| Book V. | ||||||||||||||
| If the inner Surface of the orbit of | { | Saturn | } | be taken at 1000, then the outer one of | { | Jupiter | = | 577 | } | According to Copernicus they are | { | 635 | Ch. | 9 |
| Jupiter | Mars | = | 333 | 333 | — | 14 | ||||||||
| Mars | Earth | = | 795 | 757 | — | 19 | ||||||||
| Earth | Venus | = | 795 | 794 | — | 21, 22 | ||||||||
| Venus | Mercury | = | 577 | 723 | — | 27 | ||||||||
It will be observed, that Kepler's results were far from being entirely satisfactory; but he seems to have flattered himself, that the differences might be attributed to erroneous measurements. Indeed, the science of observation was then so much in its infancy, that such an assertion might be made without incurring much risk of decisive refutation.
Kepler next endeavoured to determine why the regular solids followed in this rather than any other order; and his imagination soon created a variety of essential distinctions between the cube, pyramid, and dodecahedron, belonging to the superior planets, and the other two.
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:—
| ♄Saturn | ||||||
| D. Scr. | ♃Jupiter | |||||
| ♄Saturn | 10759.12 | D. Scr. | ♂Mars | |||
| ♃Jupiter | 6159 | 4332.37 | D. Scr. | ♁Earth | ||
| ♂Mars | 1785 | 1282 | 686.59 | D. Scr. | ♀Venus | |
| ♁Earth | 1174 | 843 | 452 | 365.15 | D. Scr. | ☿Mercury |
| ♀Venus | 844 | 606 | 325 | 262.30 | 224.42 | D. Scr. |
| ☿Mercury | 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.
| For if each of the periods of | { | ♄Saturn | 10759.27 | } | be successively taken to consist of 1000 equal parts, the periods of the planet next below will contain of those parts in | { | ♃Jupiter | 403 |
| ♃Jupiter | 4332.37 | ♂Mars | 159 | |||||
| ♂Mars | 686.59 | ♁Earth | 532 | |||||
| ♁Earth | 365.15 | ♀Venus | 615 | |||||
| ♀Venus | 244.42 | ☿Mercury | 392 |
| But if the distance of each planet in succession be taken to consist of 1000 equal parts, the distance of the next below will contain, according to Copernicus, in | { | ♃Jupiter | 572 |
| ♂Mars | 290 | ||
| ♁Earth | 658 | ||
| ♀Venus | 719 | ||
| ☿Mercury | 500 |
From this table he argued that to make the proportions agree, we must assume one of two things, "either that the moving intelligences of the planets are weakest in those which are farthest from the Sun, or that there is one moving intelligence in the Sun, the common centre forcing them all round, but those most violently which are nearest, and that it languishes in some sort, and grows weaker at the most distant, because of the remoteness and the attenuation of the virtue."
We stop here to insert a note added by Kepler to the later editions, and shall take advantage of the same interruption to warn the reader not to confound this notion of Kepler with the theory of a gravitating force towards the Sun, in the sense in which we now use those words. According to our theory, the effect of the presence of the Sun upon the planet is to pull it towards the centre in a straight line, and the effect of the motion thus produced combined with the motion of the planet, which if undisturbed would be in a straight line inclined to the direction of the radius, is, that it describes a curve round the Sun. Kepler considered his planets as perfectly quiet and unwilling to move when left alone; and that this virtue supposed by him to proceed in every direction out of the Sun, swept them round, just as the sails of a windmill would carry round anything which became entangled in them. In other parts of his works Kepler mentions having speculated on a real attractive force in the centre; but as he knew that the planets are not always at the same distance from the Sun, and conceived erroneously, that to remove them from their least to their greatest distance a repulsive force must be supposed alternating with an attractive one, he laid aside this notion as improbable. In a note he acknowledges that when he wrote the passage just quoted, imbued as he then was with Scaliger's notions on moving intelligences, he literally believed "that each planet was moved by a living spirit, but afterwards came to look on the moving cause as a corporeal though immaterial substance, something in the nature of light which is observed to diminish similarly at increased distances." He then proceeds as follows in the original text.