that is, the obliquity of the ecliptic. From good observations, made in 1772, this obliquity was found to be 23° 28'.

OF THE MEASURE OF TIME.

All astronomical observations depend on, or have a reference to, time. To measure this with accuracy, is one of the primary objects of an astro

nomer.

As the diurnal revolution of the earth is found to be uniform, they have taken this for the measure of time, comparing it with the sun. Astronomers consider noon as the beginning of the diurnal revolution; or, in other words, an astronomical day commences at the instant the centre of the sun is in the plane of our meridian, and finishes when it has returned thereto, after one entire revolution.

The astronomical day begins, therefore, twelve hours later than the civil day of the same denomination, and is counted up to twenty-four hours, or the succeeding noon, when the next day begins. Thus the day of the month, and the hour of the day, are the same in this method as in the civil account at noon, and from noon till midnight; but from midnight till noon they differ; for in the civil account a fresh day begins at midnight, and the hours also begin again, but in the astronomical method the day is still continued beyond the midnight. Hence five o'clock in the morning of April the 10th, is called by astronomers April 9, 17 hours.

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As the earth revolves uniformly on its axis, if it had no real annual motion, and consequently the sun no apparent annual motion, or if this motion was uniform, the days would be all necessarily of one length, and that would be about 23 hours 56 minutes, for in that time a diurnal revolution of the earth is completed, as appears by an easy observation for any fixed star that is on the meridian at a given hour of the night, will, after 23 hours 56 minutes, be on the meridian again the night following. This interval of time is called a siderial day.

But accurate observations have shewn, that the solar days are not equal to each other, and that the time which elapses between the sun's being on the meridian of any place, and its return thereto again, is considerably longer sometimes than at

others.

Hence astronomers have been obliged to distinguish two sorts of time; one they call apparent, the other mean time.

Apparent time, called by foreign writers true time, is that determined immediately from the sun, by observing when his centre transits the meridian, which is at the instant of apparent noon, when a new astronomical day commences.

Mean time is that which would be observed every day, if the apparent diurnal motion of the sun was regular; or that shewn by good clocks or watches, which go uniformly. The mean day of 24 hours,

pointed out by these, must necessarily be always of the same length.

The inequality in the length of the natural days is termed the equation of time. Now as astronomical tables can only be calculated to mean or uniform time, the proper results from an observation cannot be obtained, till the observed or apparent time is reduced to mean time; for which purpose proper tables are calculated, called tables of the equation of time.

These are inserted on the second page of every month in the Nautical Almanack, for the noon of each day at Greenwich. It is marked subtractive, when the sun comes to the meridian sooner, and additive, when it comes to the meridian later than the time of mean noon; that is, the quantity given by the table is to be subtracted from apparent, in order to obtain mean time, in the first case, and added to it in the second.

OF CORRESPONDING OR EQUAL ALTITUDES.

At equal distances from the meridian, a star has equal altitudes. If, therefore, equal altitudes of an heavenly body be taken on different sides of the meridian, the middle point of time between the observations will give the time when the body is upon the meridian, if it has not changed its declination. By this means the time when any body comes to the

meridian may be ascertained; and when applied to the sun, or a fixed star, the rate at which a clock (adjusted to the mean solar or siderial time) gains or loses be determined with accuracy.

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The method of ascertaining time by equal altitudes is universally used by practical astronomers, because it depends neither on an accurate knowledge of the latitude, nor on that of the declination ; for these elements are only necessary in taking out the equation of declination, and any probable error therein will not sensibly affect that equation; neither does it depend on the exact quantity of the altitude, provided only it be the same in both ob

servations.

OF THE RIGHT ASCENSION AND DECLINATION OF

THE STARS.

The declination of stars, &c. is easily found by observing their meridian altitudes; and their right ascension is also easily attained by knowing how to measure time.

For as all stars in the same circle of declination have the same right ascension, it follows, 1st, That all stars passing at the same time through the same meridian, have then the same right ascension. 2dly, The right ascension of stars passing the meridian at different times, differ in proportion to the intervals of the times of their passage,

Example. The stars make a revolution in 23h 56′4′′ mean time. If, therefore, by a clock regulated to

mean time, and an instrument fixed in the plane of the meridian, or by corresponding altitudes, or otherwise, a star be observed to pass the meridian one hour after the other; say as 23h 56′ 4′′, the time of one revolution, is to 360° of the equator passed over the meridian in the same time, so is one hour, the difference between the transit of the stars, to 15°2′28′′, difference between their right ascensions; then the right ascension of one being known, the other is also known.

Whence it follows, that to determine the right ascension of any star, or even of all the stars, it is sufficient to know the right ascension of one star only, and to have a clock which shews an equal interval of time for the diurnal revolution of the several different fixed stars.

PROBLEM IX. To reduce the degrees of the equator into time, and time into degrees of the equator.

1. To reduce degrees into time, multiply by 4; observing that minutes, when multiplied by 4, produce seconds, and degrees produce minutes.

Reduce 23° 56' into time.

23° 56'

4

1h 53' 44"