Royal Astronomical Society. H3 



4. The expression for the parallax of the planet is 



These instances suffice to show the nature of the proposed sym- 

 bolical method. 



ROYAL ASTRONOMICAL SOCIETY. 

 [Continued from vol. xxx. p. 211.] 



April 9, 1847. — On an important error in Bouvard's Tables of 

 Saturn. By Mr. Adams. 



Having lately entered upon a comparison of the theory of Saturn 

 witli the Greenvirjch observations, I was immediately struck with the 

 magnitude of the tabular errors in heliocentric latitude, and the more 

 so, since the whole perturbation in latitude is so small, that it could 

 not be imagined that these errors arose from any imperfection in the 

 theory. In order to examine the nature of the errors, I treated them 

 by the method of curves, taking the times of observation as abscissae, 

 and the corresponding tabular errors as ordinates. After elimina- 

 ting, by a graphical process, the effects of a change in the node and 

 inclination, a well-defined inequality became apparent, the period of 

 which M^as nearly twice that of Saturn. One of the principal terms 

 of the perturbation in latitude (viz. that depending on the mean lon- 

 gitude of Jupiter minus twice that of Saturn) having nearly the same 

 period, I was next led to examine whether this term had been cor- 

 rectly tabulated by Bouvard. The formula in the introduction ap- 

 peared to be accurate; but on inspecting the Table XLIL, which 

 professes to be constructed by means of this formula, I was surprised 

 to find that there was not the smallest correspondence between the 

 numbers given by the formula and those contained in the table, the 

 latter following the simple progression of sines, while the formula 

 contained two terms. The origin of this mistake is rather curious. 

 Bouvard's formula for the terms in question is 



9"-67sin{(p-2^'-60°-29}-f.28"-19sin{2^-4^'-h66°-12}; 



but in tabulating the last term he appears to have taken the simple 

 argument ^ — 2^' instead of 2f — 4ip', so that the two parts may be 

 united into a single term, 



25"-85 8in{^-2^' + 43°-88}. 



which I find very closely to represent Bouvard's Table XLII. 



After correcting the above error, and making a proper alteration 

 in the inclinations and place of the node, the remaining errors of 

 latitude are in general very small. I subjoin a correct table to be 

 used instead of Bouvard's. The constant added being 36"'0 instead 

 of 26"'0, it will be necessary to subtract 10''"0 from the final result. 



