118 



COSMOS. 



the discovery of Pallas by Olbers, aptly criticised the so- 

 called law of distances in a letter to Zach (October, 1802). 

 " The statement of Titius," says he, " contrary to the nature 

 of all truths which merit the name of laws, agrees only ap- 

 proximatively with observed facts in the case of most plan- 

 ets, and, what does not appear to have been once observed, not 

 at all in the case of Mercury. It is evident that the series 



4, 4 + 3, 4 + 6, 4+12, 4 + 48, 4 + 96, 4+192, 



with which the distances should correspond, is not a continu- 

 ous series at all. The member which precedes 4 + 3 should 

 not be 4 ; i. e., 4 + 0, but 4 + 1^. Therefore, between 4 and 

 4 + 3, there should be an infinite number ; or, as Wurm ex- 

 presses it, for n = l, there is obtained from 4 + 2"~ 2 .3, not 4, 

 but 5±. Otherwise, the attempt to discover such approxi- 

 mative similarities in nature is by no means to be censured." 

 5. Masses of the Planets. — These elements are determined 

 by satellites when there are any, by the mutual disturbances 

 of the principal planets among each other, or by the influence 

 of a comet of brief revolution. In this way the hitherto un- 

 known mass of Mercury was determined by Encke in 1841, 

 by the disturbances which his comet suffered. The same 

 comet offers a prospect of a future improvement in the esti- 

 mation of the mass of Venus. The disturbances of Vesta aie 

 applied to Jupiter. The mass of the Sun being taken as 

 unity, those of the planets are (according to Encke, vierte 

 Abhandlung iiber den Cometen von Pons in den Schriften 

 der Berliner Akademie der Wissenschaften for 1842, p. 5) ■ 



Mercury 



Venus 



Earth 



_i 



4 8 6 5T5 1 



_1_ 



4 18 3 9 



_1 



3 5 955 1 



numbers which Kepler considered, in accordance with the Tychonic 

 system, to be the true ones. I quote the latter from Newton's work 

 De Mundi Systemate (Opuscula Math. Philos. et Philol., 1744, torn, ii., 

 p. 22) : 



