196 Astronomical and Nautical Collections. 



than is consistent with collateral evidence ; the changes in 

 the position of the earth's axis, for example, both in its 

 direction and its inclination, being considerably greater than 

 the results of the best theories would lead us to expect in the 

 time that has elapsed. 



We may suppose, in the first instance, that the epoch of 

 the sun's mean longitude (P. 81) is correctly laid down as 

 330° 45', and his true longitude 333° 8'; the great equation,. 

 2° 23', being found in the table of Prosthaphaereses (P. 78), 

 opposite to the mean anomaly 265° 15': then, taking the sun's 

 mean longitude at the beginning of the corresponding Gre- 

 gorian year, as about 280°, the difference in the sun's longi- 

 tude becomes about 50° 45' ; and it will be most convenient 

 to reduce the places of the planet to the beginning of such 

 a year, in order to compare them with the modern tables, 

 which are arranged according to Julian years ; the difference 

 of these years not being material for the present purpose. 

 We thus obtain from the epochs of the tables, which are 

 296° 43' and 184° 41' (P. 213, 216), 295° for Saturn, and 

 180° 23' for Jupiter ; that is, in the decimal notation of Bou- 

 vard, about 328^'^" and 200^'' respectively. 



We now find that Saturn had returned nearly to the same 

 mean longitude at the beginning of 1814 ; for which we have 

 327.07 : and if we look back for all the years at the begin- 

 ning of which the longitude is the same within a very few 

 degrees, we shall observe recurrences more or less exact at 

 periods of 2, of 7, and of 12 revolutions, corresponding to 

 59, 206, and 353 years ; and we may easily make a table of 

 all those which particularly require attention. 



^ GR 



335/ 



322 f 



327 



333 



326 



331 



323 



Among these dates, those which afford the nearest coinci- 

 dences are -893, -834, -687, and -746: and it is sufii- 



