Chap. IX The Method of finding the Distances of the Sun, Moon, and Planets.
PLATE IV.
190. Those who have not learnt how to take the [47]Altitude of any Celestial Phenomenon by a common Quadrant, nor know any thing of Plain Trigonometry, may pass over the first Article of this short Chapter, and take the Astronomer’s word for it, that the distances of the Sun and Planets are as stated in the first Chapter of this Book. But, to every one who knows how to take the Altitude of the Sun, the Moon, or a Star, and can solve a plain right-angled Triangle, the following method of finding the distances of the Sun and Moon will be easily understood.
Fig I.
Let BAG be one half of the Earth, AC it’s semi-diameter, S the Sun, m the Moon, and EKOL a quarter of the Circle described by the Moon in revolving from the Meridian to the Meridian again. Let CRS be the rational Horizon of an observer at A, extended to the Sun in the Heavens, and HAO his sensible Horizon; extended to the Moon’s Orbit. ALC is the Angle under which the Earth’s semi-diameter AC is seen from the Moon at L, which is equal to the Angle OAL, because the right lines AO and CL which include both these Angles are parallel. ASC is the Angle under which the Earth’s semi-diameter AC is seen from the Sun at S, and is equal to the Angle OAf because the lines AO and CRS are parallel. Now, it is found by observation, that the Angle OAL is much greater than the Angle OAf; but OAL is equal to ALC, and OAf is equal to ASC. Now, as ASC is much less than ALC, it proves that the Earth’s semi-diameter AC appears much greater as seen from the Moon at L than from the Sun at S: and therefore the Earth is much farther from the Sun than from the Moon[48]. The Quantities of these Angles are determined by observation in the following manner.
The Moon’s horizontal Parallax, what.
The Moon’s distance determined.
Let a graduated instrument as DAE, (the larger the better) having a moveable Index and Sight-holes, be fixed in such a manner, that it’s plane surface may be parallel to the Plan of the Equator, and it’s edge AD in the Meridian: so that when the Moon is in the Equinoctial, and on the Meridian at E, she may be seen through the sight-holes when the edge of the moveable index cuts the beginning of the divisions at o, on the graduated limb DE; and when she is so seen, let the precise time be noted. Now, as the Moon revolves about the Earth from the Meridian to the Meridian again in 24 hours 48 minutes, she will go a fourth part round it in a fourth part of that time, viz. in 6 hours 12 minutes, as seen from C, that is, from the Earth’s center or Pole. But as seen from A, the observer’s place on the Earth’s surface, the Moon will seem to have gone a quarter round the Earth when she comes to the sensible Horizon at O; for the Index through the sights of which she is then viewed will be at d, 90 degrees from D, where it was when she was seen at E. Now, let the exact moment when the Moon is seen at O (which will be when she is in or near the sensible Horizon) be carefully noted[49], that it may be known in what time she has gone from E to O; which time subtracted from 6 hours 12 minutes (the time of her going from E to L) leaves the time of her going from O to L, and affords an easy method for finding the Angle OAL (called the Moon’s horizontal Parallax, which is equal to the Angle ALC) by the following Analogy: As the time of the Moon’s describing the arc EO is to 90 degrees, so is 6 hours 12 minutes to the degrees of the Arc DdE, which measures the Angle EAL; from which subtract 90 degrees, and there remains the Angle OAL, equal to the Angle ALC, under which the Earth’s Semi-diameter AC is seen from the Moon. Now, since all the Angles of a right-lined Triangle are equal to 180 degrees, or to two right Angles, and the sides of a Triangle are always proportional to the Sines of the opposite Angles, say, by the Rule of Three, as the Sine of the Angle ALC at the Moon L is to it’s opposite side AC the Earth’s Semi-diameter, which is known to be 3985 miles, so is Radius, viz. the Sine of 90 degrees, or of the right Angle ACL to it’s opposite side AL, which is the Moon’s distance at L from the observer’s place at A on the Earth’s surface; or, so is the Sine of the Angle CAL to its opposite side CL, which is the Moon’s distance from the Earth’s centre, and comes out at a mean rate to be 240,000 miles. The Angle CAL is equal to what OAL wants of 90 degrees.
The Sun’s distance cannot be yet so exactly determined as the
Moon’s;
How near the truth it may soon be determined.
191. The Sun’s distance from the Earth is found the same way, but with much greater difficulty; because his horizontal Parallax, or the Angle OAS equal to the Angle ASC, is so small as, to be hardly perceptible, being only 10 seconds of a minute, or the 360th part of a degree. But the Moon’s horizontal Parallax, or Angle OAL equal to the Angle ALC, is very discernible; being 57ʹ 49ʺ, or 3469ʺ at it’s mean state; which is more than 340 times as great as the Sun’s: and therefore, the distances of the heavenly bodies being inversely as the Tangents of their horizontal Parallaxes, the Sun’s distance from the Earth is at least 340 times as great as the Moon’s; and is rather understated at 81 millions of miles, when the Moon’s distance is certainly known to be 240 thousand. But because, according to some Astronomers, the Sun’s horizontal Parallax is 11 seconds, and according to others only 10, the former Parallax making the Sun’s distance to be about 75,000,000 of miles, and the latter 82,000,000; we may take it for granted, that the Sun’s distance is not less than as deduced from the former, nor more than as shewn by the latter: and every one who is accustomed to make such observations, knows how hard it is, if not impossible, to avoid an error of a second; especially on account of the inconstancy of horizontal Refractions. And here, the error of one second, in so small an Angle, will make an error of 7 millions of miles in so great a distance as that of the Sun’s; and much more in the distances of the superiour Planets. But Dr. Halley has shewn us how the Sun’s distance from the Earth, and consequently the distances of all the Planets from the Sun, may be known to within a 500th part of the whole, by a Transit of Venus over the Sun’s Disc, which will happen on the 6th of June, in the year 1761; till which time we must content ourselves with allowing the Sun’s distance to be about 81 millions of miles, as commonly stated by Astronomers.
The Sun proved to be much bigger than the Moon.
192. The Sun and Moon appear much about the same bulk: And every one who understands Geometry knows how their true bulks may be deduced from the apparent, when their real distances are known. Spheres are to one another as the Cubes of their Diameters; whence, if the Sun be 81 millions of miles from the Earth, to appear as big as the Moon, whose distance does not exceed 240 thousand miles, he must, in solid bulk, be 42 millions 875 thousand times as big as the Moon.
193. The horizontal Parallaxes are best observed at the Equator; 1. Because the heat is so nearly equal every day, that the Refractions are almost constantly the same. 2. Because the parallactic Angle is greater there as at A (the distance from thence to the Earth’s Axis being greater,) than upon any parallel of Latitude, as a or b.
The relative distances of the Planets from the Sun are known to great precision, though their real distances are not well known.
194. The Earth’s distance from the Sun being determined, the distances of all the other Planets from him are easily found by the following analogy, their periods round him being ascertained by observation. As the square of the Earth’s period round the Sun is to the cube of it’s distance from him, so is the square of the period of any other Planet to the cube of it’s distance, in such parts or measures as the Earth’s distance was taken; see § 111. This proportion gives us the relative mean distances of the Planets from the Sun to the greatest degree of exactness; and they are as follows, having been deduced from their periodical times, according to the law just mentioned, which was discovered by Kepler and demonstrated by Sir Isaac Newton.
Periodical Revolution to the same fixed Star in days and decimal parts of a day.
| Of Mercury | Venus | The Earth | Mars | Jupiter | Saturn |
|---|---|---|---|---|---|
| 87.9692 | 224.6176 | 365.2564 | 686.9785 | 4332.514 | 10759.275 |
| Relative mean distances from the Sun. | |||||
| 38710 | 72333 | 100000 | 152369 | 520096 | 954006 |
| From these numbers we deduce, that if the Sun’s horizontal Parallax be 10ʺ, the real mean distances of the Planets from the Sun in English miles are | |||||
| 31,742,200 | 59,313,060 | 82,000,000 | 124,942,580 | 426,478,720 | 782,284,920 |
| But if the Sun’s Parallax be 11ʺ their distances are no more than | |||||
| 29,032,500 | 54,238,570 | 75,000,000 | 114,276,750 | 390,034,500 | 715,504,500 |
| Errors in distance a rising from the mistake of 1ʺ in the Sun’s Parallax | |||||
| 2,709,700 | 5,074,490 | 7,000,000 | 10,665,830 | 36,444,220 | 66,780,420 |
195. These last numbers shew, that although we have the relative distances of the Planets from the Sun to the greatest nicety, yet the best observers have not hitherto been able to ascertain their true distances to within less than a twelfth part of what they really are. And therefore, we must wait with patience till the 6th of June, A. D. 1761; wishing that the Sky may then be clear to all places where there are good Astronomers and accurate instruments for observing the Transit of Venus over the Sun’s Disc at that time: as it will not happen again, so as to be visible in Europe, in less than 235 years after.
Why the celestial Poles seem to keep still in the same points of the Heavens, notwithstanding the Earth’s motion round the Sun.
196. The Earth’s Axis produced to the Stars, being carried [50]parallel to itself during the Earth’s annual revolution, describes a circle in the Sphere of the fixed Stars equal to the Orbit of the Earth. But this Orbit, though very large in itself, if viewed from the Stars, would appear no bigger than a point; and consequently, the circle described in the Sphere of the Stars by the Axis of the Earth produced, if viewed from the Earth, must appear but as a point; that is, it’s diameter appears too little to be measured by observation: for Dr. Bradley has assured us, that if it had amounted to a single second, or two at most, he should have perceived it in the great number of observations he has made, especially upon γ Dragonis; and that it seemed to him very probable that the annual Parallax of this Star is not so great as a single second: and consequently, that it is above 400 thousand times farther from us than the Sun. Hence the celestial poles seem to continue in the same points of the Heavens throughout the year; which by no means disproves the Earth’s annual motion, but plainly proves the distance of the Stars to be exceeding great.
The amazing velocity of light.
PLATE IV.
197. The small apparent motion of the Stars § 113, discovered by that great Astronomer, he found to be no ways owing to their annual Parallax (for it came out contrary thereto) but to the Aberration of their light, which can result from no known cause besides that of the Earth’s annual motion; and as it agrees so exactly therewith, it proves beyond dispute that the Earth has such a motion: for this Aberration compleats all it’s various Phenomena every year; and proves that the velocity of star-light is such as carries it through a space equal to the Sun’s distance from us in 8 minutes 13 seconds of time. Hence, the velocity of light is [51]10 thousand 210 times as great as the Earth’s velocity in it’s Orbit; which velocity (from what we know already of the Earth’s distance from the Sun) may be affected to be at least between 57 and 58 thousand miles every hour: and supposing it to be 58000, this number multiplied by the above 10210, gives 592 million 180 thousand miles for the hourly motion of light: which last number divided by 3600, the number of seconds in an hour, shews that light flies at the rate of more than 164 thousand miles every second of time, or swing of a common clock pendulum.
CHAP. X.
The Circles of the Globe described. The different lengths of days and nights, and the vicissitudes of seasons, explained. The explanation of the Phenomena of Saturn’s Ring concluded. (See § 81 and 82.)
Circles of the Sphere.
Fig. II
Equator, Tropics, Polar Circles, and Poles.
Fig. II.
Earth’s Axis.
PLATE IV.
Meridians.
198. If the reader be hitherto unacquainted with the principal circles of the Globe, he should now learn to know them; which he may do sufficiently for his present purpose in a quarter of an hour, if he sets the ball of a terrestrial Globe before him, or looks at the Figure of it, wherein these circles are drawn and named. The Equator is that great circle which divides the northern half of the Earth from the southern. The Tropics are lesser circles parallel to the Equator, and each of them is 231⁄2 degrees from it; a degree in this sense being the 360th part of any great circle which divides the Earth into two equal parts. The Tropic of Cancer lies on the north side of the Equator, and the Tropic of Capricorn on the south. The Arctic Circle has the North Pole for it’s center, and is just as far from the north Pole as the Tropics are from the Equator: and the Antarctic Circle (hid by the supposed convexity of the Figure) is just as far from the South Pole, every way round it. These Poles are the very north and south points of the Globe: and all other places are denominated northward or southward according to the side of the Equator they lie on, and the Pole to which they are nearest. The Earth’s Axis is a straight line passing through the center of the Earth, perpendicular to the Equator, and terminating in the Poles at it’s surface. This, in the real Earth and Planets is only an imaginary line; but in artificial Globes or Planets it is a wire by which they are supported, and turned round in Orreries, or such like machines, by wheel-work. The circles 12. 1. 2. 3. 4, &c. are Meridians to all places they pass through; and we must suppose thousands more to be drawn, because every place that is ever so little to the east or west of any other place, has a different Meridian from that other place. All the Meridians meet in the Poles; and whenever the Sun’s center is passing over any Meridian, in his apparent motion round the Earth, it is mid-day or noon to all places on that Meridian.
Zones.
199. The broad Space lying between the Tropics, like a girdle surrounding the Globe, is called the torrid Zone, of which the Equator is in the middle, all around. The Space between the Tropic of Cancer and Arctic Circle is called the North temperate Zone. That between the Tropic of Capricorn and the Antarctic Circle, the South temperate Zone. And the two circular Spaces bounded by the Polar Circles are the two Frigid Zones; denominated north or south, from that Pole which is in the center of the one or the other of them.
200. Having acquired this easy branch of knowledge, the learner may proceed to make the following experiment with his terrestrial ball; which will give him a plain idea of the diurnal and annual motions of the Earth, together with the different lengths of days and nights, and all the beautiful variety of seasons, depending on those motions.
Fig. III.
A pleasant experiment shewing the different lengths of days
and nights, and the variety of seasons.
Summer Solstice.
Take about seven feet of strong wire, and bend it into a circular form, as abcd, which being viewed obliquely, appears elliptical as in the Figure. Place a lighted candle on a table, and having fixed one end of a silk thread K, to the north pole of a small terrestrial Globe H, about three inches diameter, cause another person to hold the wire circle so that it may be parallel to the table, and as high as the flame of the candle I, which should be in or near the center. Then, having twisted the thread as towards the left hand, that by untwisting it may turn the Globe round eastward, or contrary to the way that the hands of a watch move; hang the Globe by the thread within this circle, almost contiguous to it; and as the thread untwists, the Globe (which is enlightened half round by the candle as the Earth is by the Sun) will turn round it’s Axis, and the different places upon it will be carried through the light and dark Hemispheres, and have the appearance of a regular succession of days and nights, as our Earth has in reality by such a motion. As the Globe turns, move your hand slowly so as to carry the Globe round the candle according to the order of the letters abcd, keeping it’s center even with the wire circle; and you will perceive, that the candle being still perpendicular to the Equator will enlighten the Globe from pole to pole in it’s motion round the circle; and that every place on the Globe goes equally through the light and the dark, as it turns round by the untwisting of the thread, and therefore has a perpetual Equinox. The Globe thus turning round represents the Earth turning round it’s Axis; and the motion of the Globe round the candle represents the Earth’s annual motion round the Sun, and shews, that if the Earth’s Orbit had no inclination to it’s Axis, all the days and nights of the year would be equally long, and there would be no different seasons. But now, desire the person who holds the wire to hold it obliquely in the position ABCD, raising the side ♋ just as much as he depresses the side ♑, that the flame may be still in the plane of the circle; and twisting the thread as before, that the Globe may turn round it’s Axis the same way as you carry it round the candle; that is, from west to east, let the Globe down into the lowermost part of the wire circle at ♑, and if the circles be properly inclined, the candle will shine perpendicularly on the Tropic of Cancer, and the frigid Zone, lying within the arctic or north polar Circle, will be all in the light, as in the Figure; and will keep in the light let the Globe turn round it’s Axis ever so often. From the Equator to the north polar Circle all the places have longer days and shorter nights; but from the Equator to the south polar Circle just the reverse. The Sun does not set to any part of the north frigid Zone, as shewn by the candle’s shining on it so that the motion of the Globe can carry no place of that Zone into the dark: and at the same time the south frigid Zone is involved in darkness, and the turning of the Globe brings none of it’s places into the light. If the Earth were to continue in the like part of it’s Orbit, the Sun would never set to the inhabitants of the north frigid Zone, nor rise to those of the south. At the Equator it would be always equal day and night; and as the places are gradually more and more distant from the Equator, towards the arctic Circle, they would have longer days and shorter nights, whilst those on the south side of the Equator would have their nights longer than their days. In this case there would be continual summer on the north side of the Equator, and continual winter on the south side of it.
Plate V.
J. Ferguson delin.
J. Mynde Sc.
PLATE IV.
Autumnal Equinox.
But as the Globe turns round it’s Axis, move your hand slowly forward so as to carry the Globe from H towards E, and the boundary of light and darkness will approach towards the north Pole, and recede towards the south Pole; the northern places will go through less and less of the light, and the southern places through more and more of it; shewing how the northern days decrease in length, and the southern days increase, whilst the Globe proceeds from H to F. When the Globe is at E, it is at a mean state between the lowest and highest parts of it’s Orbit; the candle is directly over the Equator, the boundary of light and darkness just reaches to both the Poles, and all places on the Globe go equally through the light and dark Hemispheres, shewing that the days and nights are then equal at all places of the Earth, the Poles only excepted; for the Sun is then setting to the north Pole, and rising to the south Pole.
Winter Solstice.
Continue moving the Globe forward, and as it goes through the quarter A, the north Pole recedes still farther into the dark Hemisphere, and the south Pole advances more into the light, as the Globe comes nearer to ♋; and when it comes there at F, the candle is directly over the Tropic of Capricorn, the days are at the shortest, and nights at the longest, in the northern Hemisphere, all the way from the Equator to the arctic Circle; and the reverse in the southern Hemisphere from the antarctic Circle; within which Circles it is dark to the north frigid Zone and light to the south.
Vernal Equinox.
Continue both motions, and as the Globe moves through the quarter B, the north Pole advances toward the light, and the south Pole recedes as fast from it; the days lengthen in the northern Hemisphere, and shorten in the southern; and when the Globe comes to G the candle will be again over the Equator (as when the Globe was at E) and the days and nights will again be equal as formerly: and the north Pole will be just coming into the light, the south Pole going out of it.
Thus we see the reason why the days lengthen and shorten from the Equator to the polar Circles every year; why there is no day or night for several turnings of the Earth, within the polar Circles; why there is but one day and one night in the whole year at the Poles; and why the days and nights are equally long all the year round at the Equator, which is always equally cut by the circle bounding light and darkness.
Remark.
Fig. III.
PLATE V.
201. The inclination of an Axis or Orbit is merely relative, because we compare it with some other Axis or Orbit which we consider as not inclined at all. Thus, our Horizon being level to us whatever place of the Earth we are upon, we consider it as having no inclination; and yet, if we travel 90 degrees from that place, we shall then have an Horizon perpendicular to the former; but it will still be level to us. And, if this Book be held so that the [52]Circle ABCD be parallel to the Horizon, both the Circle abcd, and the Thread or Axis K will be inclined to it. But if Book or Plate be held, so that the Thread be perpendicular to the Horizon, then the Orbit ABCD will be inclined to the Thread, and the Orbit abcd perpendicular to it, and parallel to the Horizon. We generally consider the Earth’s annual Orbit as having no inclination, and the Orbits of all the other Planets as inclined to it § 20.
202. Let us now take a view of the Earth in it’s annual course round the Sun, considering it’s Orbit as having no inclination; and it’s Axis as inclining 231⁄2 degrees from a line perpendicular to it’s Orbit, and keeping the same oblique direction in all parts of it’s annual course; or, as commonly termed, keeping always parallel to itself § 196.
Fig. I.
A concise view of the seasons.
Let a, b, c, d, e, f, g, h be the Earth in eight different parts of it’s Orbit, equidistant from one another; Ns it’s Axis, N the north Pole, s the south Pole, and S the Sun nearly in the center of the Earth’s Orbit § 18. As the Earth goes round the Sun according to the order of the letters abcd, &c. it’s Axis Ns keeps the same obliquity, and is still parallel to the line MNs. When the Earth is at a, it’s north Pole inclines toward the Sun, and brings all the northern places more into the light than at any other time of the year. But when the Earth is at e in the opposite time of the year, the north Pole declines from the Sun, which occasions the northern places to be more in the dark than in the light; and the reverse at the southern places, as is evident by the Figure, which I have taken from Dr. Long’s Astronomy. When the Earth is either at c or g, it’s Axis inclines not either to or from the Sun, but lies sidewise to him; and then the Poles are in the boundary of light and darkness; and the Sun, being directly over the Equator, makes equal day and night at all places. When the Earth is at b it is half way between the Summer Solstice and Harvest Equinox; when it is at d it is half way from the Harvest Equinox to the Winter Solstice; at f half way from the Winter Solstice to the Spring Equinox: and at h half way from the Spring Equinox to the Summer Solstice.
Fig. II.
PLATE V.
The Ecliptic.
The seasons shewn in another view of the Earth, and it’s Orbit.
203. From this oblique view of the Earth’s Orbit, let us suppose ourselves to be raised far above it, and placed just over it’s center S, looking down upon it from it’s north pole; and as the Earth’s Orbit differs but very little from a Circle, we shall have it’s figure in such a view represented by the Circle ABCDEFGH. Let us suppose this Circle to be divided into 12 equal parts called Signs, having their names affixed to them; and each Sign into 30 equal parts called Degrees, numbered 10, 20, 30, as in the outermost Circle of the Figure, which represents the great Ecliptic in the Heavens. The Earth is shewn in eight different positions in this Circle, and in each position Æ is the Equator, T the Tropic of Cancer, the dotted Circle the parallel of London, U the arctic or north polar Circle, and P the north Pole where all the Meridians or hour Circles meet § 198. As the Earth goes round the Sun the north Pole keeps constantly towards one part of the Heavens, as it keeps in the Figure towards the right hand side of the Plate.
Vernal Equinox.
When the Earth is at the beginning of Libra, namely on the 20th of March, in this Figure (as at g in Fig. I.) the Sun S as seen from the Earth appears at the beginning of Aries in the opposite part of the Heavens[53], the north Pole is just coming into the light, the Sun is vertical to the Equator; which, together with the Tropic of Cancer, parallel of London, and arctic Circle, are all equally cut by the Circle bounding light and darkness, coinciding with the six o’clock hour Circle, and therefore the days and nights are equally long at all places: for every part of the Meridian ÆTLa comes into the light at six in the morning, and revolving with the Earth according to the order of the hour-letters, goes into the dark at six in the evening. There are 24 Meridians or hour-Circles drawn on the Earth in this Figure, to shew the time of Sun rising and setting at different Seasons of the Year.
Fig. II.
As the Earth moves in the Ecliptic according to the order of the letters ABCD, &c. through the Signs Libra, Scorpio, and Sagittarius, the north Pole comes more and more into the light; the days increase as the nights decrease in length, at all places north of the Equator Æ; which is plain by viewing the Earth at b on the 5th of May, when it is in the 15th degree of Scorpio[54], and the Sun as seen from the Earth appears in the 15th degree of Taurus. For then, the Tropic of Cancer T is in the light from a little after five in the morning till almost seven in the evening; the parallel of London from half an hour past four till half an hour past seven; the polar Circle U from three till nine; and a large track round the north Pole P has day all the 24 hours, for many rotations of the Earth on it’s Axis.
Summer Solstice.
When the Earth comes to c, at the beginning of Capricorn, and the Sun as seen from the Earth appears at the beginning of Cancer, on the 21st of June, as in this Figure, it is in the position a in Fig. I; and it’s north Pole inclines toward the Sun, so as to bring all the north frigid Zone into the light, and the northern parallels of Latitude more into the light than the dark from the Equator to the polar Circles; and the more so as they are farther from the Equator. The Tropic of Cancer is in the light from five in the morning till seven at night, the parallel of London from a quarter before four till a quarter after eight; and the polar Circle just touches the dark, so that the Sun has only the lower half of his Disc hid from the inhabitants on that Circle for a few minutes about midnight, supposing no inequalities in the Horizon and no Refractions.
Autumnal Equinox.
Winter Solstice.
A bare view of the Figure is enough to shew, that as the Earth advances from Capricorn toward Aries, and the Sun appears to move from Cancer toward Libra, the north Pole recedes toward the dark, which causes the days to decrease, and the nights to increase in length, till the Earth comes to Aries, and then they are equal as before; for the boundary of light and darkness cut the Equator and all it’s parallels equally, or in halves. The north pole then goes into the dark, and continues therein until the Earth goes half way round it’s Orbit; or, from the 23d of September till the 20th of March. In the middle between these times, viz. on the 22d of December, the north Pole is as far as it can be in the dark, which is 231⁄2 degrees, equal to the inclination of the Earth’s Axis from a perpendicular to it’s Orbit: and then, the northern parallels are as much in the dark as they were in the light on the 21 of June; the winter nights being as long as the summer days, and the winter days as short as the summer nights. It is needless to multiply words on this subject, as we shall have occasion to mention the seasons again in describing the Orrery, § 439. Only this must be noted, that all that has been said of the northern Hemisphere, the contrary must be understood of the southern; for on different sides of the Equator the seasons are contrary, because, when the northern Hemisphere inclines toward the Sun the southern declines from him.
The Phenomena of Saturn’s Ring.
PLATE V.
204. As Saturn goes round the Sun, his obliquely posited ring, like our Earth’s Axis, keeps parallel to itself, and is therefore turned edgewise to the Sun twice in a Saturnian year, which is almost as long as 30 of our years § 81. But the ring, though considerably broad, is too thin to be seen when it is turned round edgewise to the Sun, at which time it is also edgewise to the Earth; and therefore it disappears once in every fifteen years to us. As the Sun shines half a year on the north pole of our earth, then disappears to it, and shines as long on the south pole; so, during one half of Saturn’s year the Sun shines on the north side of his ring, then disappears to it, and shines as long on it’s south side. When the Earth’s Axis inclines neither to nor from the Sun, but sidewise to him, he instantly ceases to shine on one pole, and begins to enlighten the other; and when Saturn’s Ring inclines neither to nor from the Sun, but sidewise to him, he ceases to shine on the one side of it, and begins to shine upon the other.
Fig. III.
Let S be the Sun, ABCDEFGH Saturn’s Orbit, and IKLMNO the Earth’s Orbit. Both Saturn and the Earth move according to the order of the letters, and when Saturn is at A his ring is turned edgewise to the Sun S, and he is then seen from the Earth as if he had lost his ring, let the Earth be in any part of it’s Orbit whatever, except between N and O; for whilst it describes that space, Saturn is apparently so near the Sun as to be hid in his beams. As Saturn goes from A to C his ring appears more and more open to the Earth: at C the ring appears most open of all; and seems to grow narrower and narrower as Saturn goes from C to E; and when he comes to E, the ring is again turned edgewise both to the Sun and Earth: and as neither of it’s sides are illuminated, it is invisible to us, because it’s edge is too thin to be perceptible: and Saturn appears again as if he had lost his ring. But as he goes from E to G, his ring opens more and more to our view on the under side; and seems just as open at G as it was at C; and may be seen in the night-time from the Earth in any part of it’s Orbit, except about M, when the Sun hides the Planet from our view. As Saturn goes from G to A his ring turns more and more edgewise to us, and therefore it seems to grow narrower and narrower; and at A it disappears as before. Hence, while Saturn goes from A to E the Sun shines on the upper side of his ring, and the under side is dark; but whilst he goes from E to A the Sun shines on the under side of his ring, and the upper side is dark.
Fig. I and III.
It may perhaps be imagined that this Article might have been placed more properly after § 81 than here: but when the candid reader considers that all the various Phenomena of Saturn’s Ring depend upon a cause similar to that of our Earth’s seasons, he will readily allow that they are best explained together; and that the two Figures serve to illustrate each other.
PLATE VI.
The Earth nearer the Sun in winter than in summer.
Why the weather is coldest when the Earth is nearest the Sun.
205. The Earth’s Orbit being elliptical, and the Sun constantly keeping in it’s lower Focus, which is 1,377,000 miles from the middle point of the longer Axis, the Earth comes twice so much, or 2,754,000 miles nearer the Sun at one time of the year than at another: for the Sun appearing under a larger Angle in our winter than summer, proves that the Earth is nearer the Sun in winter, (see the Note on Art. 185.) But here, this natural question will arise, Why have we not the hottest weather when the Earth is nearest the Sun? In answer it must be observed, that the excentricity of the Earth’s Orbit, or 1 million 377 miles bears no greater proportion to the Earth’s mean distance from the Sun than 17 does to 1000; and therefore, this small difference of distance cannot occasion any great difference of heat or cold. But the principal cause of this difference is, that in winter the Sun’s rays fall so obliquely upon us, that any given number of them is spread over a much greater portion of the Earth’s surface where we live; and therefore each point must then have fewer rays than in summer. Moreover, there comes a greater degree of cold in the long winter nights, than there can return of heat in so short days; and on both these accounts the cold must increase. But in summer the Sun’s rays fall more perpendicularly upon us, and therefore come with greater force, and in greater numbers on the same place; and by their long continuance, a much greater degree of heat is imparted by day than can fly off by night.
Fig. II.
206. That a greater number of rays fall on the same place, when they come perpendicularly, than when they come obliquely on it, will appear by the Figure. For, let AB be a certain number of the Sun’s rays falling on CD (which, let us suppose to be London) on the 22d of June: but, on the 22d of December, the line CD, or London; has the oblique position Cd to the same rays; and therefore scarce a third part of them falls upon it, or only those between A and e; all the rest eB being expended on the space dP, which is more than double the length of CD or Cd. Besides, those parts which are once heated, retain the heat for some time; which, with the additional heat daily imparted, makes it continue to increase, though the Sun declines toward the south: and this is the reason why July is hotter than June, although the Sun has withdrawn from the summer Tropic; as we find it is generally hotter at three in the afternoon, when the Sun has gone toward the west, than at noon when he is on the Meridian. Likewise, those places which are well cooled require time to be heated again; for the Sun’s rays do not heat even the surface of any body till they have been some time upon it. And therefore we find January for the most part colder than December, although the Sun has withdrawn from the winter Tropic, and begins to dart his beams more perpendicularly upon us, when we have the position CF. An iron bar is not heated immediately upon being put into the fire, nor grows cold till some time after it has been taken out.
CHAP. XI.
The Method of finding the Longitude by the Eclipses of Jupiter’s Satellites: The amazing Velocity of Light demonstrated by these Eclipses.
First Meridian, and Longitude of places, what.
207. Geographers arbitrarily choose to call the Meridian of some remarkable place the first Meridian. There they begin their reckoning; and just so many degrees and minutes as any other place is to the eastward or westward of that Meridian, so much east or west Longitude they say it has. A degree is the 360th part of a Circle, be it great or small; and a minute the 60th part of a degree. The English Geographers reckon the Longitude from the Meridian of the Royal Observatory at Greenwich, and the French from the Meridian of Paris.
PLATE V.
Fig. II.
Hour Circles.
An hour of time equal to 15 degrees of motion.
208. If we imagine twelve great Circles, one of which is the Meridian of any given place, to intersect each other in the two Poles of the Earth, and to cut the Equator Æ at every 15th degree, they will be divided by the Poles into 24 Semicircles which divide the Equator into 24 equal parts; and as the Earth turns on it’s Axis, the planes of these Semicircles come successively after one another every hour to the Sun. As in an hour of time there is a revolution of 15 degrees of the Equator, in a minute of time there will be a revolution of 15 minutes of the Equator, and in a second of time a revolution of 15 seconds. There are two tables annexed to this Chapter, for reducing mean solar time into degrees and minutes of the terrestrial Equator; and also for converting degrees and parts of the Equator into mean solar time.
209. Because the Sun enlightens only one half of the Earth at once, as it turns round it’s Axis he rises to some places at the same moments of absolute Time that he sets to others; and when it is mid-day to some places, it is mid-night to others. The XII on the middle of the Earth’s enlightened side, next the Sun, stands for mid-day; and the opposite XII on the middle of the dark side, for mid-night. If we suppose this Circle of hours to be fixed in the plane of the Equinoctial, and the Earth to turn round within it, any particular Meridian will come to the different hours so, as to shew the true time of the day or night at all places on that Meridian. Therefore,
And consequently to 15 degrees of Longitude.
Lunar Eclipses useful in finding the Longitude.
210. To every place 15 degrees eastward from any given Meridian, it is noon an hour sooner than on that Meridian; because their Meridian comes to the Sun an hour sooner: and to all places 15 degrees westward it is noon an hour later § 208, because their Meridian comes an hour later to the Sun; and so on: every 15 degrees of motion causing an hour’s difference in time. Therefore they who have noon an hour later than we, have their Meridian, that is, their Longitude 15 degrees westward from us; and they who have noon an hour sooner than we, have their Meridian 15 degrees eastward from ours: and so for every hour’s difference of time 15 degrees difference of Longitude. Consequently, if the beginning or ending of a Lunar Eclipse be observed, suppose at London, to be exactly at mid-night, and in some other place at 11 at night, that place is 15 degrees westward from the Meridian of London: if the same Eclipse be observed at one in the morning at another place, that place is 15 degrees eastward from the said Meridian.
Eclipses of Jupiter’s Satellites much better for that purpose.
211. But as it is not easy to determine the exact moment either of the beginning or ending of a Lunar Eclipse, because the Earth’s shadow through which the Moon passes is faint and ill defined about the edges; we have recourse to the Eclipses of Jupiter’s Satellites, which disappear so instantaneously as they enter into Jupiter’s shadow, and emerge so suddenly out of it, that we may fix the phenomenon to half a second of time. The first or nearest Satellite to Jupiter is the most advantageous for this purpose, because it’s motion is quicker than the motion of any of the rest, and therefore it’s immersions and emersions are more frequent.
How to solve this important problem.
PLATE V.
212. The English Astronomers have made Tables for shewing the times of the Eclipses of Jupiter’s Satellites to great precision, for the Meridian of Greenwich. Now, let an observer, who has these Tables with a good Telescope and a well-regulated Clock at any other place of the Earth, observe the beginning or ending of an Eclipse of one of Jupiter’s Satellites, and note the precise moment of time that he saw the Satellite either immerge into, or emerge out of the shadow, and compare that time with the time shewn by the Tables for Greenwich; then, 15 degrees difference of Longitude being allowed for every hour’s difference of time, will give the Longitude of that place from Greenwich, as above § 210; and if there be any odd minutes of time, for every minute a quarter of a degree, east or west must be allowed, as the time of observation is before or after the time shewn by the Tables. Such Eclipses are very convenient for this purpose at land, because they happen almost every day; but are of no use at sea, because the rolling of the ship hinders all nice telescopical observations.
Fig. II.
Illustrated by an example.
213. To explain this by a Figure, let J be Jupiter, K, L, M, N his four Satellites in their respective Orbits 1, 2, 3, 4; and let the Earth be at f (suppose in November, although that month is no otherways material than to find the Earth readily in this scheme, where it is shewn in eight different parts of it’s Orbit.) Let Q be a place on the Meridian of Greenwich, and R a place on some other Meridian. Let a person at R observe the instantaneous vanishing of the first Satellite K into Jupiter’s shadow, suppose at three o’clock in the morning; but by the Tables he finds the immersion of that Satellite to be at midnight at Greenwich: he can then immediately determine, that as there are three hours difference of time between Q and R, and that R is three hours forwarder in reckoning than Q, it must be 45 degrees of east Longitude from the Meridian of Q. Were this method as practicable at sea as at land, any sailor might almost as easily, and with equal certainty, find the Longitude as the Latitude.
Fig. II.
We seldom see the beginning and end of the same Eclipse of
any of Jupiter’s Moons.
214. Whilst the Earth is going from C to F in it’s Orbit, only the immersions of Jupiter’s Satellites into his shadow are generally seen; and their emersions out of it while the Earth goes from G to B. Indeed, both these appearances may be seen of the second, third, and fourth Satellite when eclipsed, whilst the Earth is between D and E, or between G and A; but never of the first Satellite, on account of the smallness of it’s Orbit and the bulk of Jupiter; except only when Jupiter is directly opposite to the Sun; that is, when the Earth is at g: and even then, strictly speaking, we cannot see either the immersions or emersions of any of his Satellites, because his body being directly between us and his conical shadow, his Satellites are hid by his body a few moments before they touch his shadow; and are quite emerged from thence before we can see them, as it were, just dropping from him. And when the Earth is at c, the Sun being between it and Jupiter hides both him and his Moons from us.
In this Diagram, the Orbits of Jupiter’s Moons are drawn in true proportion to his diameter; but, in proportion to the Earth’s Orbit they are drawn 81 times too large.
PLATE VI.
Jupiter’s conjunctions with the Sun, or oppositions to him,
are every year in different parts of the Heavens.
215. In whatever month of the year Jupiter is in conjunction with the Sun, or in opposition to him, in the next year it will be a month later at least. For whilst the Earth goes once round the Sun, Jupiter describes a twelfth part of his Orbit. And therefore, when the Earth has finished it’s annual period from being in a line with the Sun and Jupiter, it must go as much forwarder as Jupiter has moved in that time, to overtake him again: just like the minute hand of a watch, which must, from any conjunction with the hour hand, go once round the dial-plate and somewhat above a twelfth part more, to overtake the hour hand again.
The surprising velocity of light.
216. It is found by observation, that when the Earth is between the Sun and Jupiter, as at g, his Satellites are eclipsed about 8 minutes sooner than they should be according to the Tables: and when the Earth is at B or C, these Eclipses happen about 8 minutes later than the Tables predict them. Hence it is undeniably certain, that the motion of light is not instantaneous, since it takes about 161⁄2 minutes of time to go through a space equal to the diameter of the Earth’s Orbit, which is 162 millions of miles in length: and consequently the particles of light fly about 164 thousand 494 miles every second of time, which is above a million of times swifter than the motion of a cannon bullet. And as light is 161⁄2 minutes in travelling across the Earth’s Orbit, it must be 81⁄4 minutes in coming from the Sun to us: therefore, if the Sun were annihilated we should see him for 81⁄4 minutes after; and if he were again created he would be 81⁄4 minutes old before we could see him.
Fig. V.
Illustrated by a Figure.
217. To illustrate this progressive motion of light, let A and B be the Earth in two different parts of it’s Orbit, whose distance is 81 millions of miles, equal to the Earth’s distance from the Sun S. It is plain, that if the motion of light were instantaneous, the Satellite 1 would appear to enter into Jupiter’s shadow FF at the same moment of time to a spectator in A as to another in B. But by many years observations it has been found, that the immersion of the Satellite into the shadow is seen 81⁄4 minutes sooner when the Earth is at B, than when it is at A. And so, as Mr. Romer first discovered, the motion of light is thereby proved to be progressive, and not instantaneous, as was formerly believed. It is easy to compute in what time the Earth moves from A to B; for the chord of 60 degrees of any Circle is equal to the Semidiameter of that Circle; and as the Earth goes through all the 360 degrees of it’s Orbit in a year, it goes through 60 of those degrees in about 61 days. Therefore, if on any given day, suppose the first of June, the Earth is at A, on the first of August it will be at B: the chord, or straight line AB, being equal to DS the Radius of the Earth’s Orbit, the same with AS it’s distance from the Sun.
218. As the Earth moves from D to C, through the side AB of it’s Orbit, it is constantly meeting the light of Jupiter’s Satellites sooner, which occasions an apparent acceleration of their Eclipses: and as it moves through the other half H of it’s Orbit, from C to D, it is receding from their light, which occasions an apparent retardation of their Eclipses, because their light is then longer ere it overtakes the Earth.
219. That these accelerations of the immersions of Jupiter’s Satellites into his shadow, as the Earth approaches towards Jupiter, and the retardations of their emersions out of his shadow, as the Earth is going from him, are not occasioned by any inequality arising from the motions of the Satellites in excentric Orbits, is plain, because it affects them all alike, in whatever parts of their Orbits they are eclipsed. Besides, they go often round their Orbits every year, and their motions are no way commensurate to the Earth’s. Therefore, a Phenomenon not to be accounted for from the real motions of the Satellites, but so easily deducible from the Earth’s motion, and so answerable thereto, must be allowed to result from it. This affords one very good proof of the Earth’s annual motion.
220. TABLES for converting mean solar Time into Degrees and Parts of the terrestrial Equator; and also for converting Degrees and Parts of the Equator into mean solar Time.
Table I. For converting Time into Degrees and Parts of the Equator.
| Hours | Degrees | *Min. | Deg. | Min. | *Min. | Deg. | Min. |
|---|---|---|---|---|---|---|---|
| Sec. | Min. | Sec. | Sec. | Min. | Sec. | ||
| Thirds | Sec. | Thirds | Thirds | Sec. | Thirds | ||
| 1 | 15 | 1 | 0 | 15 | 31 | 7 | 45 |
| 2 | 30 | 2 | 0 | 30 | 32 | 8 | 0 |
| 3 | 45 | 3 | 0 | 45 | 33 | 8 | 15 |
| 4 | 60 | 4 | 1 | 0 | 34 | 8 | 30 |
| 5 | 75 | 5 | 1 | 15 | 35 | 8 | 45 |
| 6 | 90 | 6 | 1 | 30 | 36 | 9 | 0 |
| 7 | 105 | 7 | 1 | 45 | 37 | 9 | 15 |
| 8 | 120 | 8 | 2 | 0 | 38 | 9 | 30 |
| 9 | 135 | 9 | 2 | 15 | 39 | 9 | 45 |
| 10 | 150 | 10 | 2 | 30 | 40 | 10 | 0 |
| 11 | 165 | 11 | 2 | 45 | 41 | 10 | 15 |
| 12 | 180 | 12 | 3 | 0 | 42 | 10 | 30 |
| 13 | 195 | 13 | 3 | 15 | 43 | 10 | 45 |
| 14 | 210 | 14 | 3 | 30 | 44 | 11 | 0 |
| 15 | 225 | 15 | 3 | 45 | 45 | 11 | 15 |
| 16 | 240 | 16 | 4 | 0 | 46 | 11 | 30 |
| 17 | 255 | 17 | 4 | 15 | 47 | 11 | 45 |
| 18 | 270 | 18 | 4 | 30 | 48 | 12 | 0 |
| 19 | 285 | 19 | 4 | 45 | 49 | 12 | 15 |
| 20 | 300 | 20 | 5 | 0 | 50 | 12 | 30 |
| 21 | 315 | 21 | 5 | 15 | 51 | 12 | 45 |
| 22 | 330 | 22 | 5 | 30 | 52 | 13 | 0 |
| 23 | 345 | 23 | 5 | 45 | 53 | 13 | 15 |
| 24 | 360 | 24 | 6 | 0 | 54 | 13 | 30 |
| 25 | 375 | 25 | 6 | 15 | 55 | 13 | 45 |
| 26 | 390 | 26 | 6 | 30 | 56 | 14 | 0 |
| 27 | 405 | 27 | 6 | 45 | 57 | 14 | 15 |
| 28 | 420 | 28 | 7 | 0 | 58 | 14 | 30 |
| 29 | 435 | 29 | 7 | 15 | 59 | 14 | 45 |
| 30 | 450 | 30 | 7 | 30 | 60 | 15 | 0 |
Table II. For converting Degrees and Parts of the Equator into Time.
| *Deg. | Hours | Min. | *Deg. | Hours | Min. | Degrees | Hours | Minutes |
|---|---|---|---|---|---|---|---|---|
| Min. | Min. | Sec. | Min. | Min. | Sec. | |||
| Sec. | Sec. | Thirds | Sec. | Sec. | Thirds | |||
| 1 | 0 | 4 | 31 | 2 | 4 | 70 | 4 | 40 |
| 2 | 0 | 8 | 32 | 2 | 8 | 80 | 5 | 20 |
| 3 | 0 | 12 | 33 | 2 | 12 | 90 | 6 | 0 |
| 4 | 0 | 16 | 34 | 2 | 16 | 100 | 6 | 40 |
| 5 | 0 | 20 | 35 | 2 | 20 | 110 | 7 | 20 |
| 6 | 0 | 24 | 36 | 2 | 24 | 120 | 8 | 0 |
| 7 | 0 | 28 | 37 | 2 | 28 | 130 | 8 | 40 |
| 8 | 0 | 32 | 38 | 2 | 32 | 140 | 9 | 20 |
| 9 | 0 | 36 | 39 | 2 | 36 | 150 | 10 | 0 |
| 10 | 0 | 40 | 40 | 2 | 40 | 160 | 10 | 40 |
| 11 | 0 | 44 | 41 | 2 | 44 | 170 | 11 | 20 |
| 12 | 0 | 48 | 42 | 2 | 48 | 180 | 12 | 0 |
| 13 | 0 | 52 | 43 | 2 | 52 | 190 | 12 | 40 |
| 14 | 0 | 56 | 44 | 2 | 56 | 200 | 13 | 20 |
| 15 | 1 | 0 | 45 | 3 | 0 | 210 | 14 | 0 |
| 16 | 1 | 4 | 46 | 3 | 4 | 220 | 14 | 40 |
| 17 | 1 | 8 | 47 | 3 | 8 | 230 | 15 | 20 |
| 18 | 1 | 12 | 48 | 3 | 12 | 240 | 16 | 0 |
| 19 | 1 | 16 | 49 | 3 | 16 | 250 | 16 | 40 |
| 20 | 1 | 20 | 50 | 3 | 20 | 260 | 17 | 20 |
| 21 | 1 | 24 | 51 | 3 | 24 | 270 | 18 | 0 |
| 22 | 1 | 28 | 52 | 3 | 28 | 280 | 18 | 40 |
| 23 | 1 | 32 | 53 | 3 | 32 | 290 | 19 | 20 |
| 24 | 1 | 36 | 54 | 3 | 36 | 300 | 20 | 0 |
| 25 | 1 | 40 | 55 | 3 | 40 | 310 | 20 | 40 |
| 26 | 1 | 44 | 56 | 3 | 44 | 320 | 21 | 20 |
| 27 | 1 | 48 | 57 | 3 | 48 | 330 | 22 | 0 |
| 28 | 1 | 52 | 58 | 3 | 52 | 340 | 22 | 40 |
| 29 | 1 | 56 | 59 | 3 | 56 | 350 | 23 | 20 |
| 30 | 2 | 0 | 60 | 4 | 0 | 360 | 24 | 0 |
These are the Tables mentioned in the 208th Article, and are so easy that they scarce require any farther explanation than to inform the reader, that if, in Table I. he reckons the columns marked with Asterisks to be minutes of time, the other columns give the equatoreal parts or motion in degrees and minutes; if he reckons the Asterisk columns to be seconds, the others give the motion in minutes and seconds of the Equator; if thirds, in seconds and thirds: And if in Table II. he reckons the Asterisk columns to be degrees of motion, the others give the time answering thereto in hours and minutes; if minutes of motion, the time is minutes and seconds; if seconds of motion, the corresponding time is given in seconds and thirds. An example in each case will make the whole very plain.
EXAMPLE I.
In 10 hours 15 minutes 24 seconds 20 thirds, Qu. How much of the Equator revolves through the Meridian?
| Deg. | M. | S. | ||
|---|---|---|---|---|
| Hours | 10 | 150 | 0 | 0 |
| Min. | 15 | 3 | 45 | 0 |
| Sec. | 24 | 6 | 0 | |
| Thirds | 20 | 5 | ||
| Answer | 153 | 51 | 5 | |
EXAMPLE II.
In what time will 153 degrees 51 minutes 5 seconds of the Equator revolve through the Meridian?
| H. | M. | S. | T. | ||
|---|---|---|---|---|---|
| Deg. | 150 | 10 | 0 | 0 | 0 |
| 3 | 12 | 0 | 0 | ||
| Min. | 51 | 3 | 24 | 0 | |
| Sec. | 5 | 20 | |||
| Answer | 10 | 15 | 24 | 20 | |
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