390 Proceedings of Philosophical Societies. [Mat, 



may be perceptible. If this error continue for a considerable time, 

 and if the variations seen in it be so slow as not to be ascribable to 

 any of the equations employed in the tables, recourse is had to the 

 combination of angles, whose periods are longer. What is trouble- 

 some in these attempts, instead of one of those combinations called 

 arguments, several occur, and it is difficult to determine upon 

 which one the choice should fall. In that case every thing is un- 

 certain, the argument as well as the coefficient of the inequality 

 sought. The observed error may be a combination of various 

 inequalities equally unknown, which will not be brought into viewr 

 for several centuries. One is therefore reduced to the necessity of 

 trying them one after another, and thus engaging in endless calcu- 

 lation without any reasonable expectation of success. The combi- 

 nation adopted may agree with preceding observations, but there is 

 little chance of their agreeing with future observations. Calculation 

 has been lengthened, and the tables increased, without any demon- 

 strated utility ; but the more thorny this path is, the more praise is 

 due to those astronomers who have the courage to enter upon it. 

 Such has been the conduct of those astronomers who have attempted 

 to ameliorate the lunar tables. But when the formula of the 

 movement of a planet is given, when all the quantities composing 

 it are known, or may be Reduced from those that are known, then 

 nothing more is wanted than patience to follow out all the 

 developeraents, apd to determine all the equations which 

 ought to enter into the tables. This at least is the advantage 

 which the formulas of the planetary disturbances present. Those 

 for which we are indebted to the author of the Mecanicjite Celeste 

 are given in his work, with an extent which appears more than 

 sufficient for the inferior planets. Nothing is wanted but a more 

 perfect knowledge of their quantity of matter : but the contrary is 

 the case with the three superior planets. Their quantities of matter 

 ought to be sufficiently known, since all the three have satellites ; 

 but tiieir motions are slower, and their relotionssucli that it becomes 

 necessary to push t!ie approximations to quantities of higher orders. 

 To this, as well as to a want of oljservations, are owing the slight 

 errors which have been found in the first tables of Jupiter and 

 Saturn, printed about 22 years ago. Since that time I\I. Laplace 

 has airaiu reviewed his theory. By making slight corrections on the 

 quantity of matter, by employing the observations made since that 

 time, and by abandoning the observations of Flamsteed, and all 

 ihoie tiiat preceded l7-^0, because they rather injure than amelio- 

 rate the fables, M. Bouvard had been able to make the calculations 

 nearly agree with the n)odern observations. He has carried his 

 hopes itilj farther, and is at present at work still more to diminish 

 the errors. Under these circumstances M. Burckhardt, who had 

 already given the analytical dcvelopemerits of the formulas of 

 Lajjlace, has con^^idercd it as useful to consider what these formulas 

 wojld give for the inecjualities of Jupiter, iis far as those of the 



