16. 



ON AN IMPORTANT ERROR IN BOUVARD'S TABLES OF SATURN. 



[From the Memoirs of the Royal Astronomical Society (1849), Vol. XVII., and Monthly 

 Notices of the Royal Astronomical Society (1847), Vol. vn.]. 



HAVING lately entered upon a comparison of the theory of Saturn with 

 the Greenwich 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 abscissas, and the corresponding tabular 

 errors as ordinates. After eliminating, by a graphical process, the effects of 

 a change in the node and inclination, a well-defined inequality became 

 apparent, the period of which was nearly twice that of Saturn. One of 

 the principal terms of the perturbation in latitude (viz. that depending on 

 the mean longitude of Jupiter minus twice that of Saturn] having nearly 

 the same period, I was next led to examine whether this term had 

 been correctly 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"'67 sin {^ - 2<f>' - 60'29} + 28"'19 sin {2< - 4<' + 66'12} 



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

 argument <j) 2(f>' instead of 2< 4<', so that the two parts may be united 



