[AS]In this Manner Astronomers having procur'd a comparative Standard, reduc'd to some known Measure, as English Miles, Leagues, Semi-Orbs or Orbits, with all the Force of analogical Reasoning, clearly can demonstrate the Place and Distance of any Object within the Reach of Observation, and judge of Distances almost indefinite.
[AS] Parallax is the changeable Position of Bodies to different Situations of the Eye. First having found the Quantity of a Degree (i. e. a 60th Part of the Circumference) upon the Earth's Surface, Aratosthenes discover'd that the Magnitude of the whole was easily known; and then from the Moon's horizontal Parallax having given the Radius of the Earth, the Distance of the Moon is soon determined; next by the menstrual Parallax of the Lunar Orbit, the Distance of the Sun is found; and by the Elongation of the inferior Planets, their mutual Distance from each other; and, lastly, from the annual Parallax of the Earth's Orbit, all the other Orbits of the superior Planets are easily found.
PLATE XXX.
Will help you to very correct Ideas of the real Magnitude of the Globe of the Earth, compar'd with the just Extent of the Island of Great-Britain, which you will find with Ireland, and the rest of its Islands, seated near the Center of the Projection. This as a Standard will enable you to judge of all other Distances more perfectly; and first I shall consider that of the Sun.
The Sun is found to be mean distant from the Earth nearly 81 Millions of Miles, or 6877,5 Diameters of the Earth; and Saturn, the remotest Planet from him is at his greatest Distance from us about 858 Millions of Miles: Yet these Distances are but the beginning of Space, and only serve to open our Ideas for farther Search.
The great Comet of 1680, as I have some where said before, was found to move in so vast an excentrick Orbit, that in its aphelion Point it would be 14,4 Times as far from the Sun, as the Orbit of Saturn, and hence at least eleven thousand and two hundred Millions of Miles from us. Now since the wise Creator hath so dispos'd all the independent Parts of the Creation, such as the several Systems of primary and secondary Planets, &c. at so great a Distance from each other, that the Laws of any one in no wise shall interfere, disturb, or interrupt the Principles of another; this Comet, which we can easily prove belong'd to our own Sun, we may well imagine came not near any other; and tho' at that vast Distance from the solar Body, yet still there must have remain'd a Space sufficient to divide or seperate the sensible activity of neighbouring Systems, that they may not rush upon each other. Hence we may reasonably suppose, that the nearest Star can be no nearer than a triple Radius of its active Sphere; and provided they are all in regular Order, and much of the same Magnitude with one another (which no Arguments can possibly contradict) this Radius we may justly make 2000 times the Distance of our Earth. For admitting the utmost Limits of the Sun's Attraction to exceed this Sphere of the Comets, as far as the Sphere of the Comets exceeds that of the Planets, which is nearly 14,4 times, the Radius of the solar System will be extended every way 200 Radius's of the Orbit of Saturn, and consequently the Distance from Star to Star will not be less than 6000 times the Radius of our Orbis Magnus, and consequently upwards of 480,000,000,000 Miles. That this is even less than the real Truth, and may be defended as a very moderate Computation, grounded upon Reason, we have infallible Demonstration to witness, and make appear as thus.
Plate XXX.
We know from the Nature of Distance and Motion that the Stars may have an annual Parallax, but it is so very small, that the very best Astronomers have never yet been able to assign what the Quantity really is. Yet it is allow'd by universal Consent, that it can't possibly be more that one Minute of a Degree, and may probably be much less. Mr. Flamstead, by repeated Observations, made it in some of them upwards of 40″; but Mr. Bradley has endeavour'd to prove it is every where too small to be determined, and assigns this Angle to another Cause. This way then we cannot make their Distance less; and to prove that it is something more than I have said it is, let us even increase the doubtful Parallax of 40″ to the most it possibly can be, viz. to 60″ or 1′; and by the Solution of the Triangle, we shall find that the nearest Star is 6875 times the Radius of the Earth's Orbit from the Sun: And this tho' more than any other Proportion makes them, is still undeniably less than the Truth, which every Mathematician will of course be convinc'd of; and you yourself of force must believe, when you are told, that the smaller the Angle of Parallax is, the farther the Body is remov'd from us. By which Rule, according to Mr. Flamstead's Observations, the Distance must be still greater: By the optical Experiment of [AT]Mr. Huygins, greater still than this; and according to Mr. Bradley, so much more as not even too be determin'd.
[AT] 27664 Radius's of the Orbis Magnus, equal to the Distance of Syrius, whose Parallax should be to answer it but 14″ 48‴.