368 ADDRESS ON PRESENTING THE GOLD MEDAL OP THE [46 



perturbations he derives the disturbed longitude and radius vector by the 

 ordinary formulae of elliptic motion. 



Where the perturbations are large, M. Le Verrier considers this prefer- 

 able to the ordinary method of proceeding. 



The perturbations of latitude being small, he applies to the inclination 

 and longitude of the node their secular variations alone, and then determines 

 directly the periodic inequalities of latitude. 



All these perturbations, whether of the elements or of the latitude, are 

 developed in a series of sines and cosines of multiples of the mean longitude 

 of Saturn, including a constant term, the coefficients multiplying these several 

 terms being functions of the mean elongation of Saturn from Jupiter, which 

 for a given elongation are developed in powers of the time reckoned from 

 the epoch 1850. 



These coefficients only are tabulated with the mean elongation as the 

 argument, and the perturbations are thence calculated by means of the 

 ordinary trigonometrical tables. 



The intervals of the argument are so small, that the requisite interpo- 

 lations are very simple, and the coefficients which relate to the four elements, 

 and depend on the same argument, are given at the same opening of the 

 tables. 



The tables have been calculated specially for the 500 years included 

 between the years 1850 and 2350. Nevertheless they may be applied to 

 epochs anterior to 1850, by simply changing the sign of the time reckoned 

 from 1850. For one or two centuries before 1850 this extension will have 

 all the rigour of modern observations, while for still earlier times the accuracy 

 of the tables will greatly surpass that of the observations which we have to 

 compare with them. 



M. Le Terrier's Tables of Jupiter are now employed in the computations 

 of the Nautical Almanac, beginning with the year 1878. 



The 13th Volume of the Annals is devoted to the theories of Uranus 

 and Neptune. These theories are not unattended with difficulties. 



In the first place, these planets are disturbed by the actions of the two 

 great masses, Jupiter and Saturn, interior to their orbits, and these actions 

 are modified by the great inequalities of Jupiter and Saturn depending on 



