THOMAS U. TAYLOR-rRISMOIDAL FORMULAE. 
51 
Substitute the value of C obtained from (38) in (36) and (37), and 
then eliminate B, and we get 
2y—1 0 , 1—2x , 6xy—3x—3y+2 
M: 
S a 
+ 
2 (y — x) 2(y— x) 6 
The same conditions and results follow as in article 11, etc. 
(39) 
18. To find an expression for the mean area of the prismoid in terms of 
the mid-section and two sections Si and S 3 equidistant from the mid-section. 
From (12) we have 
3x—1 . So , „ 2—3x 
M = B 
6x 
6x(l —x) ^~^6(1 — x)‘ 
Then again 
M = B 
2—3x 
6(l-x) 
6x(l—x) 
+C 
3x—l 
~6x • 
But C = 6M-B-4Sy 2 . 
Substitute this value of C in the preceding equations, and then elimin¬ 
ate B, and we have 
7 % 
,, S^S 3 _ 6(4x 8 —4x+l) 
M - 6(4x 8 —4x+1) + 6(4x s —4x+1 f l/ *' 
=K(S 1 +S a )+jS%. 
The following table of coefficients is readily calculated: 
(40) 
X. 
k. 
j- 
0.000 
.166 
.666 
.100 
.260 
, .479 
. 1456 
.333 
.333 
.2000 
.463 
.019 
.2114 
.500 
.000 
. 2500 
.667 
— .333 
.2959 
1.000 
— 1.000 
.3333 
1.509 
—1.333 
.5000 
CO 
-CO 
.6670 
1.500 
—1.333 
.7041 
1.000 
— 1.000 
.7500 
.667 
— .333 
.7886 
.500 
0.000 
.8564 
.333 
.333 
1.0000 
.167 
.667 
