158 PROF. E. G. COKER AND MR. K. C. CHAKKO: THE STRESS-STRAIN PROPERTIES 
Now the bending moment 
r+id 
M = fb.y.dy 
J -id 
for a breadth = b and a depth = d , or 
M = b . a 2 . 0 f + * X.Y.dY 
J -u 
= 2 . a 2 (3 . b x first moment of the area of the diagram about the neutral axis. 
If now any point C on the curve is projected on to the edge line at D and the 
line OD is drawn to the origin of co-ordinates intersecting the horizontal through C 
at E, then 
BE : Y :: AD : AO = X : - , 
2 
or 
XY = BEx - • 
2 
rid 
Hence X . Y . dY represents the area OEFAO x d. 
J-id 
A typical example of one of these diagrams is shown in the accompanying fig. 15, 
of which about forty were actually prepared. The first moment areas M 7 , as deter¬ 
mined by planimeter measurements, are shown in Table III., and when these are 
divided by the bending moment a value of a 2 /3b is obtained. If, however, the relative 
