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These are the tables mentioned in the 208th Ar. ticle, 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 se. conds, 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 asterisk. columns 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 nutes 24 seconds 20 degrees 51 minutes 5 sethirds, Qu. How much conds of the

equator of the equator revolves revolve through the methrough the meridian? ridian? Deg. M. S.

H. M.S. T. Hours 10 150 0 0 S 150 10 0 0 Min. 15 3 45 0

3 12 0 0 Sec. 24

6 0 Min. 51 3 24 0 Thirds 20 5 Sec. 5

20

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days shor. 221.

ter than

T:

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 ex. actly 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. Let N m be any particular meridian of the Earth, and Na given point or place upon that meridian.

When the Earth is at A the Sun Shides 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 Nwould 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 Na twelfth part of a natural day, or two hours, sooner to the star than to the Sun, for the angle N B 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 al. ways comes to the meridian when N mis parallel to RS A; because D S is 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 H, the star comes to the meridian at 10 in the evening; at I it comes to the me. ridian 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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6 90 14 47 6 1 30 15 369 1 29 60 7 105 17 151 7 1 45 17 37 9 16 31 710 8120 19 43 & 2 0 20.589 31 341 EO 9 135 22 11 9 2 15 221391 9 46 36|| 90 10 150 24 38 10 2 30 25 40 10 1

S9ico

23 35 27 31 31 27 35 23 39 19

11 165 27 611 2 45 2741/10 16 41|110 43 15 12 180 29 34 12) 3 0 30 42 10 31 43120 47 11 13195 32 213 3 15 3243 10 46 461|130 51 7 14210 34 3014 3 30 34 4411 1 48|1410 55 3 15/225 36 58 15 3 45 37 45 11 16 51|1510 58 59

16240 39 25 16 4 0 39 4011

31 53||161 2 55 17 255 41 5317| 4 15 41 4711 46 561711 6 50 18270 44 2118 4 30 44 48 12 1 58||18|1 10 46 19 285 46 49 19 4 45 47 49 12 17 191

14 42 20 800 49 17 2015 0 49 50112 32 3201 18 38

21 315 51 4521 5 15 52 5112 47

6211

22 34 22 330 54 12 29 5 30 54 52/13 2 8|di 26 30 23|345 56 40231 5 45 57 53 13 17 11 31 30 26 24 360 59 & 24 6 0 59 54 13 32 13241 34 22 25 376 1 3625 6 16 255 13 47

38 18

101|25/1

46 10

120391 4 420 6 31
27|406 6 32/271 6
28 121 3 592917 1
29 136 11 27 291 7 16
30 151 13 55130 7 31

450/14 2 181 142 14
757|14 17 201|2711
9 514 32 23

50 5 11:14 47 25.1291 54

1 14|60|15 2 a 8 goli 57 57

Plate III.

of the

its axis

222. Thus it is plain, that an absolute turn of An abso. the Earth on its axis (which is always completed lute turn when any particular meridian comes to be parallel to

its situation at any time of the day before) never Earth on

brings the same meridian round from the Sun to the never fi- Sun again; but that the Earth requires as much solar day. more than one turn on its axis to finish a natural day,

as it has gone forward in that time; which, at a mean state, is a 365th part of a circle. Hence, in 365 days, the Earth turns 366 times round its axis ; and therefore, as a turn of the Earth on its axis completes a sidereal day, there must be one sidereal day more in a year than the number of solar days, be the number what it will, on the Earth, or any other planet, one turn being lost with respect to the number of solar days in a year, by the planet's going round the Sun; just as it would be lost to a traveller, who, in going round the Earth, would lose one day by following the apparent diurnal motion of the Sun; and consequently would reckon one day less at his return (let him take what time he would to go round the Earth) than those who remained all the while at the place from which he set out.

So, if there were two Earths revolving equally on their axes, and if one remained at A until the other had gone round the Sun from A to A again, that Earth which kept its place at A would have its solar and sidereal days always of the same length; and so would have one solar day more than the other at its return. Hence, if the Earth turned but once round its axis in a year, and if that turn were made the same way as the Earth goes round the Sun, there would be continual day on one side of the Earth, and continual night on the other.

223. The first part of the preceding table shews how much of the celestial equator passes over the meridian in any given part of a mean solar day, and is to be understood the same way as the table in the 220th article. The latter part, intituled,

Fig. II.

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