2,0 8 Mr. maseres’s Method of 
dexes of the powers of t are greater than 999, or 1000, 
or in which the numeral co-efficients of the terms 
(which, by the law of this feries, are equal to 1 divided 
by thefe indexes) are lefs than or it is neceffary 
to compute 500 of its terms. Now when t is = r, and 
confequently the literal parts of the terms of this feries 
do not converge at all, it is evidently neceffary to carry 
the computation as far as thofe terms in which the nu- 
meral co-efficients of the terms are lefs than ~ or rizzt 
in order to get the value of the feries exaft to the th 
or T^th part of the radius r, or to the place of thou- 
fandths, or the third place of decimal figures. There- 
fore, when t is = r, or the arch is =45°, it is neceffary to 
compute at leaf! 500 terms of the feries 
r 
^ 3 r r 5 r* 7 r 6 9 r 8 
11 r 
+ 
l 3 r 
— + + 8cc., in or- 
der to obtain the value of it exadf to three places of de- 
cimal figures, that is, to the fame degree of exadtnefs to 
which we attained In art. 13. by computing only eight 
terms of the above-mentioned differential feries. ^.E.D. 
Art. 15. But the beft way of applying the aforefaid 
differential feries to the inveftigation of the value of one 
of thefe very flow feriefes, is to compute a moderate 
number of the firft terms of the flow feries in the com- 
mon way, and then apply the differential feries to the 
3 computation 
