THOMAS U. TAYLOR-PRISMOIDAL FORMULAE. 
47 
13. The coordinates of 7, 8, 6, and 4 locate the sections for Kinklin’s 
two-term formulae, and the ordinates to the “coefficient” curve give f 
and £ for Si and Sa, and vice versa. 
The coordinates of 2 and 5 locate the two sections equidistant from the 
bases where x=.2114 and y = .7886, as given by Prof. Echols, and the 
“coefficient” curve crosses the asjunptote on same ordinate, and gives 
p=.50 and q = .50. The graphical construction shows that no real sec¬ 
tion of the prismoid (between bases) can occur for values of x between 8 
and 6; i. e., within the middle third. However, good results can be ob¬ 
tained for all values of x from 0 to .45 and from .55 to 100. 
No sections can be taken at or very near the center. 
Example: For any position, ov=x, vt=y, fg=q, and vg=p. 
14. “ Position ” and ‘‘ coefficient” curves. 
(1) To find the volume of any prismoid measure one section (S 3 ) at a 
distance xH=ot) in Fig. 7, and measure the other section (Si) at a dis¬ 
tance from same base yH=the ordinate to the “ position ” curve 728 =vt 
for the abscissa vo. Then multiply the first section by vg, and the second 
section by/g, where H=OQ=OR=unity. 
(2) The “ position ” curves are asymptotic to the lines y=4 and x=A, 
or to OM 1 and 0 1 0 1 . 
(3) The vertices of the “position” curves (hyperbolas) are on the 
diagonal QR of the square ORDQ. 
(4) The point of inflection of the “coefficient” curve is vertically be¬ 
low (above) the points 8 and 6. 
