( 327 ) 



changed, but applied the following corrections to the remaining ones : 



II -I- 0^005 127 374, 



III + 029 084 25, 



IV — 092 654 834, 



the amount of which is even respectively nearly 3, nearly 6 and 

 somewhat over 5 times that of the uncertainties derived just now. 

 But even if we increase the number of intervening years from 156 to 



176, our estimated uncertainties are only diminished by about — of 



their amount. We thus conclude that these periods can only be con- 

 sidered to be determined with certainty : 



that of I to 3 decimals of the second 



,, „ II, III and IV to 2 decimals ,, ,, „ 



Th'e Nautical Almanac, which, where it gives the superior conjunc- 

 tions of the satellites, gives also the synodic periods, wisely confines 

 itself to three decimals. The use of 9 decimals may therefore provi- 

 sionally be taken for astronomical humbug. Some other instances of 

 the same kind might be quoted e. g. the formerly well known con- 

 stants, 20"-4451 for the aberration and 8"-57116 for the parallax of 

 the sun ! 



3'^ Appendix. Meaning of the equations taken into account in 

 the 2°'^ part of the tables of Damoiseau. 



On p. 321 we have referred to the 3"^ appendix for information 

 as to the equations which have been taken into account for each 

 satellite in the second part of the tables of Damoiseau. We will now 

 supply this information; we will denote by U, Uo, u\, z^ii,W]iiand 

 Miv the mean longitudes of the sun, of Jupiter and of the four 

 satellites; by :to the longitude of the perihelium of Jupiter, by rt' that 

 of the Earth, by :i'iii and ttiy the perijovia of III and IV ; by //the 

 longitude of the ascending node of Jupiter's equator on its orbit ; 

 finally by An, Am and Aiy the longitudes of the ascending nodes 

 of II, III and IV each on its own fixed plane. 



In order to be able to supply the data follo^ving below we have 

 taken the daily motion of the argument of each equation from the 

 tables in the second part of Damoiseau. This amount was then mul- 

 tiplied by the synodic period expressed in days ; the product thus 

 obtained was then compared with the factor by which, in the first 



