A, and the other at the sun S, then whilst the planet is describing the arc HEx, which is between them, it will appear to move from the right hand of the man at S, towards his left; and from the left hand of the man at A, towards his right.

Whilst the motion of Venus is direct, or while it is describing the arc aGH, it appears to move from V to T, among the fixed stars. But, after it has been carried in its orbit from H to z, it appears in the line AzR, and is seen among the fixed stars at R. When it comes to E, it appears at Q; and when at y, its apparent place in the heavens is at P. Thus, as the planet passes from its greatest elongation H, on one side of the sun, through its inferior conjunction E, to its greatest elongation r, on the other side, it apparently runs back from T to V, or its motion is retrograde.

Our third proposition is, that Venus is stationary, or has no apparent motion for some time, when it is at its two greatest elongations; that is, when it is at H or æ, and its apparent place is either at T or V.

When either of the inferior planets, Venus for instance, is at its greatest elongation H or x, a line drawn from the earth through the planet, as AHT, or ArV, is a tangent to the orbit. Now, though a right line touches a circle but in one point, yet some part of the circle greater than a point is so near to the tangent, as not to be distinguished from it. Thus the arc bd, so nearly coincides with the tangent AHT, that a spectator's eye, placed at A, could not distinguish the tangent from this part of the curve ;

consequently, while the planet is describing this arc, no other change will be made in its geocentric place, than if it was to move in the tangent.

But the geocentric place of the planet would not be altered, if the planet was to move in the tangent. For if it was to move from T towards A, or from A to V, the apparent place of it in the heavens would, in one case, be at T, in the other case at V. Therefore, while the planet is at its greatest elongation, and is describing a small arc in its orbit, that nearly coincides with the tangent, its geocentric place does not alter, but it appears to continue for some time in the same part of the heavens, or is stationary.

I have hitherto supposed the earth to be at rest; and, upon that supposition, have explained the progress and regress, the conjuctions and stations of the inferior planets. If this supposition was true, VT, or the arc which the planet at any time describes in its progress, and TV, the arc which it describes in its regress, would always be in the same part of the heavens. The planet, when in conjunction, would always appear at Q among the same fixed stars; and at its elongation, or when it is stationary, it would always appear among the same fixed stars at T, on one side of the sun, and at V on the other.

But this supposition is not true; for the earth revolves in its orbit ABO round the sun. Now, if the earth is at A, at the time of either conjunction, the planet at this conjunction would appear among the fixed stars at Q; and the arcs of the greatest elongation QV and QT, would be on each side of those

stars. But, if the earth is at B, at the time of either of the conjunctions; then, at the time of this conjunction, the planet will appear in the line BST, and be seen among the fixed stars at T; and the arcs of the greatest elongation will be on each side of these stars; that is, the conjunctions and elongations will happen in a different part of the heavens, when the earth is at B, from what they happen when the earth is at A. In other respects, the foregoing phenomena will be much the same, notwithstanding the motion of the earth, only the planet will be more direct in the farthest part of the orbit, and less retrograde in the nearest.

The inferior planets always appear very near the sun; but, by the motion of the earth in its orbit, the sun appears in different parts of the heavens, in different times of the year. Therefore, the inferior planets, as they are always very near the sun, will also appear in different parts of the heavens, at different times of the year. And, consequently, their conjunctions and greatest elongations will sometimes happen when they are in one part of the heavens, and sometimes when they are in another part. Venus, seen from the earth, will appear to vibrate in an arc VT, half of which is on one side of the sun's apparent place, and half on the other side.

When an inferior planet, viewed from a superior, moves apparently retrograde, the superior planet has also an apparently retrograde motion.

When a superior planet, viewed from an inferior, appears stationary, the inferior planet viewed at the same time from the superior, is also stationary.

OF THE PHASES OF VENUS.

That the planets are all opake or dark bodies; and, consequently, shine only by the light they receive from the sun, is plain, because they are not visible when they are in such parts of their orbits as are between the sun and earth; that is, when their illuminated side is turned from us.

The sun enlightens only half a planet at once; the illuminated hemisphere is always that which is turned towards the sun, the other hemisphere of the planet is dark. To speak with accuracy, the sun, being larger than any of the planets, will illuminate rather more than half; but this difference, on account of the great distance of the sun from any of the planets, is so small, that its light may be considered as coming to them in lines physically parallel.

Like other opake bodies, they cast a shadow behind them, which is always opposite to the sun. The line in the planet's 'body, which distinguishes the lucid from the obscure part, appears sometimes straight, sometimes crooked. The convex part of the curve is sometimes towards the splendid, and the concave towards that which is obscure; and vice versa, according to the situation of the eye, with respect to the planet, and of the sun which enlightens the planet.

Hence the inferior planets, going round the sun in less orbits than our earth does, will sometimes have more, sometimes less of their illuminated side

towards us; and, as it is the illuminated part only which is visible to us, Mercury and Venus, will, through a good telescope, exhibit the several appearances of the moon, from a fine thin crescent to the enlightened hemisphere.

If we view Venus through a telescope, when she follows the sun's rays on the eastern side, and appears above the horizon after sun-set, we shall see her appear nearly round, and but small; she is at that time beyond the sun, and presents to us an enlightened hemisphere. As she departs from the sun towards the east, she augments in her apparent size; and on viewing her through a telescope, is seen to alter her figure, abating of her apparent roundness, and appearing, successively, like the moon in the different stages of her decrease. At length, when she is at her greatest elongation, she is like the moon in her first quarter, and appears as she does; when from a full, she has decreased to a half-moon.

the sun,

After this, as she approaches (in appearance) to she appears concave in her illuminated part, as the moon when she forms a crescent; thus she continues, till she is hid entirely in the sun's rays, and presents to us her whole dark hemisphere, as the moon does in her conjunction, no part of the planet being then visible.

When she departs out of the sun's rays, on the western side, we see her in the morning just before day-break. It is in this situation that Venus is called the morning-star, as in the other she is called the evening-star. She at this time appears very beau