322 SPECIAL RESULTS IN THE URANOLOGICAL 



with which the distances should agree, is not even a conti- 

 nuous series at all. The number preceding 4 + 3 ought 

 to be not 4 i. e. 4 + but 4 + lj. So between 4 and 

 4 + 3 there should be an indefinite number of intermediate 

 quantities ; or, as Wurm expresses it, for n= 1 the result of 

 4 + 3 x 2 n ~ 2 is not 4, but 5J. Attempts to discover such 

 approximate agreements in Nature are, however, by no 

 means to be censured ; the greatest men of all periods have 

 been fond of such lusus ingenii/' 



5. Masses of the Planets. The masses of the planets 

 are investigated by means of their satellites (where such 

 exist), of their mutual perturbations, or of the effects suf- 

 fered or produced by a comet of short period. Thus in 

 1841 Encke determined, from the perturbations undergone 

 by the comet which bears his name, the previously unknown 

 mass of Mercury. The same comet affords a prospect of 

 future corrections for the mass of Venus. The perturba- 

 tions of Yesta are made use of for Jupiter. The mass of 

 the Sun being taken as unity, we have (according to Encke's 

 fourth memoir on the comet of Pons, in the " Schriften der 

 Berliner Akademie der Wissenschaften" fur 1842, S. 5) : 



Mercury . . 



Yenus 



Earth 



Earth and Moon together 



Mars .... 



Jupiter with his satellites 



Saturn . - i 



Uranus . V .* : < 



"Neptune -, 1 -- . '- 



