370 ADDRESS ON PRESENTING THE GOLD MEDAL OF THE [46 



By the application of his own general formulae, M. Le Verrier deduces 

 from these elements the values of the mean elliptic elements corresponding 

 to the same epoch. 



It may be remarked that the mean elements thus determined will depend 

 on the assumed masses of the two planets, and will therefore require small 

 corrections when more accurate values of the masses have been obtained. 



When the secular variations of Uranus and Neptune given in Chapter It) 

 were found, the elements were less accurately known, and M. Le Verrier has 

 therefore recalculated the values of the eccentricities and longitudes of the 

 perihelia of the two planets for the same five epochs as before, starting from 

 the mean elliptic values of the elements above referred to. 



Chapter 26 contains the completion of the theory of Uranus. The last 

 chapter, which contains the completion of the theory of Neptune, is not yet 

 printed. 



The 23rd Chapter also, which contains the comparison of the theory of 

 Saturn with observations, together with the tables of the planet, and which 

 will form the latter part of the 12th Volume of the Annals, is not yet 

 printed. The results of this comparison of the theory with observations 

 have, however, been fully published in the Comptes Rendus, and I under- 

 stand that the tables will be used for computing the place of Saturn in the 

 forthcoming volume of the Nautical Almanac. 



Although the comparison of the theory of Saturn with observations shews 

 in general a satisfactory accordance, there occur some discrepancies in indi- 

 vidual years which are larger than might be desired. 



During the thirty-two years over which the modern observations extend, 

 viz. from 1837 to 1869, the discrepancy between theory and observation, 

 however, remains constantly less than 2"'5 of arc, excepting in two instances, 

 viz. in the years 1839 and 1844, when the differences amount to 4"'5 of arc. 



In the ancient observations only, made in the time of Maskelyne, rather 

 larger differences occur, amounting in two instances to nearly 9" of arc. 



In order to test whether these discrepancies could be due to any imper- 

 fections in the theory, M. Le Verrier has not shrunk from the immense 

 labour of forming a second theory of the planet independent of the former, 

 employing methods of interpolation instead of the analytical developments. 



