Permanent Contraction of the Planetary Orbits. 103 



others. The large amount of this contraction is strong 

 presumptive evidence against the existence of a planetary- 

 body beyond Neptune. 



The contraction of the orbit of Uranus would appear to 

 have been greatly influenced by the counter attraction of 

 the larger mass of Neptune, so that the difference from 

 Bode's numbers does not amount to more than 0*41, as 

 shown in the table. For like reasons, through the joint 

 attraction of Uranus and Neptune, the contraction of the 

 radius vector of Saturn only amounts to 0*46, notwithstanding 

 his comparative nearness to the enormous mass of Jupiter. 



The very near coincidence of Bode's numbers with the 

 •actual radius vector of Jupiter is equally interesting with 

 the abrupt variation in the magnitude and order of the 

 intra-jovial planets, the united masses of which are insuffi- 

 cient to overcome the counter attraction of Saturn, Uranus, 

 and Neptune. Hence the radius vector of Jupiter remains 

 ■without change up to the present time, or is even extended 

 by the small fractional quantity shown in the table. 



The minor planets also offer an interesting case of con- 

 traction of the radii vectores by their interaction on each 

 other. Out of the total number of these bodies which have 

 so far been discovered (more than 300) only one-fourth of 

 them have orbits above the theoretic distance 2 - 8 ; the 

 actual mean distance of the whole number being 275. 



The very near agreement of the Earth's mean distance 

 with Bode's numbers may be regarded as the result of the 

 •equilibrium established by the opposite attractions of Venus 

 and the outer planets. The small mass of Mars in relation 

 to the Earth and Venus would appear to be the cause of 

 the contraction of his radius vector within the theoretic 

 •distance ; while the joint attractions of the Earth and 

 •exterior planets increase the radius vector of Venus a 

 fraction above the amount required by Bode's law, as is seen 

 in the orbit of Jupiter. 



