344 



Mr. H. Breeu on the Corrections 



[Mar. 18, 



III. " On the Corrections of BouvarcVs Elements of Jupiter and 

 Saturn (Paris, 1821) ." By Hugh Breen, formerly of the 

 Royal Observatory, Greenwich. Communicated by Professor 

 G. G. Stokes, Sec. R. S. Received December 17, 1868. 



The Tables of Jupiter and Saturn which have been used for some years 

 past in the computations of the 'Berliner Jahrbuch' and ' Nautical Al- 

 manac/ differ more from observation than is consistent with the present re- 

 quirements of astronomy ; and, moreover, abundant means for the correction 

 ofBouvard's ' Elements' exist in the publication of the Greenwich Plane- 

 tary Observations, 1750-1835, and the annual volumes issued from the 

 Royal Observatory since 1836. The present work, which has been under- 

 taken for this purpose, is based exclusively on the Greenwich Observations, 

 1750-1865. 



Each mean group of observations in the Greenwich Planetary Reduc- 

 tions &c. gives the mean error of the planet's tabular geocentric place, 

 with its equivalent in terms of the heliocentric errors of the earth and 

 planet ; but in the present investigation the places of Carlini's Solar 

 Tables, which have been used throughout the whole period (with the ex- 

 ception of 1864 and 1865), have been accepted without alteration ; for 

 Jupiter and Saturn the factors of the earth's heliocentric errors are so 

 small, that the difference of Carlini's Solar Tables from the recent investiga- 

 tions of Leverrier may be neglected. 



The coefficients of the errors of the elements in heliocentric longitude 

 and radius vector, for different values of the mean anomaly, are calculated in 

 the usual way ; and the formation of the equations of condition is effected 

 by their multiplication by the printed factors of the heliocentric errors of 

 the planet in the Greenwich Observations. A weight is assigned to each 

 equation of condition, dependent on the number of observations in the 

 group, and the relation of the geocentric and heliocentric errors. The 

 equations thus, multiplied by the weights, are then solved by the method 

 of least squares. The results are given in the following Table : — 



Jupiter. 



1750, October 29, to 1771, July 14. 

 $a =- 0-000331873. 

 $e =+ 0-00000123252. 

 8t =- 4"-284354. 

 §Tf =-22"-36544. 

 SI =- 0"-311. 



SN= + 99"-1819 (neglecting Mas insensible). 



8a is the error of the planet's semiaxis major, Se is the error of the 

 eccentricity, $t is the error of the epoch of the mean longitude, and for is 

 the error of the longitude of the perihelion, 81 is the error of the inclina- 

 tion, and 8N is the error of the longitude of the node. 



