Cliase.] bZo [Sept. 17, 



to reduce them to the centrifugal units wliicli are given in the first table. 

 Majcing the reduction, we find that the values found by the two methods 

 differ by less than three-quarters of one per cent. 



Let us take the differences between the perihelion planets of successive 

 two-planet groups. 



Neptune 392.1344 



Uranus 280.0496 



Jupiter 105.2344 1^4-8152 



Earth 30.5480 '^^•6864 



Sun 0.0000 30-^480 



^Yenus ■ 11.9800 l^-^^OO 



i Mercury 7.4956 ^"^^^^ 



If we then divide Neptune by the first difference, the first difference 

 by the second, and so on, we get the harmonic series f|, ff, f|, ||-, ff ; 

 the numerator being the quantity which is contained 9 times in the 

 prime multiple, 7 times in Neptune, 5 times in Uranus, and 3 times 

 in Saturn, and the greatest error in any of the theoretical denomina- 

 tors being less than one-half of one per cent. As the relative values of 

 the rotation-radii depend on the square-roots of the orbital times, which 

 have been determined with more precision than any other astronomical 

 elements, these harmonies are known with great exactness. 



The harmonies of which Earth forms a constituent seem, as I have re- 

 peatedly shown,* to be moi'e numerous than those in which other planets 

 are exclusively involved. Is it because we are best fitted for observing 

 things with which we are most nearly concerned, or because Earth is 

 really of more present importance and is therefore purposely provided 

 with more various adaptations for the nurture of intelligence than either 

 of its sister orbs, or is it for merely aesthetic reasons, the harmonies 

 being chords in the eternal hymn of praise which ascends from every por- 

 tion of the created universe to its Creator ? 



A new modification of the harmonic law, in the case of Venus and 

 Mercury, is shown, not only by the fact already mentioned, that the half- 

 radius is introduced, (as if through a renewed operation of the relations 

 between the radii which equalize the velocity of infinite fall and circu- 

 lar orbital velocity), but also by the intervention of Sun, which may per- 

 haps be taken as an additional evidence that the parabolic connection of 

 the solar system with its proper stellar system has produced a parabolic 

 spiral, and may therefore be regarded as a further confirmation of Prof. 

 Alexander's views. If we suppose, in accordance with the analogies of 

 organic development, that the orderly processes were going on simul- 

 taneously throughout the universe, we may readily conceive that the 

 assignment of the interior planets to their appointed places was not only 

 the completion of our own Cosmos, but that it was also synchronous with 

 the completion of the stellar- nebular group to which we belong. 



* Perhaps the most important of those harmonies may be the retention by Earth of 

 one-half Sun's angular rotation enerj<y; Sun's superficial gravity giving the velocity 

 of light in a half- rotation, Earth's, in a whole revolution. 



