

406 — Dr. Warine on the ga , 
ble, which, properly corrected, let be A; in the quantity A 
fuppofe all the quantities invariable but fome other v, and find 
the fum of the feries thence refulting, which let be B, and fo 
on; and the fum of the feries will be deduced. 
: I 2h a 
Ex. Let the term be 2st oe en eee? the dimenfions | 
of z and v, &c. in the denominator muft be at leaft greater 
than its dimenfions in the numerator by a quantity greater 
than the number of the quantities %, v, &c. which proceed 
in infinitum increafed by unity. Firft, fuppofe = only 
variable, and the fum of the infinite feries refulting will be 
it 
BZGevuev+i1.v+2 
= A; then fuppofe v only variable, and the fum 
refulting will be = : == B, which is the fum required. 
If it be fuppofed, that the quantities z and v, &c. in the 
fame term fhall never have the fame values, then fuppofe 
z and v always to have the fame values, and the general term 


I I e 
—__—___- = hecomes ——_—_—-——, of, whieh erie 
Be Zt VU. v-+1 ~ U+2 ieee F - 2+2 : 
fum be V, then will B = V bethe fum required. | 
On this and fome other fubje€ts more have been given in the 
Meditationes. | 
14. If the fum of the feries cannot be found in finite terms, 
and it is neceflary to recur to infinite feries; it is obferved in 
the Meditationes to be generally neceflary to add fo many 
terms together, that the diftance from the firft term of the 
{eries may confiderably exceed the greateft root of an equation 7 
refulting from the general term made=o; and afterwards a7 
{eries more converging may commonly be deduced from 
the fluents of fluxions refulting from neglecting all but the 
greateft quantities in the general terms refulting ; and by other 
2 different — 

