221. The fixed Stars appear to go round the Earth in 23 hours 56 minutes 4 seconds, and the Sun in 24 hours: so that the Stars gain three minutes 56 seconds upon the Sun every day, which amounts to one diurnal revolution in a year; and 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.

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 it’s Axis, any given Meridian will revolve from any Star to the same Star again in every absolute turn of the Earth on it’s 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 it’s 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 four minutes shorter than the solar.

Let ABCDEFGHIKLM be the Earth’s Orbit, 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 it’s Axis the same way from the Sun to the Sun again 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 Nm be any particular Meridian of the Earth, and N a given point or place upon that Meridian. When the Earth is at A, the Sun S hides the Star R, which would always be hid if the Earth never removed from A; and consequently, as the Earth turns round it’s 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 it’s Orbit from A to B, it’s motion round it’s Axis will bring the point N a twelfth part of a day or two hours sooner to the Star than to the Sun; for the Angle NBn 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 it’s Meridian at 8 in the morning, or four hours sooner than it comes round to the Sun; for it must revolve from N to n, before it has the Sun in it’s Meridian. When the Earth comes to D, the point N will have the Star on it’s Meridian at six 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 NDn; that is, the Earth has advanced 90 degrees in it’s 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 Nm is parallel to RSA; because DS is but a point in respect of RS. When the Earth is at E, the Star comes to the Meridian at 4 in the morning; at F, at two in the morning; and at G, the Earth having gone half round it’s Orbit, N points to the Star R at midnight, 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 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.

222. Thus it is plain, that an absolute turn of the Earth on it’s Axis (which is always completed when the same Meridian comes to be parallel to it’s situation at any time of the day before) never brings the same Meridian round from the Sun to the Sun 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 state is a 365th part of a Circle. Hence, in 365 days the Earth turns 366 times round it’s Axis; and therefore, as a turn of the Earth on it’s Axis compleats 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 equably on their Axes, and if one remained at A until the other travelled round the Sun from A to A again, that Earth which kept it’s place at A would have it’s solar and sidereal days always of the same length; and so, would have one solar day more than the other at it’s return. Hence, if the Earth turned but once round it’s Axis in a year, and if that turn was 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, intitled, Accelerations of the fixed Stars, affords us an easy method of knowing whether or no our clocks and watches go true: For if, through a small hole in a window-shutter, or in a thin plate of metal fixed to a window, we observe at what time any Star disappears behind a chimney, or corner of a house, at a little distance; and if the same Star disappears the next night 3 minutes 56 seconds sooner by the clock or watch; and on the second night, 7 minutes 52 seconds sooner; the third night 11 minutes 48 seconds sooner; and so on, every night, as in the Table, which shews this difference for 30 natural days, it is an infallible Sign that the machine goes true; otherwise it does not go true; and must be regulated accordingly: and as the disappearing of a Star is instantaneous, we may depend on this information to half a second.