144 



Royal Astronomical Society. 



Table XLII. — Argument III. de la Longitude. 



Constante ajoutee 36"'0. 



On the Development of the Disturbing Function R. By Sir John 

 Lubbock. 



The greatest practical difficulty which is encountered in the pla- 

 netary theory consists in the development of the expression for the 

 reciprocal of the linear distance between the disturbed and disturbing 

 planets. The algebraical expression of this development may be 

 obtained either by means of the binomial theorem or by Taylor's 

 theorem applied to several variables ; by the latter method M. Binet 

 has carried the development as far as terms of the 7th order. But 

 when high powers of the eccentricities and inclinations are retained, 

 the expressions become excessively complicated, so that further pro- 

 gress in this direction appears utterly hopeless. 



The numerical coefficients of the series may also be obtained by 

 quadratures ; but to determine all the coefficients in this way would 

 involve very great labour. 



In considering the problem of the perturbations of bodies whose 

 eccentricities and inclinations are considerable, the author has been 

 led to another mode of development, which he conceives to possess 

 great advantages over those just mentioned, and the use of which 

 may be greatly facilitated in all cases by special tables, which may 

 be prepared beforehand. 



