MATHEMATICAL SECTION. Tz 
sion of the argument of the inequalities under consideration, are 
necessarily quite large, approximate values of the coefficients may 
be obtained by semi-convergent series similar to the well-known 
theorem of Stirling. This matter was first elaborated by Cauchy,* 
but in the method as left by him we are directed to compute special 
values of the successive derivatives of the functions to be developed. 
Now it unfortunately happens that these functions are enormously 
complicated by successive differentiation, so that it is almost impos- 
sible to write at length their second derivatives. Manifestly then, 
it would be a great saving of labor to substitute for the computation 
of special values of these derivatives a computation of a certain 
number of special values of the original function, distributed in 
such a way that the maximum advantage may be obtained. This 
modification has given rise to an elegant piece of analysis. 
It will be noticed that in this method it is necessary to substitute 
in the formule, from the outset, the numerical values of the elements 
of the orbits of the earth and planet. There seems to be no objec- 
tion to this on the practical side, as for the computation of the 
inequalities sought no partial derivatives of R, with respect to 
these elements, are required. 
The paper is printed in full in the American Journal of Mathe- 
matics, Vol. VI. 
Mr. E. B. Evutorr made a communication on 
UNITS OF FORCE AND ENERGY, INCLUDING ELECTRIC UNITS. 
SeventH MEETING. NOVEMBER 21, 1883. 
The Chairman presided. 
Thirteen members present. 
* Mémoire sur les approximations des fonctions de trés-grands nombres, and 
, Rapport sur un Mémoire de M. Le Verrier, qui a pour objet la détermination 
dune grande inégalité du moyen mouvement de la planéte Pallas. Comptes 
Rendus de Académie des Sciences de Paris. Tom. XX, pp. 691-726, 767-786, 
825-847. 
