8. 



MASSES OF JUPITER'S SATELLITES CONSISTENT WITH DAMOISEAU'S 



CONSTANTS. 



[!N Damoiseau's "Tables Ecliptiques des Satellites de Jupiter" the 

 following masses are attached to the Satellites, that of Jupiter being unity. 



I 0-0000168770 



II 0-00002322696 



III 0-0000884370 



IV 0-0000424751 



Jupiter's Compression ,-^-TQO 



1 O 4*7 j 



These results as well as others whose determination depends upon 

 theory are based upon constants which Delambre derived from the obser- 

 vations. Damoiseau's own reduction of the observations educed constants 

 sensibly different, and, as he remarks, it is to be expected that the values 

 of the masses, &c., which are consistent with them will also differ sensibly 

 from the above. However he does not consider the degree of exactness 

 to be expected from such tables warrants a new computation. It appears 

 from the following note that his constants imply very considerable departures 

 from the above values.] 



The process followed is that of the Mecanique Celeste, 1. vin. ch. IX., 

 with certain modifications. 



The first equation is derived from the coefficient of the great in- 

 equality of I which depends upon the action of II. In his Introduction, 

 p. iv, Damoiseau gives this the value 3 m 13 9 -079 = d '00223471. This is the 



