and again call it forth again as often as he pleases? To say that the workman infuses any new power into the bar, is saying too much; since the needle and filings, to which he has done nothing, re-attract the bar. And from this it appears that the power was originally imprest on the matter of which the bar, needle, and filings are composed; but does not seem to act until the bar be properly prepared by the artificer: somewhat like a rope coiled up in a ship, which will never draw a boat or any other thing towards the ship, unless one end be tied to it, and the other end to that which is to be hauled up; and then it is no matter which end of the rope the sailors pull at, for the rope will be equally stretched throughout, and the ship and boat will move towards one another. To say that the Almighty has infused no such virtue or power into the materials which compose the bar, but that he waits till the operator be pleased to prepare it by due position and friction, and then, when the needle or filings are brought pretty near the bar, the Deity presses them towards it, and withdraws his hand whenever the workman either for use, curiosity or whim, does what appears to him to destroy the action of the bar, seems quite ridiculous and trifling; as it supposes God not only to be subservient to our inconstant wills, but also to do what would be below the dignity of any rational man to be employed about.

161. That the projectile force was at first given by the Deity is evident. For, since matter can never put itself into motion, and all bodies may be moved in any direction whatsoever; and yet all the Planets both primary and secondary move from west to east, in planes nearly coincident; whilst the Comets move in all directions, and in planes so different from one another; these motions can be owing to no mechanical cause of necessity, but to the free choice and power of an intelligent Being.

162. Whatever Gravity be, ’tis plain that it acts every moment of time: for should it’s action cease, the projectile force would instantly carry off the Planets in straight lines from those parts of their Orbits where Gravity left them. But, the Planets being once put into motion, there is no occasion for any new projectile force, unless they meet with some resistance in their Orbits; nor for any mending hand, unless they disturb one another too much by their mutual attractions.

[Sidenote: The Planets disturb one another’s motion.

The consequences thereof.]

163. It is found that there are disturbances among the Planets in their motions, arising from their mutual attractions when they are in the same quarter of the Heavens; and that our years are not always precisely of the same length[33]. Besides, there is reason to believe that the Moon is somewhat nearer the Earth now than she was formerly; her periodical month being shorter than it was in former ages. For, our Astronomical Tables, which in the present Age shew the times of Solar and Lunar Eclipses to great precision, do not answer so well for very ancient Eclipses. Hence it appears, that the Moon does not move in a medium void of all resistance, § 174; and therefore her projectile force being a little weakened, whilst there is nothing to diminish her gravity, she must be gradually approaching nearer the Earth, describing smaller and smaller Circles round it in every revolution, and finishing her Period sooner, although her absolute motion with regard to space be not so quick now as it was formerly: and therefore, she must come to the Earth at last; unless that Being, which gave her a sufficient projectile force at the beginning, adds a little more to it in due time. And, as all the Planets move in spaces full of æther and light, which are material substances, they too must meet with some resistance. And therefore, if their gravities are not diminished, nor their projectile forces increased, they must necessarily approach nearer and nearer the Sun, and at length fall upon and unite with him.

[Sidenote: The World not eternal.]

164. Here we have a strong philosophical argument against the eternity of the World. For, had it existed from eternity, and been left by the Deity to be governed by the combined actions of the above forces or powers, generally called Laws, it had been at an end long ago. And if it be left to them it must come to an end. But we may be certain that it will last as long as was intended by it’s Author, who ought no more to be found fault with for framing so perishable a work, than for making man mortal.

CHAP. VIII.

_Of Light. It’s proportional quantities on the different Planets. It’s
Refractions in Water and Air. The Atmosphere; it’s weight and
properties. The Horizontal Moon._

[Sidenote: The amazing smallness of the particles of light.]

165. Light consists of exceeding small particles of matter issuing from a luminous body; as from a lighted candle such particles of matter continually flow in all directions. Dr. NIEWENTYT[34] computes, that in one second of time there flows 418,660,000,000,000,000,000,000,000,000,000,000,000,000,000 particles of light out of a burning candle; which number contains at least 6,337,242,000,000 times the number of grains of sand in the whole Earth; supposing 100 grains of sand to be equal in length to an inch, and consequently, every cubic inch of the Earth to contain one million of such grains.

[Sidenote: The dreadful effects that would ensue from their being
larger.]

166. These amazingly small particles, by striking upon our eyes, excite in our minds the idea of light: and, if they were so large as the smallest particles of matter discernible by our best microscopes, instead of being serviceable to us, they would soon deprive us of sight by the force arising from their immense velocity, which is above 164 thousand miles every second[35], or 1,230,000 times swifter than the motion of a cannon bullet. And therefore, if the particles of light were so large, that a million of them were equal in bulk to an ordinary grain of land, we durst no more open our eyes to the light than suffer sand to be shot point blank against them.

[Sidenote: How objects become visible to us.

PLATE II.]

167. When these small particles, flowing from the Sun or from a candle, fall upon bodies, and are thereby reflected to our eyes, they excite in us the idea of that body by forming it’s picture on the retina[36]. And since bodies are visible on all sides, light must be reflected from them in all directions.

[Sidenote: The rays of Light naturally move in straight lines.

A proof that they hinder not one another’s motions.]

168. A ray of light is a continued stream of these particles, flowing from any visible body in straight lines. That they move in straight, and not in crooked lines, unless they be refracted, is evident from bodies not being visible if we endeavour to look at them through the bore of a bended pipe; and from their ceasing to be seen by the interposition of other bodies, as the fixed Stars by the interposition of the Moon and Planets, and the Sun wholly or in part by the interposition of the Moon, Mercury, or Venus. And that these rays do not interfere, or jostle one another out of their ways, in flowing from different bodies all around, is plain from the following Experiment. Make a little hole in a thin plate of metal, and set the plate upright on a table, facing a row of lighted candles standing by one another; then place a sheet of paper or pasteboard at a little distance from the other side of the plate, and the rays of all the candles, flowing through the hole, will form as many specks of light on the paper as there are candles before the plate, each speck as distinct and large, as if there were only one candle to cast one speck; which shews that the rays are no hinderance to each other in their motions, although they all cross in the hole.

[Sidenote: Fig. XI.

In what proportion light and heat decrease at any given
distance from the Sun.

PLATE II.]

169. Light, and therefore heat so far as it depends on the Sun’s rays (§ 85, towards the end) decreases in proportion to the squares of the distances of the Planets from the Sun. This is easily demonstrated by a Figure which, together with it’s description, I have taken from Dr. SMITH’s Optics[37]. Let the light which flows from a point _A_, and passes through a square hole _B_, be received upon a plane _C_, parallel to the plane of the hole; or, if you please, let the figure _C_ be the shadow of the plane _B_; and when the distance _C_ is double of _B_, the length and breadth of the shadow _C_ will be each double of the length and breadth of the plane _B_; and treble when _AD_ is treble of _AB_; and so on: which may be easily examined by the light of a candle placed at _A_. Therefore the surface of the shadow _C_, at the distance _AC_ double of _AB_, is divisible into four squares, and at a treble distance, into nine squares, severally equal to the square _B_, as represented in the Figure. The light then which falls upon the plane _B_, being suffered to pass to double that distance, will be uniformly spread over four times the space, and consequently will be four times thinner in every part of that space, and at a treble distance 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_, built 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 quarter, one ninth, one sixteenth 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.

[Sidenote: Why the Planets appear dimmer when viewed thro’ telescopes
than by the bare eye.]

170. The more a telescope magnifies the disks of the Moon and Planets, they appear so much dimmer than to the bare eye; because the telescope cannot magnify the quantity of light, as it does the surface; and, by spreading the same quantity of light over a surface so much larger than the naked eye beheld, just so much dimmer must it appear when viewed by a telescope than by the bare eye.

[Sidenote: Fig. VIII.

Refraction of the rays of light.]

171. When a ray of light passes out of one medium[38] into another, it is refracted, or turned out of it’s 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 money as _DB_, and then retire from it as to _A_, till the edge of the bason at _E_ just hides the money from your sight: then, keeping your head steady, let another person fill the bason gently with water. As he fills it, you will see more and more of the piece _DB_; which will be all in view when the bason is full, and appear as if lifted up to _C_. For, the ray _AEB_, which was straight whilst the bason was empty, is now bent at the surface of the water in _E_, and turned out of it’s rectilineal course into the direction _ED_. Or, in other words, the ray _DEK_, that proceeded in a straight line from the edge _D_ whilst 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 downwards into it.

172. The less obliquely the rays of light fall upon the surface of any medium, the less they are refracted; and if they fall perpendicularly thereon, 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 full bason. And, 3dly, if a stick be laid over the bason, and the Sun’s rays be reflected perpendicularly into it from a looking-glass, 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.

[Sidenote: The Atmosphere.

The Air’s compression and rarity at different heights.]

174. The Earth is surrounded by a thin fluid mass of matter, called the _Air_, or _Atmosphere_, which gravitates to the Earth, revolves with it in it’s diurnal motion, and goes round the Sun with it every year. This fluid is of an elastic or springy nature, and it’s lowermost parts being pressed by the weight of all the Air above them, are squeezed the closer together; and are therefore densest of all at the Earth’s surface, and gradually rarer the higher up. “It is well known[39] 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 foot 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 foot high[40]; and therefore if from the whole cylinder of Air, the lower part of 1200 foot high is taken away, the remaining upper part will be of equal weight with a cylinder of water 32 foot 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 having this ratio we may compute the rarity of the Air at all heights whatsoever, 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. The result of the computation I have set down in the annexed 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 it’s rarity or expansion, supposing gravity to decrease in the duplicate ratio of the distances from the Earth’s center. And the small numeral figures are here used to shew what number of cyphers must be joined to the numbers expressed by the larger figures, as 0.^{17}1224 for 0.000000000000000001224, and 26956^{15} for 26956000000000000000.

+-----------------------------------------+ | AIR’s | | _________________/\ _________________ | | / \ | | Height. Compression. Expansion. | +-----------+---------------+-------------+ | 0 | 33 | 1 | | 5 | 17.8515 | 1.8486 | | 10 | 9.6717 | 3.4151 | | 20 | 2.852 | 11.571 | | 40 | 0.2525 | 136.83 | | 400 | 0.^{17}1224 | 26956^{15} | | 4000 | 0.^{105}4465 | 73907^{102} | | 40000 | 0.^{192}1628 | 26263^{189} | | 400000 | 0.^{210}7895 | 41798^{207} | | 4000000 | 0.^{212}9878 | 33414^{209} | | Infinite. | 0.^{212}6041 | 54622^{209} | +-----------+---------------+-------------+

From this Table it appears that the Air in proceeding upwards is rarefied 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, according to the preceding computation of their distance[41].” And it likewise appears that the Moon does not move in a perfectly free and un-resisting medium; although the air at a height equal to her distance, is at least 34000^{190} times thinner than at the Earth’s surface; and therefore cannot resist her motion so as to be sensible in many ages.

[Sidenote: It’s weight how found.

PLATE II.]

175. The weight of the Air, at the Earth’s surface, is found by experiments made with the air-pump; and also by the quantity of mercury that the Atmosphere balances in the barometer; in which, at a mean state; the mercury stands 29-1/2 inches high. And if the tube were a square inch wide, it would at that height contain 29-1/2 cubic inches of mercury, which is just 15 pound weight; and so much weight of air every square inch of the Earth’s surface sustains; and every square foot 144 times as much, because it contains 144 square inches. Now as the Earth’s surface contains about 199,409,400 square miles, it must be of no less than 5,559,215,016,960,000 square feet; which, multiplied by 2016, the number of pounds on every foot, amounts to 11,207,377,474,191,360,000; or 11 trillion 207 thousand 377 billion 474 thousand 191 million and 360 thousand pounds, for the weight of the whole Atmosphere. At this rate, a middle sized man, whose surface may be about 14 square feet, is pressed by 28,224 pound weight of Air all round; 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 internal Air in our blood vessels, it is not felt.

[Sidenote: A common mistake about the weight of the Air.]

176. Oftentimes the state of the Air is such that we feel ourselves languid and dull; which is commonly thought to be occasioned by the Air’s being foggy and heavy about us. But that the Air is then 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, the Air is more elastic and weighty about 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.

[Sidenote: Without an Atmosphere the Heavens would always appear dark,
and we should have no twilight.]

177. According to [42]Dr. KEILL, and other astronomical writers, it is entirely owing to the Atmosphere that the Heavens appear bright in the day-time. For, without an Atmosphere, only that part of the Heavens would shine in which the Sun was placed: and if an observer could live without Air, and should turn his back towards the Sun, the whole Heavens would appear as dark as in the night, and the Stars would be seen as clear as in the nocturnal sky. In this case, we should have no twilight; but a sudden transition from the brightest sunshine to the blackest darkness immediately after sun-set; and from the blackest darkness to the brightest sun-shine at sun-rising; which would be extremely inconvenient, if not blinding, to all mortals. But, by means of the Atmosphere, we enjoy the Sun’s light, reflected from the aerial particles, before he rises and after he sets. For, when the Earth by its rotation has withdrawn the Sun from our sight, the Atmosphere being still higher than we, has his light imparted to it; which gradually decreases until he has got 18 degrees below the Horizon; and then, all that part of the Atmosphere which is above us is dark. From the length of twilight, the Doctor has calculated the height of the Atmosphere (so far as it is dense enough to reflect any light) to be about 44 miles. But it is seldom dense enough at two miles height to bear up the Clouds.

[Sidenote: It brings the Sun in view before he rises, and keeps him in
view after he sets.]

178. The Atmosphere refracts the Sun’s rays so, as to bring him in sight every clear day, before he rises in the Horizon; and to keep him in view for some minutes after he is really set below it. For, at some times of the year, we see the Sun ten minutes longer above the Horizon than he would be if there were no refractions: and about six minutes every day at a mean rate.

[Sidenote: Fig. IX.

PLATE II.]

179. To illustrate this, let _IEK_ be a part of the Earth’s surface, covered with the Atmosphere _HGFC_; and let _HEO_ be the[43] sensible Horizon of an observer at _E_. When the Sun is at _A_, really below the Horizon, a ray of light _AC_ proceeding from him comes straight to _C_, where it falls on the surface of the Atmosphere, and there entering a denser medium, it is turned out of its rectilineal course _ACdG_, and bent down to the observer’s eye at _E_; who then sees the Sun in the direction of the refracted ray _edE_, which lies above the Horizon, and being extended out to the Heavens, shews the Sun at _B_ § 171.

[Sidenote: Fig. IX.]

180. The higher the Sun rises, the less his rays are refracted, because they fall less obliquely on the surface of the Atmosphere § 172. Thus, when the Sun is in the direction of the line _EfL_ continued, he is so nearly perpendicular to the surface of the Earth at _E_, that his rays are but very little bent from a rectilineal course.

[Sidenote: The quantity of refraction.]

181. The Sun is about 32-1/4 min. of a deg. in breadth, when at his mean distance from the Earth; and the horizontal refraction of his rays is 33-3/4 min. which being more than his whole diameter, brings all his Disc in view, when his uppermost edge rises in the Horizon. At ten deg. height the refraction is not quite 5 min. at 20 deg. only 2 min. 26 sec.; at 30 deg. but 1 min. 32 sec.; between which and the Zenith, it is scarce sensible: the quantity throughout, is shewn by the annexed table, calculated by Sir ISAAC NEWTON.

+-------------------------------------------------+ | | | 182. _A_ TABLE _shewing the Refractions | | of the Sun, Moon, and Stars; | | adapted to their apparent Altitudes_. | | | +-------+---------++----+---------++----+---------+ | Appar.| Refrac- ||Ap. | Refrac- ||Ap. | Refrac- | | Alt. | tion. ||Alt.| tion. ||Alt.| tion. | +-------+---------++----+---------++----+---------+ | D. M. | M. S. || D. | M. S. || D. | M. S. | +-------+---------++----+---------++----+---------+ | 0 0 | 33 45 || 21 | 2 18 || 56 | 0 36 | | 0 15 | 30 24 || 22 | 2 11 || 57 | 0 35 | | 0 30 | 27 35 || 23 | 2 5 || 58 | 0 34 | | 0 45 | 25 11 || 24 | 1 59 || 59 | 0 32 | | 1 0 | 23 7 || 25 | 1 54 || 60 | 0 31 | +-------+---------++----+---------++----+---------+ | 1 15 | 21 20 || 26 | 1 49 || 61 | 0 30 | | 1 30 | 19 46 || 27 | 1 44 || 62 | 0 28 | | 1 45 | 18 22 || 28 | 1 40 || 63 | 0 27 | | 2 0 | 17 8 || 29 | 1 36 || 64 | 0 26 | | 2 30 | 15 2 || 30 | 1 32 || 65 | 0 25 | +-------+---------++----+---------++----+---------+ | 3 0 | 13 20 || 31 | 1 28 || 66 | 0 24 | | 3 30 | 11 57 || 32 | 1 25 || 67 | 0 23 | | 4 0 | 10 48 || 33 | 1 22 || 68 | 0 22 | | 4 30 | 9 50 || 34 | 1 19 || 69 | 0 21 | | 5 0 | 9 2 || 35 | 1 16 || 70 | 0 20 | +-------+---------++----+---------++----+---------+ | 5 30 | 8 21 || 36 | 1 13 || 71 | 0 19 | | 6 0 | 7 45 || 37 | 1 11 || 72 | 0 18 | | 6 30 | 7 14 || 38 | 1 8 || 73 | 0 17 | | 7 0 | 6 47 || 39 | 1 6 || 74 | 0 16 | | 7 30 | 6 22 || 40 | 1 4 || 75 | 0 15 | +-------+---------++----+---------++----+---------+ | 8 0 | 6 0 || 41 | 1 2 || 76 | 0 14 | | 8 30 | 5 40 || 42 | 1 0 || 77 | 0 13 | | 9 0 | 5 22 || 43 | 0 58 || 78 | 0 12 | | 9 30 | 5 6 || 44 | 0 56 || 79 | 0 11 | | 10 0 | 4 52 || 45 | 0 54 || 80 | 0 10 | +-------+---------++----+---------++----+---------+ | 11 0 | 4 27 || 46 | 0 52 || 81 | 0 9 | | 12 0 | 4 5 || 47 | 0 50 || 82 | 0 8 | | 13 0 | 3 47 || 48 | 0 48 || 83 | 0 7 | | 14 0 | 3 31 || 49 | 0 47 || 84 | 0 6 | | 15 0 | 3 17 || 50 | 0 45 || 85 | 0 5 | +-------+---------++----+---------++----+---------+ | 16 0 | 3 4 || 51 | 0 44 || 86 | 0 4 | | 17 0 | 2 53 || 52 | 0 42 || 87 | 0 3 | | 18 0 | 2 43 || 53 | 0 40 || 88 | 0 2 | | 19 0 | 2 34 || 54 | 0 39 || 89 | 1 1 | | 20 0 | 2 26 || 55 | 0 38 || 90 | 0 0 | +-------+---------++----+---------++----+---------+

[Sidenote: PLATE II.

The inconstancy of Refractions.

A very remarkable case concerning refraction.]

183. In all observations, to have the true altitude of the Sun, Moon, or Stars, the refraction must be subtracted from the observed altitude. But the quantity of refraction is not always the same at the same altitude; because heat diminishes the air’s refractive power and density, and cold increases both; and therefore no one table can serve precisely for the same place at all seasons, nor even at all times of the same day; much less for different climates: it having been observed that the horizontal refractions are near a third part less at the Equator than at _Paris_, as mentioned by Dr. SMITH in the 370th remark on his Optics, where the following account is given of an extraordinary refraction of the sun-beams by cold. “There is a famous observation of this kind made by some _Hollanders_ that wintered in _Nova Zembla_ in the year 1596, who were surprised to find, that after a continual night of three months, the Sun began to rise seventeen days sooner than according to computation, deduced from the Altitude of the Pole observed to be 76°: which cannot otherwise be accounted for, than by an extraordinary quantity of refraction of the Sun’s rays, passing thro’ the cold dense air in that climate. KEPLER computes that the Sun was almost five degrees below the Horizon when he first appeared; and consequently the refraction of his rays was about nine times greater than it is with us.”

184. The Sun and Moon appear of an oval figure as _FCGD_, just after their rising, and before their setting: the reason is, that the refraction being greater in the Horizon than at any distance above it, the lowermost limb _G_ appears more elevated than the uppermost. But although the refraction shortens the vertical Diameter _FG_, it has no sensible effect on the horizontal Diameter _CD_, which is all equally elevated. When the refraction is so small as to be imperceptible, the Sun and Moon appear perfectly round, as _AEBF_.

[Sidenote: Our imagination cannot judge rightly of the distance of
inaccessible objects.]

185. We daily observe, that the objects which appear most distinct are generally those which are nearest to us; and consequently, when we have nothing but our imagination to assist us in estimating of distances, bright objects seem nearer to us than those which are less bright, or than the same objects do when they appear less bright and worse defined, even though their distance in both cases be the same. And as in both cases they are seen under the same angle[44], our imagination naturally suggests an idea of a greater distance between us and those objects which appear fainter and worse defined than those which appear brighter under the same Angles; especially if they be such objects as we were never near to, and of whose real Magnitudes we can be no judges by sight.

[Sidenote: Nor always of those which are accessible.]

186. But, it is not only in judging of the different apparent Magnitudes of the same objects, which are better or worse defined by their being more or less bright, that we may be deceived: for we may make a wrong conclusion even when we view them under equal degrees of brightness, and under equal Angles; although they be objects whose bulks we are generally acquainted with, such as houses or trees: for proof of which, the two following instances may suffice.

[Sidenote: The reason assigned.

PLATE II.]

First, When a house is seen over a very broad river by a person standing on low ground, who sees nothing of the river, nor knows of it beforehand; the breadth of the river being hid from him, because the banks seem contiguous, he loses the idea of a distance equal to that breadth; and the house seems small, because he refers it to a less distance than it really is at. But, if he goes to a place from which the river and interjacent ground can be seen, though no farther from the house, he then perceives the house to be at a greater distance than he imagined; and therefore fancies it to be bigger than he did at first; although in both cases it appears under the same Angle, and consequently makes no bigger picture on the retina of his eye in the latter case than it did in the former. Many have been deceived, by taking a red coat of arms, fixed upon the iron gate in _Clare-Hall_ walks at _Cambridge_, for a brick house at a much greater distance[45].

[Sidenote: Fig. XII.]

Secondly, In foggy weather, at first sight, we generally imagine a small house, which is just at hand, to be a great castle at a distance; because it appears so dull and ill defined when seen through the Mist, that we refer it to a much greater distance than it really is at; and therefore, under the same Angle, we judge it to be much bigger. For, the near object _FE_, seen by the eye _ABD_, appears under the same Angle _GCH_, that the remote object _GHI_ does: and the rays _GFCN_ and _HECM_ crossing one another at _C_ in the pupil of the eye, limit the size of the picture _MN_ on the retina; which is the picture of the object _FE_, and if _FE_ were taken away, would be the picture of the object _GHI_, only worse defined; because _GHI_, being farther off, appears duller and fainter than _FE_ did. But if a Fog, as _KL_, comes between the eye and the object _FE_, it appears dull and ill defined like _GHI_; which causes our imagination to refer _FE_ to the greater distance _CH_, instead of the small distance _CE_ which it really is at. And consequently, as mis-judging the distance does not in the least diminish the Angle under which the object appears, the small hay-rick _FE_ seems to be as big as _GHI_.

[Sidenote: Fig. IX.

Why the Sun and Moon appear biggest in the Horizon.]