LITERARY NOTICES. 



625 



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 ex- 

 press 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 " charac- 

 teristics of half planets." That is, one of 

 thera 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 character- 

 istics of a " double planet " because we are 

 forced to consider it in its two positions, 

 aphelioyi 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 or- 

 der; for, putting nine-fifths (the reciprocal 

 of f ths) equal to r, we have seen that the 

 ratio r does very well for Mars, Jupiter, 

 Saturn, and Neptune {ivhole planets); by 

 trial we can see that r f does well for the 

 ''exterior half planets" (those beyond the 

 terms of the primary series), and also that 

 r J 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 f ths we have satisfied three terms 

 out oi seven, and to reduce the four remain- 

 ing terms to order we have made three arbi- 

 trary assumptions. The author now pro- 

 poses as a test to use the mean distance of 

 the asteroid-ring between Mars and Jupi- 



ter according to his primitive scries. 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 ( = ths) 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 variabiUty is determined from four 

 terms (Mars, Jupiter, Saturn, and asteroids) 

 the value of one of which (the mean dis- 

 tance 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 sci- 

 ence ; 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 rep- 

 resented by theory is in error by -^ 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 appi'opriate position, may be con- 

 sidered 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 \ and r \, here must become 'r\,r^,r\, 

 r f, while for Uranus's satellites r becomes 

 r |. Moreover, while in the planetary sys- 

 tem r regularly increased from Neptune in- 

 ward, 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 con- 

 ditions 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 fol- 

 low the author, since what we have just ex^ 

 amined is there assumed as fact. 



The author's theory of the Zodiacal 

 light is given at some length, and the book. 



VOL. TII.- 



10 



