2 6 % 
Mr. Atwood’s Disquisition on 
Number of equi- 
distant ordinates. 
2 
Table of Areas. 
Areas. 
3 
4 < 
5 
6 
7 
8 
9 
A -j- 4 B -j-j 
— 6 — xR 
A + 3B 
R 
7 A -f 32 B 4 12C 
~~ 9 ° 
l 9 A + 75 B 4- 5 °C 
288 
X 
R 
x 
R 
41 A 4- 2 16 B 4- 27 C 4- 272 D 
840 
x 
R 
36799 A 4- 175273 B 4- 64827 C -f 146461 D R 
846720 x 
989 A 4- 588 8 B — 928 C 4. 10496 D — 4540 E 
28350 
X 
R 
In this table, the letter A denotes the sum of the first and 
last ordinate of the number opposite to it in the first column : 
B is the sum of the second and last but one: C is the sum of 
the third and last but two, and so on. The extreme letter, sup- 
pose D, (as in the rule opposite 8 ordinates,) is the sum of the 
two middle ordihates, if the number of ordinates is even; or the 
extreme letter, suppose D, (as in the rule opposite 7 ordinates,) 
is the middle ordinate alohe, if the number of ordinates is odd. 
R is the entire length of the abscissa, which is always equal to 
the common interval between the ordinates, multiplied by the 
number of ordinates diminished by unity. 
Let the area to be measured be terminated by the curve line 
ABCD, &c. ( Tab. XIII. fig. 24.) : AT is an abscissa, on which 
a number of equidistant ordinates AA', BB', CC', &c. are erected 
at right angles. If ABCD, &c. represents a parabolic line of any 
dimension, suppose ;z,the relation between the ordinates and ab- 
s 
