/ 
sums of several classes of infinite series. 281 
3*« — &c. is equal to zero for any finite value of n> yet that 
when n is infinite, the sum of this series is also infinite. 
It was my intention to have produced from several of the 
series whose sums have been found in this Paper, the values 
of several continued products ; but the length to which it 
has already extended will prevent me from more than 
merely noticing, that many very curious ones will present 
themselves by integrating the series whose sums have been 
given. 
Since this Paper was written, in a conversation with M. 
Poisson, I mentioned one of the series which it contained, and 
remarked, that the principle employed led to many erroneous 
results ; that gentleman observed, that many years before he 
had been led to series nearly similar, in endeavouring to inte- 
grate the equations representing the planetary motions, by 
means of series arranged according to some other functions 
of the time than the usual ones of the sines and cosines : he 
obligingly showed me some of his papers relating to this sub- 
ject, in one of which was a series which in a particular case 
became the one I had mentioned ; the mode of investigation 
by which he had arrived at these series he had however laid 
aside, because it rested on the sums of the diverging series 
1 2 *- ^ n + 3 2w - &c. on which he observed we cannot depend. 
To the same distinguished analyst I am indebted for some 
farther information on this subject. M. Poisson was one of 
the commissioners appointed by the Institute of France to 
examine the manuscripts which were left by Lagrange, 
amongst these was one entitled “ a method of summing 
series,” which depended on the values of the same diverging 
mdcccxix. O o 
