Body falls perpendicularly.
Let E F G be the Earth's globe, A its centre, L E the ascending effluvia: Just as the orbe of the effluvia progresses with the Earth, so also does the unmoved part of the circle at the straight line L E progress along with the general revolution. At L and E, a heavy body, M, falls perpendicularly toward E, taking the shortest way to the centre, nor is that right movement of weight, or of aggregation compounded with a circular movement, but is a simple right motion, never leaving the line L E. But when thrown with an equal force from E toward F, and from E toward G, it completes an equal distance on either side, even though the daily rotation of the Earth is in process: just as twenty paces of a man mark an equal space whether toward East or West: so the Earth's diurnal motionis by no means refuted by the illustrious Tycho Brahe, through arguments such as these.
The earth is balanced.The tendency toward its origin (which, in the case of the Earth, is called by Philosophers weight) causes no resistance to the diurnal revolution, nor does it direct the Earth, nor does it retain the parts of the Earth in place, for in regard to the Earth's solidity they are imponderous, nor do they incline further, but are at rest in the mass. If there be a flaw in the mass, such as a deep cavity (say 1000 fathoms), a homogenic portion of the Earth, or compacted terrestrial matter, descends through that space (whether filled with water or air) toward an origin more assured than air or water, seeking a solid globe. But the centre of the Earth, as also the Earth as a whole, is imponderous; the separated parts tend toward their own origin, but that tendency we call weight; the parts united are at rest; and even if they were ponderable, they would introduce no hindrance to the diurnal revolution. For if around the axis A B, there be a weight at C, it is balanced from E; if at F, from G; if at H, from I. So internally at L, they are balanced from M: the whole globe, then, having a natural axis, is balanced in æquilibrio, and is easily set in motion by the slighted cause, but especially because the Earth in her own place is nowise heavy nor lacking in balance. Therefore weight neither hinders the diurnal revolution, nor influences either the direction or continuance in position. Wherefore it is manifest that no sufficiently strong reason has yet been found out by Philosophers against the motion of the Earth.
Diurnal motion is due to causes which have now to be sought, arising from magnetick vigour and from the confederated bodies; that is to say, why the diurnal rotation of the Earth is completed in the space of twenty-four hours. For no curious art, whether of Clepsydras or of sand-clocks, or those contrivances of little toothed wheels which are set in motion by weights, or by the force of a bent steel band, can discover any degree of difference in the time. But as soon as the diurnal rotation has been gone through, it at once begins over again. But we would take as the day the absolute turning of a meridian of the Earth, from sun to sun. This is somewhat greater than one whole revolution of it; in this way the yearly course is completed in 365 and nearly ¼ turnings with respect to the sun. From this sure and regular motion of the Earth, the number and time of 365 days, 5 hours, 55 minutes, in solar tropical years is always certain and definite, except that there are some slight differences due to other causes. The Earth therefore revolves not fortuitously, or by chance, or precipitately; but with a rather high intelligence, equably, and with a wondrous regularity, in no other way than all the rest of the movable stars, which have definite periods belonging to their motions. For the Sun himself being the agent and incitor of the universe in motion, other wandering globes set within the range of his forces, when acted on and stirred, also regulate each its own proper courses by its own forces; and they are turned about in periods corresponding to the extent of their greater rotation, and the differences of their effused forces, and their intelligence for higher good. And for that cause Saturn, having a wider orbit, is borne round it in a longer time, Jupiter a shorter, and Mars still less; while Venus takes nine months, Mercury 80 days, on the hypotheses of Copernicus; the Moon going round the Earth with respect to the Sun in 29 days, 12 hours, 44 minutes. We have asserted that the Earth moves circularly about its centre, completing a day by an entire revolution with respect to the Sun. The Moon revolves in a monthly course around the Earth, and, repeating a conjunction with the Sun after a former synodic conjunction, constitutes the month or Lunar day. The Moon's mean concentrick orbit, according to numerous observations of Copernicus and later astronomers, is found to be distant 29 and about 5/6 diameters of the Earth from the Earth's centre. The Moon's revolution with respect to the Sun takes place in 29½ days and 44 minutes of time. We reckon the motion with respect to the sun, not the periodic motion,just as a day is one entire revolution of the Earth with respect to the Sun, not one periodick revolution; because the Sun is the cause of lunar as of terrestrial motion: also, because (on the hypotheses of later observers) the synodical month is truly periodic, on account of the Earth's motion in a great orbit. The proportion of diameters to circumferences is the same. And the concentrick orbit of the Moon contains twice over 29 and ½ great circles of the Earth & a little more. The Moon & the Earth, then, agree together in a double proportion of motion; & the Earth moves in the space of twenty-four hours, in its diurnal motion; because the Moon has a motion proportional to the Earth, but the Earth a motion agreeing with the lunar motion in a nearly double proportion. There is some difference in details, because the distances of the stars in details have not been examined sufficiently exactly, nor are mathematicians as yet agreed about them. The Earth therefore revolves in a space of 24 hours, as the Moon in her monthly course, by a magnetick confederation of both stars, the globes being forwarded in their movement by the Sun, according to the proportion of their orbits, as Aristotle allows,de Cœlo, bk. ii., chap. 10. "It happens" (he says) "that the motions are performed through a proportion existing between them severally, namely, at the same intervals in which some are swifter, others slower," But it is more agreeable to the relation between the Moon and the Earth, that that harmony of motion should be due to the fact that they are bodies rather near together, and very like each other in nature and substance, and that the Moon has more evident effects upon the Earth than the rest of the stars, the Sun excepted; also because the Moon alone of all the planets conducts her revolutions, directly (however diverse even), with reference to the Earth's centre, and is especially akin to the Earth, and bound to it as with chains. This, then, is the true symmetry and harmony between the motions of the Earth and the Moon; not that old oft-besung harmony of cœlestial motions, which assumes that the nearer any sphære is to thePrimum Mobileand that fictitious and pretended rapidest Prime Motion, the less does it offer resistance thereto, and the slower it is borne by its own motion from west to east: but that the more remote it is, the greater is its velocity, and the more freely does it complete its own movement; and therefore that the Moon (being at the greatest distance from thePrimum Mobile) revolves the most swiftly. Those vain tales have been conceded in order that thePrimum Mobilemay be accepted, and be thought to have certain effects in retarding the motions of the lower heavens; as though the motion of the stars arose from retardation, and were not inherent and natural; and as though a furious force were perpetually driving the rest of the heaven (except only thePrimum Mobile) with frenzied incitations. Much more likely is it that the stars are borne around symmetrically by their own forces, with a certain mutual concert and harmony.
Primarily having shown the manner and causes of the diurnal revolution of the Earth, which is partly brought about from the vigour of the magnetick virtue, partly effected by the præ-eminence and light of the Sun; there now follows an account of the distance of its poles from the poles of the Ecliptick—a supremely necessary fact. For if the poles of the universe or of the Earth remained fast at the poles of the Zodiack, then the Æquator of the Earth would lie exactly beneath the line of the Ecliptick, and there would be no variation in the seasons of the year, no Winter, no Summer, nor Spring, nor Autumn: but one and the same invariable aspect of things would continue. The direction of the axis of the Earth has receded therefore from the pole of the Zodiack (for lasting good) just so far as is sufficient for the generation and variety of things. Accordingly the declination of the tropicks and the inclination of the Earth's pole remain perpetually in the twenty-fourth degree; though now only 23 degrees 28 minutes are counted; or, as others make out, 29 minutes: But once it was 23 degrees 52 minutes, which are the extreme limits of the declinations hitherto observed. And that has been prudently ordained by nature, and is arranged by the primary excellence of the Earth. For if those poles (of the Earth and the Ecliptick) were to be parted by a much greater distance, then when the Sun approached the tropick, all things in the other deserted part of the globe, in some higher latitude, would be desolate and (by reason of the too prolonged absence of the Sun) brought to destruction. As it is, however, all is so proportioned that the whole terrestrial globe has its own varying seasons in succession, and alternations of condition, appropriate and needful: either from the more direct and vertical radiation of light, or from its increased tarriance above the horizon.
Around these poles of the Ecliptick the direction of the poles of the Earth is borne: and by this motion the præcession of the æquinoxes is apparent to us.
Primitive mathematicians, since they did not pay attention to the inequælities of the years, made no distinction between the æquinoctial, or solstitial revolving year, and that which is taken from some one of the fixed stars. Even the Olympick years, which they used to reckon from the rising of the dogstar, they thought to be the same as those counted from the solstice. Hipparchus of Rhodes was the first to call attention to the fact that these differ from each other, and discovered that the year was longer when measured by the fixed stars than by the æquinox or solstice: whence he supposed that there was in the fixed stars also some motion in a common sequence; but very slow, and not at once perceptible. After him Menelaus, a Roman geometer, then Ptolemy, and long afterward Mahometes Aractensis, and several more, in all their literary memoirs, perceived that the fixed stars and the whole firmament proceeded in an orderly sequence, regarding as they did the heaven, not the earth, and not understanding the magnetical inclinations. But we shall demomstrate that it proceeds rather from a certain rotatory motion of the Earth's axis, than that that eighth sphære (so called) the firmament, or non-moving empyrean, revolves studded with innumerable globes and stars, whose distances from the Earth have never been proved by anyone, nor can be proved (the whole universe gliding, as it were). And surely it should seem much more likely that the appearances in the heavens should be clearly accounted for by a certain inflection and inclination of the comparatively small body of the Earth, than by the setting in motion of the whole system of the universe; especially if this motion is to be regarded as ordained solely for the Earth's advantage: While for the fixed stars, or for the planets, it is of no use at all. For this motion the rising and settings of stars in every Horizon, as well as their culminations at the height of the heavens, are shifted so much that the stars which once were vertical are now some degrees distant from the zenith. For nature has taken care, through the Earth's soul or magnetick vigour, that, just as it was needful in tempering, receiving, and warding off the sun's rays and light, by suitable seasons, that the points toward which the Earth's pole is directed should be 23 degrees and morefrom the poles of the Ecliptick[250]: so now for moderating and for receiving the luminous rays of the fixed stars in due turn and succession, the Earth's poles should revolve at the same distance from the Ecliptick at the Ecliptick's arctick circle; or rather that they should creep at a gentle pace, that the actions of the stars should not always remain at the same parallel circles, but should have a rather slow mutation. For the influences of the stars are not so forceful as that a swifter course should be desired. Slowly, then, is the Earth's axis inflected; and the stars' rays, falling upon the face of the Earth, shift only in so long a time as a diameter of the arctick or polar circle is extended: whence the star at the extremity of the tail of the Cynosure, which once was 12 degrees 24 minutes (namely, in the time of Hipparchus) distant from the pole of the universe, or from that point which the pole of the Earth used to face, is now only 2 degrees and 52 minutes distant from the same point; whence from its nearness it is called by the modernsPolaris.Some time it will be only ½ degree away from the pole: afterward it will begin to recede from the pole until it will be 48 degrees distant; and this, according to the Prutenical tables, will be in Anno Domini 15000. ThusLucida Lyræ(which to us southern Britons now almost culminates) will some time approach to the pole of the world, to about the fifth degree. So all the stars shift their rays of light at the surface of the Earth, through this wonderful magnetical inflection of the Earth's axis. Hence come new varieties of the seasons of the year, and lands become more fruitful or more barren; hence the characters and manners of nations are changed; kingdoms and laws are altered, in accordance with the virtue of the fixed stars as they culminate, and the strength thence received or lost in accordance with the singular and specifick nature of each; or on account of new configurations with the planets in other places of the Zodiack; on account also of risings and settings, and of new concurrences at the meridian. The Præcession of the æquinoxes arising from the aequable motion of the Earth's pole in the arctick circle of the Zodiack is here demonstrated. Let A B C D be the Ecliptick line; I E G the arctic circle of the Zodiack. Then if the Earth's pole look to E, the æquinoxes are at D, C. Let this be at the time of Metho, when the horns of Aries were in the æquinoctial colure. Now if the Earth's pole have advanced to I; then the æquinoxes will be at K, L; and the stars in the ecliptick C will seem to have progressed, in the order of the signs, along the whole arc K C: L will be moved on by the præcession, against the order of the signs, along the arc D L. But this would occur in the contrary order, if the point G were to face the poles of the earth, and the motion were from E to G: for then the æquinoxes would be M N, and the fixed stars would anticipate the same at C and D, counter to the order of the signs.
Motion of the earth's pole.
At one time the shifting of the æquinoxes is quicker, at another slower, being not always equal: because the poles of the earth travel unequally in the arctick and antarctick circle of the Zodiack; and decline on both sides from the middle path: whence the obliquity of the Zodiack to the Æquator seems to change. And as this has become known by means of long observations, so also has it been perceived, that the true æquinoctial points have been elongated from the mean æquinoctial points, on this side and on that, by 70 minutes (when the prostaphæresis is greatest): but that the solstices either approach the equator unequally 12 minutes nearer, or recede as far behind; so that the nearest approach is 23 degrees 28 minutes, and the greatest elongation 23 degrees 52 minutes. Astronomers have given various explanations to account for this inequality of the præcession and also of the obliquity of the tropicks. Thebit, with the view oflaying down a rule for such considerable inequalities in the motion of the stars, explained that the eighth sphære does not move with a continuous motion from west to east; but is shaken with a certain motion of trepidation, by which the first points of Aries and Libra in the eighth heaven describe certain small circles with diameters equal to about nine degrees, around the first points of Aries and Libra in the ninth sphære. But since many things absurd and impossible as to motion follow from this motion of trepidation, that theory of motion is therefore long since obsolete. Others therefore are compelled to attribute the motion to the eighth sphære, and to erect above it a ninth heaven also, yea, and to pile up yet a tenth and an eleventh: In the case of mathematicians, indeed, the fault may be condoned; for it is permissible for them, in the case of difficult motions, to lay down some rule and law of equality by any hypotheses. But by no means can such enormous and monstrous celestial structures be accepted by philosophers. And yet here one may see how hard to please are those who do not allow any motion to one very small body, the Earth; and notwithstanding they drive and rotate the heavens, which are huge and immense above all conception and imagination: I declare that they feign the heavens to be three (the most monstrous of all things in Nature) in order that some obscure motions forsooth[251]may be accounted for. Ptolemy, who compares with his own the observations of Timocharis and Hipparchus, one of whom flourished 260 years, the other 460 years before him, thought that there was this motion of the eighth sphære, and of the whole firmament; and proved by help of numerous phenomena that it took place over the poles of the Zodiack, and, supposing its motion to be so far æquable, that the non-planetary stars in the space of 100 years completed just one degree beneath thePrimum Mobile. After him 750 years Albategnius discovered that one degree was completed in a space of 66 years, so that a whole period would be 23,760 years. Alphonsus made out that this motion was still slower, completing one degree and 28 minutes only in 200 years; and that thus the course of the fixed stars went on, though unequally. At length Copernicus, by means of the observations of Timocharis, Aristarchus of Samos, Hipparchus, Menelaus, Ptolemy, Mahometes Aractensis, Alphonsus, and of his own, detected the anomalies of the motion of the Earth's axis: though I doubt not that other anomalies also will come to light some ages hence. So difficult is it to observe motion so slow, unless extending over a period of many centuries; on which account we still fail to understand the intent of Nature, what she is driving after through such inequality of motion. Let A be the pole of the Ecliptick, B C the Ecliptick, D the Æquator; when the pole of the Earth near the arctick circle of the Zodiack faces the point M, then there is an anomaly of the præcession of the æquinox at F;but when it faces N, there is an anomaly of the præcession at E. But when it faces I directly, then the maximum obliquity G is observed at the solstitial colure; but when it faces L, there is the minimum obliquity H at the solstitial colure.
Obliquity.
Copernicus' contorted circlet in the Arctick circle of the Zodiack.
Let F B G be the half of the Arctick circle described round the pole of the Zodiack: A B C the solstitial colure: A the pole of the Zodiack; D E the anomaly of longitude 140 minutes at either side on both ends: B C the anomaly of obliquity 24 minutes: B the greater obliquity of 23 degrees 52 minutes: D the mean obliquity of 23 degrees 40 minutes: C the minimum obliquity of 23 degrees 28 minutes.
Variable obliquity.
Contorted circlet.
The period of motion of the præcession of the æquinoxes is 25,816 Ægyptian years; the period of the obliquity of the Zodiack is 3434 years, and a little more. The period of the anomaly of the præcession of the æquinoxes is 1717 years, and a little more. If the whole time of the motion AI were divided into eight equal parts: in the first eighth the pole is borne somewhat swiftly from A to B; in the second eighth, more slowly from B to C; in the third, with the same slowness from C to D; in the fourth, more swiftly again from D to E; in the fifth, with the same swiftness from E to F; again more slowly from F to G; and with the same slowness from G to H; in the last eighth, somewhat swiftly again from H to I. And this is the contorted circlet of Copernicus, fused with the mean motion into the curved line which is the path of the true motion. And thus the pole attains the period of the anomaly of the præcession of the æquinoxes twice; and that of the declination or obliquity once only. It is thus that by later astronomers, but especially by Copernicus (the Restorer of Astronomy)[252], the anomalies of the motion of the Earth's axis are described, so far as the observations of the ancients down to our own times admit; but there are still needed more and exact observations for anyone to establish aught certain about the anomaly of the motion of the præcessions, and at the same time that also of the obliquity of the Zodiack. For ever since the time at which, by means of various observations, this anomaly was first observed, we have only arrived at half a period of the obliquity. So that all the more all these matters about the unequal motion both of the præcession and of the obliquity are uncertain and not well known: wherefore neither can we ourselves assign any natural causes for it, and establish it for certain. Wherefore also do we to our reasonings and experiments magnetical here set an end and period.[253]
xxx.