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. [Sidenote: Fig. II.] 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_