366 ADDRESS ON PRESENTING THE GOLD MEDAL OF THE [46 



the values of the masses which would be found from the different equations 

 of condition. 



By means of the work which has just been described everything has 

 been prepared which is required for the treatment of the theories of the 

 several planets. 



The remainder of the llth Volume of the Annals is accordingly occupied 

 by the complete theories of Jupiter and Saturn, the former theory being 

 given in Chapter 20 and the latter in Chapter 21 of M. Le Terrier's 

 researches. 



The coefficients of the periodic inequalities of the mean longitudes and 

 of the elements of the orbits are not only exhibited in a general form, but 

 are also calculated numerically for the five principal epochs considered in 

 Chapter 19 of these researches, viz. for 1850, 2350, 2850, 3350, and 3850. 



The long inequalities of the second order with respect to the masses, 

 depending on twice the mean motion of Jupiter plus three times the mean 

 motion of Uranus minus six times the mean motion of Saturn, are also 

 determined in a similar form. 



Chapter 22 of M. Le Terrier's researches, forming the first part of the 

 12th Volume of the Annals, contains the comparison of the theory of Jupiter 

 with the observations, the deduction of the definitive corrections of the 

 elements therefrom, and finally the resulting tables of the motion of Jupiter. 



The observations employed are the Greenwich observations from 1750 to 

 1830 and from 1836 to 1869, together with the Paris observations from 1837 

 to 1867. 



To the results given in the Astronomer Royal's "Reduction of the 

 Greenwich Observations of Planets from 1750 to 1830" M. Le Verrier has 

 applied the corrections which he has found to be required by his own 

 reduction of Bradley's observations of stars and his redetermination of the 

 Right Ascensions of the fundamental stars, published in the 2nd Volume of 

 the Annals (Chapter 10). 



The equations of condition in longitude, for finding the corrections of 

 the elements and of the assumed mass of Saturn, are divided into two series 

 corresponding to the observations made from 1750 to 1830, and into two 

 other series corresponding to the observations made from 1836 to 1869. 



