with one another at twelve; they both turn round the fame way, but the minute hand turns round in a fhorter time than the hour hand; when the minute hand has completed one rotation, and is come round to twelve, the hour hand will be before it, or will be at one; fo that the minute hand muft move more than once round, in order to overtake the hour hand, and be even with it again.

As this fubject is of fome importance, we shall endeavour to render it more clear, by placing it in a different point of view.

The diameter of the earth's orbit is but a phyfical point, in proportion to the diftance of the ftars; for which reafon, and the earth's uniform motion on it's axis, any given meridian will revolve from any ftar to the fame ftar again, in every abfolute turn of the earth upon it's axis, without the leaft perceptible difference of time being fhewn by a clock which goes exactly true.

If the earth had only a diurnal, without an annual motion, any given meridian would revolve from the fun to the fun again, in the fame quanity of time as from any far to the fame ftar again; because the fun would never change his place, with refpect to the ftars. But as the earth advances almof a degree caftward in it's orbit, in the time that it turns eaftward round it's axis, whatever ftar paffes over the merid an on any day with the fun, will pafs over the fame meridian on the next day, when the fun is almost a degree fhort of it, that is, 3 min. 56 feconds fooner. If the year contained only 360 days, the fun's apparent place, fo far as his motion is equable, would change a degree every day, and then the fiderial days would be juft four minutes fhorter than the folar.

Let ABCDEFGH, fig. 3,

4, be the

earth's

earth's orbit, in which it goes round the fun every year, according to the order of the letters, that is, from west to eaft, and turns round it's axis the fame way, from the fun to the fun again, in every twenty-four hours. Let S be the fun, and Ra fixed ftar, at fuch an immenfe diftance, that the diameter G C of the earth's orbit bears no fenfible proportion to that diftance; N m n the earth in different points of it's orbit. Let N m be any particular meridian of the earth, and N, a given point, or place, lying under that meridian.

When the earth is at A, the fun S hides the ftar R, which would always be hid if the earth never moved from A; and confequently as the earth turus round it's axis, the point N would always come round to the fun and the ftar at the fame time.

But when the earth has advanced through an eighth part of it's orbit, or from A to B, it's motion round it's axis will bring the point N an eighth part of a day, or three hours, fooner to the ftar than to the fun. For the ftar will come to she meridian in the fame time as though the earth had continued in it's former fituation at A, but the point N muft revolve from N to n, before it can have the fun upon it's meridian. The arc Nn being therefore the fame part of a whole circle, as the arc A B, it is plain that any ftar which comes to the meridian at noon, with the fun, when the earth is at A, will come to it at nine o'clock in the forenoon, when the earth is at B.

When the earth has paffed from A to C, onefourth part of it's orbit, the point N will have the ftar upon it's meridian, or at fix in the morning, fix hours fooner than it comes round to the fun; but the point N muft revolve fix hours more, before it has mid-day by the fun for now the angle ASS is a right angle, and so is NC n'; that is,

the

the earth has advanced 90 degrees on it's axis, to carry the point N from the far to the fun; for the flar always comes to the meridian when N m is parallel to RSA; becaufe DS is but a point in refpect to RS. When the earth is at D, the ftar comes to the meridian at three in the morning, at E, the carth having gone half round it's orbit; N points to the ftar at midnight, it being then directly oppofite to the fun; and, therefore, by the earth's diurnal motion, the star comes to the meridian twelve hours before the fun, and then goes on, till at A it comes to the meridian with the fun again.

Thus it is plain, that one abfolute revolution of the earth on it's axis which is always completed when any particular flar comes to be parallel to it's fituation at any time of the day before) never brings the fame meridian round from the fun to the fun again; but that the earth requires as much more than one turn on it's axis, to finish a natural day, as it has gone forward in that time, which, at a mean ftate, is a 365th part of a circle, that is, 59 minutes, 8 feconds; for as 365 days are to 1 day, fo are 360 degrees to 59 minutes 8 feconds. Hence, in 365 days the earth turns 366 times round it's axis, and confequently, as one revolution of the earth on it's axis completes a fiderial day, there must be one more fiderial day in a year than there are folar days.

OF MEAN AND APPARENT TIME.

Further and more accurate accurate obfervations fhewed, that the folar days were not equal to each other; after inveftigating this fubject, aftronomers were under the neceffity of diftinguifhing two forts of time, one they called true and apparent time, the other mean time.

True

True and apparent time is determined by the interval between the fun's center pafling the meridian, and that of his next return to the fame meridian. It is that fhewn by a fun-dial, which marks the hours every day in such a manner, that every hour is a 24th part of the time, between the noon of that day, and the noon of the day immediately following.

Mean time is that fhewn by a clock, which goes uniformly.

The time fhewn by a fun-dial, and the mean time, or that fhewn by a well regulated clock, agree only four times in the year, on the 15th of April, the 16th of June, the 31st of Auguft, and the 24th of December.

The clock, if it goes equably and true all the year round, will be before the fun from the 24th of December to the 15th of April; from that time to the 16th of June, the fun will be before the clock; from thence to the 31ft of Auguft, the clock will be again before the fun, and from the 31st of Auguft to the 24th of December, the fun will be fafter than the clock. On any other day, if you would fet a clock by a fun-dial, you must make ufe of an equation table, which fhews, for every day in the year, how many minutes or feconds the fun is before or behind the clock; the difference between the fun and the clock is called the equation of time.

Both the folar and mean day are divided into 24 hours, or 86400 feconds.

Three hundred and fixty degrees of the equator' pafs under the meridian in a mean day more 59 minutes, 8 feconds, which is that part of 360 degrees of the fun's annual motion correfponding to the time of a mean day.

In a folar or true day, the 360 equator pafs under the meridian

degrees of the more an arc thereof

thereof anfwering to the ecliptic arc defcribed the fame day, called the fun's motion in right afcenfion.

When the fun is furtheft from the earth, or in apogee, his motion in right afcenfion in a day, is I degree, 2 minutes, 6 feconds; therefore 361 degrees, 2 minutes, 6 feconds, pafs the meridian in a folar day. By working this proportion, as 360 degrees, 59 minutes, 8 feconds, is to 24 hours, fo is 361 degrees, 2 minutes, 6 feconds, we find 24 degrees, o minutes, 12 feconds. Confequently when the fun is in apogee, the folar day is 12 feconds longer than the mean day.-From hence it follows:

1. That in every fecond of a clock well regulated to mean time, an arc of 15 minutes 28 feconds of the equator paffes the meridian; for this is the quotient of 360 degrees, 59 minutes, & feconds, divided by 86400 feconds.

2. That a flar's revolution answers to 360 degrees of the equator, while the mean day anfwers to 360 degrees, 59 minutes, 8 feconds. This difference of 59 minutes, 8 feconds, being reduced to time, gives 3 minutes, 56 feconds. Therefore the ftars anticipate 3 minutes, 56 feconds, every day on mean time; or, which is the fame, a ftar's diurnal revolution is made in 23 hours, 56 minutes, 4 feconds.

3. To find whether a clock be well regulated to mean time, obferve if it thew exactly 23 hours, 56 minutes, 4 feconds, from the inftant of any ftar's paffage through a fixed point, to that of it's return to the fame point. By what the clock exceeds this, it is fafter, by what it wants thereof, it is flower than mean time.

OF THE EQUATION OF TIME.

I have already obferved to you, that the equa