[ 7 68 ] 
is __ x, and it is required to find the fum of every 
« th term thereof, beginning at the fit ft- Heie the 
quantity fought will (according to the general rule 
be truly defined by the rc th part of the fum of ail 
the numbers whofe refpedive logarithms are — p *, 
__ q &c.j which numbers, if N be taken 
to denote the number whofe hyp. log. = I, Wl11 be 
truly exprefled by N * , N , N t 3 
From whence, by writing for p^r, &c. th eir equa s 
I, a + \/aa F * V^'aa — 1 , Z 5 + J > 
p y/ p ft i, &c. and putting a = y / 1 — a oi» 
/*' = y/T=r& &c - we flia11 have x iV ~^ + 
iV _? ' v + &c. = ,7 into AT" X + ^ * 
jsr **'/"- 1 + x iv ■ ^ + 
&c _ But j\r — ^ 
known to exprefs the double of the co-fine of the 
arch whofe meafure (to the radius 1 ) is a x. Therefore 
we have l - into N~* + N~** x 2 co-f. <Lx + 
N"** X 2 co-f. /3'*, &C. for the true fum, or value 
propofed to be determined. 
The foluion of this cafe, in a manner a little dif- 
ferent, I have given fome time fince, in another place; 
where the principles of the general method here 
extended and illuftrated, are pointed out. Ifiinll put 
an end to this paper with obferving, that if, m the 
ieries 
