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If the sun were supposed to move round the equator in a year, with an equable motion, and a uniform velocity of 59′ 8′′ per day, his motion would be measured by a well-regulated clock, and his distance from the first point of Aries on any day of the year would be the same as his mean longitude, which is found by the constant addition of 59′ 8" for every day after the vernal equinox. He would then come to the meridian every day at noon by the clock; but his real appulse to the meridian is known by the dial, and he will actually come to the meridian, by his proper motion in the ecliptic, with that point of the equator which determines his right ascension. The difference, then, between his mean longitude and right ascension, is that arch of the equator which passes under the meridian between the apparent and mean noons, i. e. between the noons by the clock and dial; and therefore when this arch is converted into time, at the rate of 15 degrees per hour, it will be the equation. Now if the sun's mean longitude be greater on any day, than his right ascension, the difference converted into time must be subtracted from the apparent noon to obtain the mean, because the mean noon will precede the apparent; but if his mean longitude be less than his right ascension, the equation of time must be added to the apparent noon to obtain the mean, because the apparent noon will then precede the mean.

The only thing now remaining is to find the sun's right ascension; which may be done by first finding the latitude of the place, by the altitude of the polestar on the meridian; and then by finding the declination, from the meridian altitude of the sun; for these, with the known obliquity of the ecliptic, will give the right ascension, by the rules of spheric trigonometry.

The earth, in her annual progress round the sun, is attended by one moon, whose motions and phenomena shall be the subject of some future lecture, when we consider the motions of the satellites that revolve round the planets as the centers of their motion.

MARS.

MARS is the next of the planets, which revolves round the sun, at the distance of 145,014,148 miles from him, and completes his period in 686d 17h 18', and at the same time turns round his axis in 24h 40'. His orbit is inclined to the orbit of the earth in an angle of 1° 52′, and cuts it in 18° 30′ of 8 and ", which points are called his nodes.* He travels in his orbit, at the rate of 52,500 miles per hour. His diameter is but two thirds of the diameter of the earth, or rather the earth is three times as large as Mars; and on account of his distance from the sun he receives but about one half of the light that we enjoy. His equatorial diameter is to his polar diameter as 1355: 1272, or as 16 is to 15, nearly. He appears sometimes gibbous, and sometimes shines with a full face in his oppositions and conjunctions, but never appears horned; which shows that his orbit includes the orbit of the earth. To his inhabitants, the earth and moon appear like two moons, changing places with each other, appearing horned, half-illuminated, and gibbous, but never full, and never above one quarter of a degree from each other, although they are 240,000 miles apart. Our earth appears almost as large to Mars as Venus does to us; and sometimes is seen passing over the

The ascending node of Mars was in 1s 17° 54′ 28. 2" in the year 1783, Dec. 8th. The annual motion of his nodes is 24. 2′′.

sun's face, attended with our moon, as Venus and Mercury appear to us to pass over him; and the transits of Venus and Mercury are also observable there as well as with us. The axis of Mars is inclined 59° 42′ to the ecliptic, and points to 17° 47′ of Pisces. Obliquity of ecliptic, 28° 42'. Venus is as seldom seen from Mars, as Mercury is seen by us; and Mercury is never seen by the inhabitants of Mars, except when he is passing over the sun's disk. Our earth never appears farther from the sun than about 48 degrees, which is the greatest elongation of Venus, and therefore we shall be the evening and morning star to Mars, in turns, as Venus is to us. As our earth's orbit is included within the orbit of Mars, it will exhibit all the different phases of illumination, conjunctions, stations, progressions, and retrogradations, that Venus does to

us.

As the phenomena of Mars from the earth are the same, in general, with those of the other superior planets, we shall consider them together, when we have mentioned the other bodies that compose the solar system.

JUPITER.

JUPITER is the next of the superior planets above Mars, in the solar system, and by far the largest, being about one thousand times as large as our earth; for his diameter is about 81,000 miles, which is more than ten times the diameter of the earth. He travels at the rate of 29,000 miles per hour in his orbit, and finishes his revolution in 11 years, 314 days and 121 hours, turning round upon his axis in 9h 56'; so that his year contains 10,470 days. By his quick rotation on his axis, his equatorial diameter is larger

than his polar diameter in the ratio of 13: 12, which will make a difference of 6230 miles; so that his poles are nearer to his center than his equator by 3115 miles. This is a necessary consequence of his quick rotation on his axis, because the fluids, and lighter particles washed away by them, will recede from the poles, which are at rest, and retire towards the equator, where the motion is quickest, until there be a sufficient quantity collected, to make up for the deficiency of gravity lost by the centrifugal force; and when this is accomplished by a sufficient accumulation, the equatorial parts can rise no higher. Our earth, being but a small planet when compared with Jupiter, and its rotation on its axis being not half so quick, is of course much less flattened at the poles, its diameters being in the ratio of 230: 229, which occasions a difference of about 35 miles. Jupiter's orbit is inclined 1°20' to the ecliptic, his ascending node being in the seventh degree of Cancer. His axis is so nearly perpendicular to his orbit, that he has scarcely any change of seasons. He is surrounded by faint substances, in the direction of his equator, called belts, in which so many changes have been observed, that they are by some supposed to be clouds, or possibly discoloured portions of his surface, less fitted to reflect the light of the sun, and sometimes obscured more than at others, by the clouds that float in his atmosphere. These belts are sometimes observed to be of different breadths, and at others to be nearly equal. Large spots have been seen in them, which have again disappeared; the broken ends of the belts revolving in the same time with the spots, and those near to the equator in about four minutes less time, than those near the poles.

The sun appears to Jupiter but a twenty-eighth part

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as large as to us, and his light and heat are in the same small proportion; but this inconvenience is compensated by the quick returns of day, and by the revolutions of four moons around him in short periods, some of which are larger and some less than our earth. So that there is scarcely any part of this large planet, whose night is not enlightened by one or more of these moons; excepting near his poles, where the outermost alone is visible. Their motions we shall consider hereafter. His distance from the sun is 494,990,976 miles.

SATURN.

SATURN, the next planet in size and situation to Jupiter, revolves round the sun in 29 years, 167 days and 62 hours of our time, which make but one year to him. His distance from the sun is 907,956,130 miles. He travels at the rate of 21,099 miles per hour in his orbit. He is nearly 600 times as large as this earth, his diameter being 67,000 miles. To such eyes as ours, Jupiter and Herschel are the only planets that can be seen from Saturn, and Saturn and Herschel the only planets that can be seen from Jupiter. The earth is less than some of the moons of Jupiter, and these are all invisible to the naked eye; consequently our earth would be invisible at the distance of Jupiter, and much more so at the distance of Saturn or Herschel. Saturn's orbit intersects the ecliptic in an angle of 2° 33′ 30′′, and his ascending node is in 21° 50′ of Cancer, about 14 degrees from the node of Jupiter, towards the east. As visible spots have been discovered on the disk of Saturn, that are distinguishable from the rest of his surface, it is now known, that he has a rotation on his axis, perpendicular to his ring. He has belts similar to those of Jupiter, lying nearly in the direction of his

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