398 Correction of an oversight in Lagrange’s Formule. 
i ; ‘ 
=i 16. Natural History of the Grub, or Vine-fretter. (Pu- 
ceron.)—The 25th of May, 1809, M. Duvau placed under a 
glass with food, a bean grub, (puceron de la féve) which he 
had just taken at the moment of its issuing from the body of 
3 ed 
‘& s 
fact was confirmed in 1740, by the nice experiments of Bon- 
net. Réamur and Degur showed, two years afterwards, that 
it is possible to obtain ten generations successively of puce- 
ngs under glasses. M. Duvau has of course 
obtained one generation more than Réamur.—Annales de 
Chim. et de Phys. Jon. 1825. 
_ APPENDIX. 
Correction of an oversight in Lagrange’s formule for de- 
termining the motions of any system of bodies immediately 
ae about a state of equilibrium, by 1. J. A.* 
It appears to the writer of this, that Lagrange, in copying 
out for the press, the formulz which he has given at page 
351, vol I. of the Mécanique Analytique, for determining the 
stability of equilibria, and the laws of the small oscillations 
of any system of bodies, has inadvertently omitted certain 
terms which are essentially necessary to the correctness of 
the results. The quantities there denoted by the characters 
[1], [2], [3], ,2], &e. are the coefficients of the terms con- 
taining two dimensions of the independent variables in the 
general value of V, which is formed by developing, accord- 
ing to the powers of the increments of the three original co- 
ordinates, the algebraic function M1, giving to these co-oF- 
. Received too late for insertion in its proper place.—Ed. 
