The next question examined in the book, is the reason why the zodiac is divided into 360 degrees; and on this subject, he soon becomes enveloped in a variety of subtle considerations, (not very intelligible in the original, and still more difficult to explain shortly to others unacquainted with it,) in relation to the divisions of the musical scale; the origin of which he identifies with his five favourite solids. The twentieth chapter is appropriated to a more interesting inquiry, containing the first traces of his finally successful researches into the proportion between the distances of the planets, and the times of their motions round the sun. He begins with the generally admitted fact, that the more distant planets move more slowly; but in order to show that the proportion, whatever it may be, is not the simple one of the distances, he exhibits the following little Table:— ♄ +--+--------+ | |D. Scr. | ♃ +--+--------+---------+ |♄ |10759.12| D. Scr. | ♂ +--+--------+---------+--------+ |♃ | 6159 | 4332.37 |D. Scr. | ♁ +--+--------+---------+--------+-------+ |♂ | 1785 | 1282 | 686.59 |D. Scr.| ♀ +--+--------+---------+--------+-------+-------+ |♁ | 1174 | 843 | 452 |365.15 |D. Scr.| ☿ +--+--------+---------+--------+-------+-------+---------+ |♀ | 844 | 606 | 325 |262.30 |224.42 | D. Scr. | +--+--------+---------+--------+-------+-------+---------+ |☿ | 434 | 312 | 167 |135 |115 | 87.58 | At the head of each vertical column is placed the real time (in days and sexagesimal parts) of the revolution of the planet placed above it, and underneath the days due to the other inferior planets, if they observed the proportion of distance. Hence it appears that this proportion in every case gives a time greater than the truth; as for instance, if the earth's rate of revolution were to Jupiter's in the proportion of their distances, the second column shows that the time of her period would be 843 instead of 365¼ days; so of the rest. His next attempt was to compare them by two by two, in which he found that he arrived at a proportion something like the proportion of the distances, although as yet far from obtaining it exactly. This process amounts to taking the quotients obtained by dividing the period of each planet by the period of the one next beyond. { ♄ 10759.27} be successively taken to { ♃ 403 { ♃ 4332.37 } consist of 1000 equal { ♂ 159 { ♂ 686.59 } parts, the planet next { ♁ 532 For if each of the { ♁ 365.15 } below will contain { ♀ 615 periods of { ♀ 244.42 } of those parts in { ☿ 392 But if the distance of each planet in { ♃ 572 succession be taken to consist of { ♂ 290 1000 equal parts, the distance of { ♁ 658 the next below will contain, according { ♀ 719 to Copernicus, in { ☿ 500