THE PLANETS. 445 



sion of 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 

 approximatively with observed facts in the case of most 

 planets, 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 + ]2, 4 + 48, 4 + 96, 4 + 192, 



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

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

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

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

 expresses it, for n = 1, there is obtained from 4 + 2 7l - 2 .3, 

 not 4, but 5^. Otherwise, the attempt to discover such 

 approximative 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 

 unknown mass of Mercury was determined byEncke 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 

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

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

 Abhandlung uber den Cometen von Pons in den Schriften dcr 

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



Mercury ; 



Venus 



Earth 



(Earth and Moon together 



Mars 



Jupiter and his satellites 



