IQO 
Mr. MasKres’S Method of 
annexed to it, expreffing the order of differences to 
which it belongs, 
Thefe things being fuppofe'd, the aforefaid infinite fe- 
ries a—bx+cxx— dx* + ex*- fxt+gx 6 — hx^ 8ec. will be 
equal to the following differential feries, to wit, 
bx 
D 1 xx 
a- 
D n tf 3 D 111 X* D IV Jf 5 
I + * I -i 
I x\ I -f- A'i I -f- a) 
1 -f- XI 
T>' r 'X 7 0 
, S ~ ■ ) 7 
I -f A 
in which feries all the terms after the firft term a are 
marked with the fign or are to be fubtra&ed from 
that term. 
Art. 3. If we infert the differences themfelves inftead 
of d 1 , D 11 , D nr , d iv , d v , &c. in the foregoing differential 
feries (which it may perhaps fometimes be convenient 
bx 
to do) that feries will be as follows: a—ff- — \b— ~c x 
XX 
I +* 
I f 
id 1 
I + A I I -f- A' 
— \b~j^c + ^d-A e e+fx df— - 
I -j- aJ 
-\b- 5 c+ io^-io^+5_/-^x=^ 
1 If 
~\b~6c+\$d-2oe+isf-6g+bx-~- & c . ad infini- 
tum. 
Of the convergency of the foregoing differential feries. 
Art. 4. The foregoing differential feries will always 
converge with a confiderable degree of fwiftnefs, fo 
that 
