49 ° 
Mr, iiutton on 
f 2 
+ — - x : 1 
r 
1 
4- 1 
1 
TTT 4- 
1 
Sec. 
3 dly, A — < 
3 
39 
5-9 
7 9 
9-9 
1 
+ — x ; 1 
1 
1 
4- 
1 
4 - 
1 
0 
Sec. 
l 7 
3-49 
5-49 
7-49 3 
9-49 
Now if each of thefe be transformed, by means of the 
differential feries in cor. 3. p. 64. of the late Mr. thomas 
simpson’s Mathematical Differtations, they will become 
of thefe very commodious forms, viz. 
iff, A — 
+ io X 
[ + - 3 -x 
2 dly, A—' 
+ - 4 X 
5 
7 
x 
50 
3 dly, A— 
r 6 
+ — ; 
-I 10 
1 
+ — x 
50 
I 4- 
I + 
I + 
I + 
I + 
I + 
4 
4- 
+ 
12? 
+ 
1 6y 
3 10 
5 -i° 
7. 10 
9.1O 
2 
> 
+ 
6£ 
+ 
8y 
3.1° 
5.10 
7.10 
9.IO 
To + 
+ 
3.10 
2 
3^5° 
8a 
+ 
12? 
4 
I 6y 
5.IO 
7.10 
9.IO 
8* 
4 - 
I2£ 
4 - 
1 6y 
5 - 100 
7. 100 
9. 100 
> Sec. 
5 See. 
> Sec. 
’ Sec. 
4- 
ACC 
6 C 
4- 
8y 
Sec. 
5 . 10 
7.10 
9.IO 
4 * 
6 S 
4- 
8y 
4- 
J- 
1 
7-5° 
5 
Sec. 
5-5° 
9-50 
Where a, £, y, Sec. denote always the preceding terms in 
each feries. 
Now it is evident, that all thefe latter feries, are much 
eafier than the former ones, to which they refpedfively 
correfpond; for, becaufe of the powers of 10 here con- 
cerned, we have little more to do than to divide by the 
feries of odd numbers 1, 3, 5, 7, 9, Sec. 
Of all thefe three forms the fecond is the fitted for 
computing the required proportion ; becaufe that, of the 
two feries’ of which it conlifts, thefeveral terms of the one 
6 arc 
