ninths, and of the number thus obtained we again take five-ninths and so on, we thus form a geometrical series of numbers. Of the first eight of these numbers four express roughly the mean distances of Mars, Jupiter, Saturn, and Neptune (of course this distance is represented as it forms the starting-point of the process): one is roughly the distance of Mercury in aphelion (not its mean distance, which is the element of the problem, but its largest distance from the sun); one lies between Venus and the earth, one between Mars and Jupiter, and one between Uranus and Saturn, but much nearer Uranus. So far all is fact, and the candid observer arrived at this point might be supposed to say. With five-ninths as a ratio I can satisfy only three out of the seven conditions I seek to satisfy, and hence five-ninths is not the ratio I want. But at this point the author makes three assumptions: 1. The earth and Venus have the "characteristics of half planets." That is, one of them is on each side of one term of the author's utterly arbitrary geometrical series. 2. Uranus being on one side of another of these terms (although no planet is on the other side), it also will be considered as a "half planet." 3. Mercury has characteristics of a "double planet" because we are forced to consider it in its two positions, aphelion and perihelion, in order to make it agree with the above-mentioned arbitrary geometrical series. Now we have the basis for reducing these disorderly half, double, and missing planets, to something like order; for, putting nine-fifths (the reciprocal of 59ths) equal to r, we have seen that the ratio r does very well for Mars, Jupiter, Saturn, and Neptune (whole planets); by trial we can see that r 34 does well for the "exterior half planets" (those beyond the terms of the primary series), and also that r 12 will serve for Venus, an "interior half planet" "the only existing example of its kind in the planetary system."
These are the principal conclusions of the first two sections of the work: with a given ratio 59ths we have satisfied three terms out of seven, and to reduce the four remaining terms to order we have made three arbitrary assumptions. The author now proposes as a test to use the mean distance of the asteroid-ring between Mars and Jupiter according to his primitive series. The terms for Saturn, Jupiter, and Mars, are known, and that for the asteroids can be put in by a simple proportion. He finds by this process that the ratio r (= 95ths) will satisfy the existing numbers better if we gradually decrease it as we go farther from the sun, and therefore this r, which at first was constant, is made variable, and the law of its variability is determined from four terms (Mars, Jupiter, Saturn, and asteroids) the value of one of which (the mean distance of the asteroid-ring) must long remain unknown; and in this way a "criterion" is set up. After this it is impossible to speak of this part of the book as a work of science; it is rather an exhibition of fancy. Tennyson has called the profession of the law "a multitude of single instances;" and, without passing the limits of decorum or truth, we may characterize the steps by which these final laws are reached in the same way. After all this adjustment of values, the mean distance of Uranus as represented by theory is in error by 150 of its entire amount—a trifle of 7,000,000 miles. A foot-note here says, "Why, after all, Uranus seems to have, as it were, fallen in from his appropriate position, may be considered in another connection."
The satellite systems of Jupiter and Saturn are next considered, and similar laws are found to obtain; except that r, which for the planetary system was altered only into r 34 and r 12, here must become r 12, r 67,r 14, r 56, while for Uranus's satellites r becomes r 23. Moreover, while in the planetary system r regularly increased from Neptune inward, in the system of Jupiter it decreases and in that of Saturn it is constant.
It seems hardly surprising that, with so much liberty of assumption, any set of conditions can be approximately fulfilled, and it is well to remember that, even if a much better fulfillment of these conditions could be made, it would not show that a physical law existed. This fallacy underlies the whole book.
Section 3 is devoted to "Theoretical Considerations," and here we will not follow the author, since what we have just examined is there assumed as fact.
The author's theory of the Zodiacal light is given at some length, and the book
