The Diurnal rotation of the Planets round their axis, was discovered by certain spots which appear on the surfaces. These spots appear first in the margin of the Planet’s disk, (or the edge of their surfaces) and seem by degrees to creep toward their middle, and so on, going still forward, ’till they come to the opposite side or edge of the disk, where they set or disappear; and after they have been hid for the same space of time, that they were visible, they again appear to rise in or near the same place, as they did at first, then to creep on progressively, taking the same course as they did before. These spots have been observed on the surfaces of the Sun, Venus, Mars, and Jupiter; by which means it has been found that these bodies turn round their own axis, in the times before-mentioned. It is very probable that Mercury and Saturn have likewise a motion round their axis, that all the parts of their surface may alternately enjoy the light and heat of the Sun, and receive such changes as are proper and convenient for their nature. But by reason of the nearness of ☿ to the Sun, and ♄’s immense distance from him, no observations have hitherto been made whereby their spots (if they have any) could be discovered, and therefore their Diurnal motions could not be determined. The Diurnal motion of the Earth is computed from the apparent revolution of the Heavens, and of all the Stars round it, in the space of a natural Day. The Solar spots do not always remain the same, but sometimes old ones vanish, and afterwards others succeed in their room; sometimes several small ones gather together and make one large spot, and sometimes a large spot is seen to be divided into many small ones. But, notwithstanding these changes, they all turn round with the Sun in the same time.
How the relative distances of the Planets from the Sun are determined.
The relative distances of the Planets from the Sun, and likewise from each other, are determined by the following methods: First, the distance of the two inferior Planets ☿ and ♀ from the Sun, in respect of the Earth’s distance from him, is had by observing their greatest Elongation from the Sun as they are seen from the Earth.
The greatest Elongation of Venus is found by observation to be about 48 degrees, which is the angle S T ♀; whence, by the known rules of Trigonometry, the proportion of S ♀, the mean distance of Venus from the Sun to ST, the mean distance of the Earth from him may be easily found. After the same manner, in the right-angled triangle S T ☿, may be found the distance S ☿ of Mercury from the Sun. And if the mean distance of the Earth from the Sun S T be made 1000, the mean distance of Venus S ♀ from the Sun will be 723; and of Mercury S ☿ 387: And if the Planets moved round the Sun in circles, having him for their center, the distances here found would be always their true distances: But as they move in Ellipses, their distances from the Sun will be sometimes greater, and sometimes less. Their Excentricities are computed to be as follows, viz.
 | Mercury | 80 |  | of the parts | |
| Excent. of | Venus | 5 | above-mentioned. | ||
| Earth | 169 |
Heliocentric and Geocentric Place, what.
The distances of the superior Planets, viz. ♂, ♃, and ♄, are found by comparing their true places, as they are seen from the Sun, with their apparent places, as they are seen from the Earth. Let S be the Sun, the circle ABC the Earth’s orbit, AG a line touching the Earth’s orbit, in which we’ll suppose the superior Planets are seen from the Earth in the points of their orbits ♂, ♃, ♄; and let DEFGH be a portion of a great circle in the Heavens, at an infinite distance: Then the place of Mars seen from the Sun is D, which is called his true, or Heliocentric Place; but from the Earth, he will be seen in G, which is called his apparent, or Geocentric Place. So likewise Jupiter and Saturn will be seen from the Sun in the points E and F, their Heliocentric places; but a spectator from the Earth will see them in the point of the Heavens G, which is their Geocentric place. The arches DG, EG, FG, the differences between the true and apparent places of the Superior Planets, are called the Parallaxes of the Earth’s annual Orb, as seen from these Planets. If thro’ the Sun we draw SH parallel to AG, the angles A ♂ S, A ♃ S, A ♄ S, will be respectively equal to the angles D S H, E S H, and F S H; and the angle A G S is equal to the angle GSH, whose measure is the arch GH; which therefore will be the measure of the angle AGS, the angle under which the semidiameter A S of the Earth’s orbit, is seen from the Starry Heavens. But this semidiameter is nothing in respect of the immense distance of the Heavens or Fixed Stars; for from thence it would appear under no sensible angle, but look like a point. And therefore in the Heavens, the angle G S H, or the arch G H vanishes; and the Points G and H coincide; and the arches D H, E H, F H, may be considered as being of the same bigness with the arches D G, E G, and F G, which are the measures of the angles A ♂ S, A ♃ S, A ♄ S; which angles are nearly the greatest elongation of the Earth from the Sun, if the Earth be observed from the respective Planets, when the line G ♄ ♃ ♂ A, touches the Earth’s orbit in A. The nearer any of the superior Planets is to the Sun, the greater is the Parallax of the annual Orb, or the angle under which the semidiameter of the Earth’s orbit is seen from that Planet. In Mars the angle ♂ S, (which is the visible elongation of the Earth seen from Mars, or the Parallax of the annual Orb seen from that Planet) is about 42 degrees, and therefore the Earth is always to the inhabitants of Mars either their Morning or Evening Star, and is never seen by them so far distant from the Sun as we see Venus. The greatest elongation of the Earth seen from Jupiter, being nearly equal to the angle A ♃ S, is about 11 degrees. In Saturn the angle A ♄ S is but 6 degrees, which is not much above ¼ part of the greatest elongation we observe in Mercury. And since Mercury is so rarely seen by us, probably the astronomers of Saturn (except they have better Optics than we have) have not yet discovered that there is such a body as our Earth in the Universe.
The Parallax of the annual Orb, or the greatest elongation of the Earth’s orbit seen from any of the superior Planets, being given; the distance of that Planet from the Sun, in respect of the Earth’s distance from him, may be found by the same methods as the distances of the inferior Planets were. Thus, to find the distance of Mars from the Sun, it will be as the Sine of the angle S ♂ A is to the Radius, so is the distance AS (the distance of the Earth from the Sun) to S ♂, the distance from the Sun to Mars. After the same manner the distances of Jupiter and Saturn are also found. The mean distance of the Earth from the Sun being made 1000, the mean distances of the superior Planets from the Sun are, viz. the mean distance from the Sun of
| ♂ | 1524 | | | 141 | | |
| ♃ | 5201 | and the Excentricity | 250 | ||||
| ♄ | 9538 | 547 |