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200. Tables for converting mean solar TIME into Degrees and Parts of the terrestrial EQUATOR; and also for converting Degrees and Parts of the EQUATOR into mean solar TIME.

TABLE I. For converting 1 ABLE il. For converting
Time into Degrees and Degrees and Parts of the

Parts of the Equator.

Equa or into Time.

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These are the tables mentioned in the 208th Article, and are so easy that they scarce require any farther explanation than to inform the reader, that if, in Table I. he reckon the columns marked with asterisks to be minutes of time, the other columns give the equatorial parts or motion in degrees and minutes; if he reckon the asterisk-columns to be seconds, the others give the motion in minutes and seconds of the equator; if thirds, in seconds and thirds: And if in Table II. he reckon the asteriskcolumns to be degrees of motion, the others give the time answering thereto in hours and minutes; if minutes of motion, the time is minutes and seconds; if seconds of motion, the corresponding time is given in seconds and thirds. An example in each case will make the whole very plain.

EXAMPLE I.

EXAMPLE II.

In 10 hours 15 mi In what time will 153

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Sidereal days shor

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221.

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153 51 5 Answer

CHAP. XII.

Of Solar and Sidereal Time.

HE stars appear to go round the Earth in 23 hours 56 minutes 4 seconds, and solar days, the Sun in 24 hours: so that the stars gain three and why. minutes 56 seconds upon the Sun every day, which

amounts to one diurnal revolution in a year; and Plate III. therefore, in 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, and the latter sidereal days.

The diameter of the Earth's orbit is but a physical point in proportion to the distance of the stars; for which reason, and the Earth's uniform motion on its axis, any given meridian will revolve from any star to the same star again in every absolute turn of the Earth on its axis, without the least perceptible difference of time shewn by a clock which goes exactly true.

If the Earth had only a diurnal motion, without an annual, any given meridian would revolve from the Sun to the Sun again in the same quantity of time as from any star to the same star again; because the Sun would never change his place with respect to the stars. But, as the Earth advances almost a degree eastward in its orbit in the time that it turns eastward round its axis, whatever star passes over the meridian on any day with the Sun, will pass over the same meridian on the next day when the Sun is almost a degree short of it; that is, 3 minutes 56 seconds sooner. If the year contained only 360 days, as the ecliptic does 360 degrees, the Sun's apparent place, so far as his motion is equable, would change a degree every day; and then the sidereal days would be just 4 minutes shorter than the solar.

Let ABCDEFGHIKLM be the Earth's orbit, Fig. 11. in which it goes round the Sun every year, according to the order of the letters, that is, from west to east; and turns round its axis the same way from the Sun to the Sun again in every 24 hours. Let S be the Sun, and R a fixed star at such an immense distance, that the diameter of the Earth's orbit bears no sensible proportion to that distance. Nm be any particular meridian of the Earth, and Na given point or place upon that meridian.

Let

When the Earth is at A the Sun S hides the star R, which would be always hid if the Earth never removed from A; and consequently, as the Earth turns round its axis, the point N would always come round to the Sun and star at the same time. But when the Earth has advanced, suppose a twelfth part of its orbit from A to B, its motion round its axis will bring the point N a twelfth part of a natural day, or two hours, sooner to the star than to the Sun, for the angle NB n is equal to the angle ASB: and therefore any star which comes to the meridian at noon with the Sun when the Earth is at A, will come to the meridian at 10 in the forenoon when the Earth is at B. When the Earth comes to C, the point N will have the star on its meridian at 8 in the morning, or four hours sooner than it comes round to the Sun; for it must revolve from Nton before it has the Sun in its meridian. When the Earth comes to D, the point N will have the star on its meridian at 6 in the morning, but that point must revolve six hours more from N to n, before it has mid-day by the Sun: for now the angle ASD is a right angle, and so is ND n; that is, the Earth has advanced 90 degrees in its orbit, and must turn 90 degrees on its axis to carry the point N from the star to the Sun: for the star always comes to the meridian when N m is parallel to RSA; because D Sis but a point in respect to RS. When the Earth is at E, the star comes to the meridian at 4 in the morning; at F, at 2 in the morning; and at G, the Earth having gone half round its orbit, N points to the star R at midnight, it being then directly opposite to the Sun. And therefore, by the Earth's diurnal motion, the star comes to the meridian 12 hours before the Sun. When the Earth is at II, the star comes to the meridian at 10 in the evening; at I it comes to the meridian at 8, that is, 16 hours before the Sun; at K 18 hours before him; at L 20 hours; at M 22; and at A equally with the Sun again.

A TABLE, shewing how much of the Celestial Equator passes over the Meridian in any Part of a mean SOLAR DAY; and how much the FIXED STARS gain upon the mean SOLAR TIME every Day, for a Month.

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