358 ADDRESS ON PRESENTING THE GOLD MEDAL OF THE [46 



Accordingly, on the 26th of August, 1872, he presented to the Academy 

 a memoir containing a complete determination of the mutual disturbances of 

 Jupiter and Saturn, and thus serving as a base for the theories of both 

 these planets, which are closely connected with each other. 



Again, on the llth of November, 1872, he presented his determination 

 of the secular variations of the elements of the orbits of the four planets, 

 Jupiter, Saturn, Uranus, and Neptune. These variations are mutually depen- 

 dent on each other, and must be treated simultaneously. Their determination 

 consequently involves the solution of sixteen differential equations, which are 

 very complicated in form, and can only be integrated by repeated approxi- 

 mations. 



This part of the work forms a necessary preliminary to the treatment 

 of the theory of any one of these planets in particular. 



On March 17, 1873, M. Le Verrier presented to the Academy the com- 

 plete theory of Jupiter; and on July 14 in the same year he followed it up 

 by the complete theory of Saturn. 



On January 12, 1874, he presented his tables of Jupiter, founded on the 

 theory which has just been mentioned, as compared with observations made 

 at Greenwich from 1750 to 1830 and from 1836 to 1869, and with obser- 

 vations made at Paris from 1837 to 1867. 



Again, on November 9, 1874, he presented to the Academy a complete 

 theory of Uranus. Already in 1846, in his researches which led to the dis- 

 covery of Neptune, M. Le Verrier had given a very full investigation of the 

 perturbations of Uranus by the action of Jupiter and Saturn. In the memoir 

 just mentioned he gives a fresh investigation, including a full treatment of 

 the perturbations of Uranus by the action of Neptune. 



On December 14, 1874, he presented a new theory of the planet Neptune, 

 thus completing the theoretical part of the immense labours which he had 

 undertaken with respect to the planetary system. 



Finally, on August 23, 1875, he presented to the Academy the com- 

 parison of the theory of Saturn with observations. 



Such is a bare enumeration of the various labours for which our science 

 is already indebted to our illustrious Associate. 



That any one man should have had the power and perseverance required 

 thus to traverse the entire solar system with a firm step, and to determine 



