230 Afr. maseres’s Method. , &c. 
meaning,, probably, in that place, not to exprefs this pro- 
portion as accurately as he could, but only as nearly as it 
could be expreffed by fmall whole numbers. However, 
the numbers 50 and 59 exprefs this proportion rather 
more accurately than 29 and 34, and with pretty much 
the fame degree of fimplicity, and therefore, upon the 
whole, are fomewhat to be preferred to them. 
Art. 27.I have endeavoured to find another differen- 
tial feries, fimilar to that above defcribed, for the purpofe 
of inveftigating the value of an infinite feries of this 
form, to wit, a + b x + e ft &+ d-x* + ex* +fx i + g x* + b x~ + &c. 
(in which all the terms are marked with the fign+,01 
are added to the firft term a ) when the co-efficients b, c, 
d, e,f,g, b> &c. decreafe very flowly, and x is very nearly 
equal to 1, and the terms of the feries decreafe confe- 
quently fo flowly as to make the fummation of it in the 
common way, or by the mere computation and addition 
of its terms, almoft impracticable ; but my endeavours 
have not been attended with fuccefs. I may therefore, 
from my own experience, fubferibe to the truth of what 
is afferted upon this fubjeft by the very learned and in- 
genious Mr. James Stirling in his Treatife, intitled, 
Summatio Serierum , p. 17. to Wit, that Series quorum 
termini Junt per vices negativi et dffirmativi, funt tttdgis 
trhclabites quam alter a, ubi de Summations agitur; 
though at firft fight one would be apt to imagine the re- 
verie of this propofition to be true. 
