V 



OF ARTS AND SCIENCES. 197 



Three hundred and twenty-seventh meeting. 



February 6, 1850. — Monthly Meeting. 



The President in the chair. 



Professor Gray, from the Publishing Committee, announced 

 the publication of a new half-vohmie of the Memoirs of the 

 Academy, namely, Vol. IV. Part I. (new series), and laid a 

 copy on the table. 



Professor Peirce made a communication on a new method 

 of computing the constants of the perturbative function of 

 planetary motion. 



" The researches of Laplace and Legendre left the theory of 

 these constants, and of their mutual relations, in a state which seems 

 to require no farther development. But their methods of computation 

 consisted in formulae, by which the constants were derived from each 

 other in such a way, that the defects of imperfect approximation were 

 aggravated at each step, and finally became intolerable in the more 

 remote constants and their higher differential coefficients. The 

 labors of Pontecoulant varied in some degree the form, but not the 

 nature or extent, of these difficulties. In his theory of Mercury, 

 Leverrier has discussed the defects of the old form of computation, 

 and proposed a new method, by which each constant and differential 

 coefficient is determined directly, either from the usual series in the 

 case of the constant itself, or from a very ingenious transformation of 

 the series in the case of the differential coefficients. Leverrier has 

 proposed and executed the exact determination, once for all, of the 

 coefficients of these series, but has not yet published them. I was 

 also permitted, several months ago, to examine a table of Leverrier's 

 coefficients, which was calculated with the greatest care by Mr. Sears 

 C. Walker. Leverrier's transformations were derived from observing 

 that the successive terms of the original series differ very little in the 

 values of their coefficients. A recent examination of the forms of 

 these coefficients has led me to make the computation of the constants 

 and of their differential coefficients depend upon certain auxiliary 

 series, which approximate as much more readily than Leverrier's as 

 his transformed series do in comparison with the original series. The 

 principle of this new approximation consists in the very small differ- 

 ence which may be observed between the corresponding terms of dif- 



