In what time does the Moon revolve about the earth

from any meridian to the same again?

What is meant by the Moon's horizontal parallax? How is the distance to the Moon found ?

How is the distance to the Sun found?

What proportions do solid bodies bear to each other? When the distance from the earth to the Sun is found, how is the distance from the Sun to the other planets ascertained?

By what method are the periodical revolutions of the planets ascertained?

How are the periods ascertained of their revolutions on their own axis ?

Why cannot the exact distance to the fixed stars be found?

How are the diameters of the planets ascertained? How the diameter of the Sun ?

SECTION EIGHTH.

OF THE EQUATION OF TIME, AND PRECESSION OF THE EQUINOXES.

THE Stars appear to go around the earth in 23 hours 56 minutes and 4 seconds, and the Sun in 24 hours. So that the stars gain 3 minutes and 56 seconds upon the Sun every day; which amounts to one diurnal revolution in a year, or 365 days, as measured by the returns of the Sun to the meridian; there are 366 days as measured by the stars returning to it. The former are called solar days; the latter sydereal.

The earth's motion on its axis being perfectly uniform, and equal at all times of the year; the sydereal days are always precisely of an equal length, and so would the solar days be if the earth's orbit were a perfect circle, and its axis perpendicular to it. But the

earth's diurnal motion on an inclined axis, and its annual motion in an elliptical orbit, cause the Sun's motion in the Heavens to be unequal; for sometimes he revolves from the meridian to the meridian again in somewhat less than 24 hours; shewn by a well regulated clock, and at other times in somewhat more; so that the time shown by a true going clock, and true Sun-dial is never the same; except on the 15th day of April, the 16th of June, the 31st of August, and the 24th day of December, The clock, if it goes equally true during the whole year, will be before the Sun from the 24th of December till the 15th of April; from that time till the 16th of June, the Sun will be faster than the clock.

The point where the Sun is at his greatest distance from the earth is called the Sun's apogee. where he is at his least distance from the earth is calThe point led his perigee; and a straight line drawn through the earth's centre from one of those points to the other is called the line of the apsides.

The distance that the Sun has his gone in apogee, is called his mean anamoly, and is reckoned any time from in signs, degrees, minutes and seconds, allowing 30 degrees to a sign.

OF THE PRECESSION OF THE EQUINOXES.

It has been observed, that by the earth's motion on its axis, there is more matter accumulated around the equatorial parts than any where else, on the surface

of the earth. The Sun and Moon, by attracting this redundency of matter, bring the equator sooner under them in every return towards it, than if there were no such accumulation. Therefore if the Sun sets out as from any star, or other fixed point in the Heavens, the moment when he is departing from the equatorial, or from either tropic, he will come to the same equinox or tropic again 20 minutes and 17 and seconds of time, or 50 seconds of a degree, before he completes his course so as to arrive at the same fixed star, or point from whence he set out. For the equinoxial points recede 50 seconds of a degree westward every year, contrary to the Sun's annual progessive motion.

When the sun arrives at the same equinoxial,* or solstitial point, he finishes what is called the tropical year; which by observation is found to contain 365 days, 5 hours, 48 minutes, and 47 seconds, and when he arrives at the same fixed star again, as seen from the earth, he completes the sydereal year, which contains 365 days, 6 hours, 9 minutes 14 and seconds.

The sydereal year is therefore 30 minutes 17 and seconds longer than the solar, or tropical year, and 9 minutes, 14 and seconds longer than the Julian or civil year; which we state at 365 days, 6 hours.

As the Sun describes the whole ecliptic, or 360 de

*The two opposite points in which the ecliptic crosses the equinox are called the equinoxial points, and the two points where the ecliptic touches the tropics, (which are likewise opposite, and 90 degrees from the tropic,) are called the solstitial points.

L

grees in a tropical year, he moves 59 minutes, 8 seconds of a degree every day, at a mean rate; therefore he will arrive at the same equinox or solstice, when he is 50 seconds of a degree short of the same star or fixed point in the Heavens, from which he set out in the year before. So that with respect to the fixed stars, the Sun and equinoxial points fall back 30 degrees in 2,160 years, which will make the stars appear to have gone 30 degrees forward with respect to the signs of the ecliptic in that space of time; for the same signs always keep in the same points of the ecliptic, without regard to the constellations.

The Julian year exceeds the solar by 11 minutes and 3 seconds, which in 1,438 years amount to eleven days, and so much our seasons had fallen back with respect to the days of the months since the time of the Nicene Council, in A. D. 325, and therefore to bring back all the feasts and festivals to the day's then settle, it was requisite to suppress 11 nominal days.*- And that the same seasons might be kept to the same time of the year, for the future to leave out the bissextile day in February, at the end of every century, not divisible by four, reckoning them only common years, as the 17th, 18th, and 19th centuries; namely, the years 1700, 1800, and 1900, &c. because a day intercalated every fourth year was too much, and retaining the bissextile at the end of those centuries of years which are

* The difference in the present century, between the old and new styles, is twelve days.