on the anomaly of the præcession of the equinoxes, and of the obliquity of the zodiack.

a t 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 of laying 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 forsooth251 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 the primum 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.

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.

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}

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