52 
TRANSACTIONS OF THE TEXAS ACADEMY OF SCIENCE. 
Let QB=altitude of prism oid = 1. Then the two coefficient curves (k) 
and (j) can be plotted as in the figure. 
If x=0 or 1 we get 
M=-J-(B+C+4S^). 
If x = --^j=.1464 or .8536 we get 
4 
M = -J(Si+S 3 -|-Si/ 2 ) (41) 
If x = -^^*=OD or OG we get Echol’s formula 
6 
M=i(Si+s 2 ). 
19. If in formula (20) we make x = ^+z, and x=|—z, the two sec¬ 
tions Si and S are equidistant from the mid-section. 
... M=!(Si+S 2 ) + ( t V— z 8 )A. (42) 
If z = 0 we get Koppe’s formula where 
M = Si/ 2 + T V A=Sy 2 +-JT. 
If z=±i } we get the associate formula where 
m=kb+c-|A). 
If z=±|\/3, we get Echol’s formula where 
M^=i(Si+Sa). 
