193. The horizontal Parallaxes are best observed at the Equator; 1. Because the heat is so nearly equal every day, that the Refractions are almost constantly the same. 2. Because the parallactic Angle is greater there as at A (the distance from thence to the Earth’s Axis being greater,) than upon any parallel of Latitude, as a or b.
The relative distances of the Planets from the Sun are known to great precision, though their real distances are not well known.
194. The Earth’s distance from the Sun being determined, the distances of all the other Planets from him are easily found by the following analogy, their periods round him being ascertained by observation. As the square of the Earth’s period round the Sun is to the cube of it’s distance from him, so is the square of the period of any other Planet to the cube of it’s distance, in such parts or measures as the Earth’s distance was taken; see § [111]. This proportion gives us the relative mean distances of the Planets from the Sun to the greatest degree of exactness; and they are as follows, having been deduced from their periodical times, according to the law just mentioned, which was discovered by Kepler and demonstrated by Sir Isaac Newton.
Periodical Revolution to the same fixed Star in days and decimal parts of a day.
| Of Mercury | Venus | The Earth | Mars | Jupiter | Saturn |
|---|---|---|---|---|---|
| 87.9692 | 224.6176 | 365.2564 | 686.9785 | 4332.514 | 10759.275 |
| Relative mean distances from the Sun. | |||||
| 38710 | 72333 | 100000 | 152369 | 520096 | 954006 |
| From these numbers we deduce, that if the Sun’s horizontal Parallax be 10ʺ, the real mean distances of the Planets from the Sun in English miles are | |||||
| 31,742,200 | 59,313,060 | 82,000,000 | 124,942,580 | 426,478,720 | 782,284,920 |
| But if the Sun’s Parallax be 11ʺ their distances are no more than | |||||
| 29,032,500 | 54,238,570 | 75,000,000 | 114,276,750 | 390,034,500 | 715,504,500 |
| Errors in distance a rising from the mistake of 1ʺ in the Sun’s Parallax | |||||
| 2,709,700 | 5,074,490 | 7,000,000 | 10,665,830 | 36,444,220 | 66,780,420 |
195. These last numbers shew, that although we have the relative distances of the Planets from the Sun to the greatest nicety, yet the best observers have not hitherto been able to ascertain their true distances to within less than a twelfth part of what they really are. And therefore, we must wait with patience till the 6th of June, A. D. 1761; wishing that the Sky may then be clear to all places where there are good Astronomers and accurate instruments for observing the Transit of Venus over the Sun’s Disc at that time: as it will not happen again, so as to be visible in Europe, in less than 235 years after.
Why the celestial Poles seem to keep still in the same points of the Heavens, notwithstanding the Earth’s motion round the Sun.
196. The Earth’s Axis produced to the Stars, being carried [[50]]parallel to itself during the Earth’s annual revolution, describes a circle in the Sphere of the fixed Stars equal to the Orbit of the Earth. But this Orbit, though very large in itself, if viewed from the Stars, would appear no bigger than a point; and consequently, the circle described in the Sphere of the Stars by the Axis of the Earth produced, if viewed from the Earth, must appear but as a point; that is, it’s diameter appears too little to be measured by observation: for Dr. Bradley has assured us, that if it had amounted to a single second, or two at most, he should have perceived it in the great number of observations he has made, especially upon γ Dragonis; and that it seemed to him very probable that the annual Parallax of this Star is not so great as a single second: and consequently, that it is above 400 thousand times farther from us than the Sun. Hence the celestial poles seem to continue in the same points of the Heavens throughout the year; which by no means disproves the Earth’s annual motion, but plainly proves the distance of the Stars to be exceeding great.
The amazing velocity of light.
[PLATE IV].
197. The small apparent motion of the Stars § [113], discovered by that great Astronomer, he found to be no ways owing to their annual Parallax (for it came out contrary thereto) but to the Aberration of their light, which can result from no known cause besides that of the Earth’s annual motion; and as it agrees so exactly therewith, it proves beyond dispute that the Earth has such a motion: for this Aberration compleats all it’s various Phenomena every year; and proves that the velocity of star-light is such as carries it through a space equal to the Sun’s distance from us in 8 minutes 13 seconds of time. Hence, the velocity of light is [[51]]10 thousand 210 times as great as the Earth’s velocity in it’s Orbit; which velocity (from what we know already of the Earth’s distance from the Sun) may be affected to be at least between 57 and 58 thousand miles every hour: and supposing it to be 58000, this number multiplied by the above 10210, gives 592 million 180 thousand miles for the hourly motion of light: which last number divided by 3600, the number of seconds in an hour, shews that light flies at the rate of more than 164 thousand miles every second of time, or swing of a common clock pendulum.