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The World's Greatest Books [Volumes 1-15, 17-20]
- Автор: Gutenberg
- Год: 1910
- Язык: английский
- Жанр: Культурология
Электронная книга - «The World's Greatest Books [Volumes 1-15, 17-20]». Краткое содержание книги:
The World's Greatest Books — Volume 01 — Fiction от Неизвестный
The World's Greatest Books — Volume 02 — Fiction от Неизвестный
The World's Greatest Books — Volume 03 — Fiction от Неизвестный
The World's Greatest Books — Volume 04 — Fiction от Неизвестный
The World's Greatest Books — Volume 05 — Fiction от Неизвестный
The World's Greatest Books — Volume 06 — Fiction от Неизвестный
The World's Greatest Books — Volume 07 — Fiction от Неизвестный
The World's Greatest Books — Volume 08 — Fiction от Неизвестный
The World's Greatest Books — Volume 09 — Lives and Letters от Неизвестный
The World's Greatest Books — Volume 10 — Lives and Letters от Неизвестный
The World's Greatest Books — Volume 11 — Ancient and Mediæval History от Неизвестный
The World's Greatest Books — Volume 12 — Modern History от Неизвестный
The World's Greatest Books — Volume 13 — Religion and Philosophy от Неизвестный
The World's Greatest Books — Volume 14 — Philosophy and Economics от Неизвестный
The World's Greatest Books — Volume 15 — Science от Неизвестный
The World's Greatest Books — Volume 17 — Poetry and Drama от Неизвестный
The world's greatest books от Mee, Arthur, 1875-1943, joint editor & Hammerton, John Alexander, Sir, 1871-1949, joint editor & McClure, S. S. (Samuel Sidney), 1857-1949, joint editor
The World's Greatest Books — Volume 19 — Travel and Adventure от Неизвестный
The World's Greatest Books — Volume 20 — Miscellaneous Literature and Index от Неизвестный
The revolutions of the satellites of Jupiter about the planet are more regular; for they describe circles concentric with Jupiter by equable motions, as exactly as our senses can distinguish.
And so the satellites of Saturn are revolved about this planet with motions nearly circular and equable, scarcely disturbed by any eccentricity hitherto observed.
That Venus and Mercury are revolved about the sun is demonstrable from their moon-like appearances. And Venus, with a motion almost uniform, describes an orb nearly circular and concentric with the sun. But Mercury, with a more eccentric motion, makes remarkable approaches to the sun and goes off again by turns; but it is always swifter as it is near to the sun, and therefore by a radius drawn to the sun still describes areas proportional to the times.
Lastly, that the earth describes about the sun, or the sun about the earth, by a radius from one to the other, areas exactly proportional to the times is demonstrable from the apparent diameter of the sun compared with its apparent motion.
These are astronomical experiments; from which it follows that there are centripetal forces actually directed to the centres of the earth, of Jupiter, of Saturn, and of the sun.[2]
That these forces decrease in the duplicate proportion of the distances from the centre of every planet appears by Cor. vi., Prop. iv., Book I.[3] for the periodic times of the satellites of Jupiter are one to another in the sesquiplicate proportion of their distances from the centre of this planet. Cassini assures us that the same proportion is observed in the circum-Saturnal planets. In the circum-solar planets Mercury and Venus, the same proportional holds with great accuracy.
That Mars is revolved about the sun is demonstrated from the phases which it shows and the proportion of its apparent diameters; for from its appearing full near conjunction with the sun and gibbous in its quadratures,[4] it is certain that it travels round the sun. And since its diameter appears about five times greater when in opposition to the sun than when in conjunction therewith, and its distance from the earth is reciprocally as its apparent diameter, that distance will be about five times less when in opposition to than when in conjunction with the sun; but in both cases its distance from the sun will be nearly about the same with the distance which is inferred from its gibbous appearance in the quadratures. And as it encompasses the sun at almost equal distances, but in respect of the earth is very unequally distant, so by radii drawn to the sun it describes areas nearly uniform; but by radii drawn to the earth it is sometimes swift, sometimes stationary, and sometimes retrograde.
That Jupiter in a higher orbit than Mars is likewise revolved about the sun with a motion nearly equable as well in distance as in the areas described, I infer from Mr. Flamsted's observations of the eclipses of the innermost satellite; and the same thing may be concluded of Saturn from his satellite by the observations of Mr. Huyghens and Mr. Halley.
If Jupiter was viewed from the sun it would never appear retrograde or stationary, as it is seen sometimes from the earth, but always to go forward with a motion nearly uniform. And from the very great inequality of its apparent geocentric motion we infer—as it has been previously shown that we may infer—that the force by which Jupiter is turned out of a rectilinear course and made to revolve in an orbit is not directed to the centre of the earth. And the same argument holds good in Mars and in Saturn. Another centre of these forces is, therefore, to be looked for, about which the areas described by radii intervening may be equable; and that this is the sun, we have proved already in Mars and Saturn nearly, but accurately enough in Jupiter.
The distances of the planets from the sun come out the same whether, with Tycho, we place the earth in the centre of the system, or the sun with Copernicus; and we have already proved that, these distances are true in Jupiter. Kepler and Bullialdus have with great care determined the distances of the planets from the sun, and hence it is that their tables agree best with the heavens. And in all the planets, in Jupiter and Mars, in Saturn and the earth, as well as in Venus and Mercury, the cubes of their distances are as the squares of their periodic times; and, therefore, the centripetal circum-solar force throughout all the planetary regions decreases in the duplicate proportion of the distances from the sun. Neglecting those little fractions which may have arisen from insensible errors of observation, we shall always find the said proportion to hold exactly; for the distances of Saturn, Jupiter, Mars, the Earth, Venus, and Mercury from the sun, drawn from the observations of astronomers, are (Kepler) as the numbers 951,000, 519,650, 152,350, 100,000, 70,000, 38,806; or (Bullialdus) as the numbers 954,198, 522,520, 152,350, 100,000, 72,398, 38,585; and from the periodic times they come out 953,806, 520,116, 152,399, 100,000, 72,333, 38,710. Their distances, according to Kepler and Bullialdus, scarcely differ by any sensible quantity, and where they differ most the differences drawn from the periodic times fall in between them.
Earth as a Centre
That the circum-terrestrial force likewise decreases in the duplicate proportion of the distances, I infer thus:
The mean distance of the moon from the centre of the earth is, we may assume, sixty semi-diameters of the earth; and its periodic time in respect of the fixed stars 27 days 7 hr. 43 min. Now, it has been shown in a previous book that a body revolved in our air, near the surface of the earth supposed at rest, by means of a centripetal force which should be to the same force at the distance of the moon in the reciprocal duplicate proportion of the distances from the centre of the earth, that is, as 3,600 to 1, would (secluding the resistance of the air) complete a revolution in 1 hr. 24 min. 27 sec.
Suppose the circumference of the earth to be 123,249,600 Paris feet, then the same body deprived of its circular motion and falling by the impulse of the same centripetal force as before would in one second of time describe 151⁄12 Paris feet. This we infer by a calculus formed upon Prop. xxxvi. ("To determine the times of the descent of a body falling from a given place"), and it agrees with the results of Mr. Huyghens's experiments of pendulums, by which he demonstrated that bodies falling by all the centripetal force with which (of whatever nature it is) they are impelled near the surface of the earth do in one second of time describe 151⁄12 Paris feet.
But if the earth is supposed to move, the earth and moon together will be revolved about their common centre of gravity. And the moon (by Prop, lx.) will in the same periodic time, 27 days 7 hr. 43 min., with the same circum-terrestrial force diminished in the duplicate proportion of the distance, describe an orbit whose semi-diameter is to the semi-diameter of the former orbit, that is, to the sixty semi-diameters of the earth, as the sum of both the bodies of the earth and moon to the first of two mean proportionals between this sum and the body of the earth; that is, if we suppose the moon (on account of its mean apparent diameter 311⁄2 min.) to be about 1⁄42 of the earth, as 43 to 3√42 + 422 or as about 128 to 127. And, therefore, the semi-diameter of the orbit—that is, the distance of the centres of the moon and earth—will in this case be 601⁄2 semi-diameters of the earth, almost the same with that assigned by Copernicus; and, therefore, the duplicate proportion of the decrement of the force holds good in this distance. (The action of the sun is here disregarded as inconsiderable.)
This proportion of the decrement of the forces is confirmed from the eccentricity of the planets, and the very slow motion of their apsides; for in no other proportion, it has been established, could the circum-solar planets once in every revolution descend to their least, and once ascend to their greatest distance from the sun, and the places of those distances remain immovable. A small error from the duplicate proportion would produce a motion of the apsides considerable in every revolution, but in many enormous.