ecliptic, is the greatest about March 30th, and October 3d; and least, or nothing, about July 1st, and December 31st; the Sun on the last two days being in the apsides of his orbit.

9. As the Sun moves from the apogee to the perigee, the time shown by the Sun precedes that shown by a well regulated clock, or mean solar time; but whilst the Sun moves round the perigee to the apogee, the mean time precedes the apparent time.

Illustration. Let ABCDA be the ecliptic, or the elliptical orbit, which the Sun, by an irregular motion, describes in the space of a year; the dotted circle abed, the orbit of an imaginary star, or sun, coincident with the piane of the ecliptic, and in which it moves through equal arcs in equal times.

Let HIK, also, be the Earth which revolves round its axis every twenty-four hours, from west to east; and suppose the Sun and star to set out together from A and a, in a right line with the plane of the meridian EH; that is the Sun at A being at his greatest distance from the Earth, at which time his motion is slowest; and the star, or fictitious sun at a, whose motion is equable, and its distance from the Earth always the same. Then because the motion of the star is always uniform, and the motion of the Sun, in this part of his orbit, is the slowest; it is plain that whilst the meridian revolves from H to h, according to the order of the letters, H, I, K, L, the sun will have proceeded forward in his orbit from A to F; and the star, moving with a quicker motion, will have gone through a larger arc, from a to f'; from which it is plain, that the meridian EH will revolve sooner from H to h, under the sun at F, than from H to k under the star at f, and consequently it will be noon by the Sun sooner than by the clock.

As the Sun moves from A to C, the swiftness of his motion will continually increase, till he comes to the point C, where it will be the greatest; and the Sun C, and the star c, will be together again, and consequently it will be noon by them both at the same time; the meridian EH having revolved to EK.

From this point, the increased velocity of the Sun being now the greatest, will carry him before the star; and, therefore, the same meridian will, in this situation, come to the star sooner than to the Sun. For, whilst the star moves from e to g, the Sun will move through a greater arc, from C to G; and, consequently, the point K has its noon by the clock when it comes to k, but not its noon by the Sun till it comes to l. And though the velocity of the Sun diminishes all the way from C to A, yet they will not be in conjunction till they come to A, and then it is noon by them both at the same instant.

From this it appears that the solar noon is always later than the clock, whilst the Sun goes from C to A, and sooner whilst he goes from A to C; and at those two points, it is noon by the Sun and clock at the same time.

'The obliquity of the ecliptic to the equator, which is the first mentioned cause of the equation of time, would make the Sun and clock agree on the four days of the year, which are when he enters Aries, Cancer, Libra, and Capricorn; but the other causes, which arise from his unequal motion in his orbit, would make the Sun and clocks agree only twice a year, that is, when he is in his apogee and perigee; and, consequently when these two points fall in the beginnings of Cancer and Capricorn, or of Aries and Libra, they will concur in making the clocks and Sun agree in those points. But the apogee, at present, is in the tenth degree of Cancer, and the perigee in the tenth degree of Capricorn; and, therefore, the times shown by the Sun and clocks cannot be equal about the beginning of those signs, nor at any other time of the year, except when the swiftness or slowness of equation, resulting from one of the causes, just balances the slowness or swiftness arising from the other. About

the 3d of November, the absolute equation of time, resulting from both these causes, will be the greatest; the time shown by a regular going clock, being then about 161 minutes slower than the time shown by the Sun.

10. The velocity of the Earth, like all the other planets, varies in different parts of its orbit, it being most rapid in the perihelion, about January the 1st, and slowest when in aphelion about July 1st. The daily motion in the perihelion is 62' 12", and in the aphelion 59' 12".

11. This unequal motion of the Earth causes the summer half year, north of the equator, to be about 8 days longer than the winter half year. Or the interval between the vernal and autumnal equinoxes, is about 8 days longer than the interval between the autumnal and vernal equinoxes.

From the spring equinox to the summer

solstice

From the summer solstice to the autumnal equinox

From the autumnal equinox to the winter solstice

From the winter solstice to the spring

days. hrs. min.

92 21 36

93 13 53

89 16 51

89 1 24

equinox Hence, from the spring equinox to the autumnal equinox is 186 days, 11 hours, 34 minutes; and from the autumnal equinox to the spring equinox is 178 days, 18 hours, 15 minutes, making a difference of 7 days, 17 hours, 29 minutes.

12. The velocity of light is to that of the Earth in its orbit as 10313 to 1; and it is found by observation to be 8 minutes 7 seconds in coming from the Sun to the Earth.

When the Earth is in its perihelion, light takes about 7 minutes, 59 seconds in passing from the Sun to the Earth; at the nean distance of the Earth from the Sun, 8 minutes, 7 seconds; and at the greatest distance of the Earth from the Sun, 8 minutes, 15 seconds.

TABLE.

Showing the mean longitude of the Earth, reckoning from the mean equinox, at the epoch of mean noon, at Paris, January 1st, 1801; longitude of the perihelion, &c.

Eccentricity in miles

1,618,000

Its sidereal revolution is performed in 365 days, 6 hours,

9 minutes, 11 seconds.

Its tropical revolution, or tropical year, 365 days, 5 hours, 48 minutes, 51 seconds.

The sidereal motion of the apsides is direct 19' 40"; but the tropical motion, is direct 1' 2" nearly in a year, or 10 43' 10' in one hundred years; making the length of the year to consist of 365 days, 6 hours, 14 minutes, 2 seconds; this is called the Anomalistic year. A complete tropical revolution of the apsides is performed in 20,931 years.

As the centrifugal force is greater at the equator than near the poles, the weight of bodies are increased as we proceed from the equator to the poles. If the gravity of a body at the equator be unity or 1, at or near the poles it will be 1.00569. This variation of the action of gravity in different latitudes, also causes the same pendulum, as has already been remarked, to vibrate slower at the equator than at or near the poles. For a pendulum to vibrate seconds at the equator, it must be 39 inches in length, and at or near the poles 39.206 inches. The density of the Earth is to that of water as 11 to 2.

The Earth is surrounded by a rare and elastic fluid, which is called the atmosphere; neither the temperature nor the density of this fluid is uniform, but diminishes in proportion to its distance from the surface of the Earth; the height of the atmosphere is supposed to be about 45 miles. If the density of the atmosphere were every where the same, at its temperature at 55 degrees, and the height of the barometer at 30 inches, the height ght of the atmosphere would be 27,600 feet. The weight of the atmosphere upon every square foot on the Earth's surface is about 2160 pounds.

QUESTIONS.

What is the Earth?

What is the figure of the Earth, and what is its mean diameter?

What is the ratio of the Earth's axis to its equatorial diameter, according to Dr. Adrain's computation?

Is the axis of the Earth perpendicular to the plane of the equinoctial?

Have the equinoctial points a retrograde motion?

What are the causes of the equation of time? When is that part of the equation of time, which depends upon the obliquity of the ecliptic greatest? When is that part depending upon the unequal motion of the Sun greatest?

How much longer is the summer half year, in northern latitude, than the winter half?

How much greater is the velocity of light than that of the earth in its orbit?

CHAPTER IX.

Of Mars. I

1. Mars is the next planet, after the Earth, in the order of distance from the Sun; it performs its sidereal revolution from west to east, or in the order of the signs, round the Sun in 686 days, 23 hours, 30 minutes and 36 seconds, at the mean rate of about 55,166 miles per hour.