RIGIDITY OF SELENIUM CRYSTALS 
107 
/ ? \ 
^ L > 
L 
Fig. 25. Sketch of one face of the truncated hexagonal prism. 
cross-section, taken at a, distant I from the expression for M is 
if we suppose the section to be a regular hexagon. As- 
16 
suming this, as a rough approximation, and using the mean of the 
six edges as and az, respectiyely, we can obtain the mean value 
of M for the section whose edge length is a, by the following 
method. 
I 
a = ai + {a 2 — ai)^ (2) 
Let 
then 
and 
ai == c, a 2 — a 1 = e 
( 3 ) 
a 
= c + 
Ml 
16 
(4) 
(5) 
where Mi is the moment of area at the distance I from Now 
if M is the mean moment of area for all sections of the frustum, 
5V3 Ch e 
ML= 16 I [c (6) 
o 
or, integrating, and substituting the limits, 
M = + 2 c^e + 2 + c +eVsl (7) 
Employing the value of M from (7) for M in (1), we have an 
expression for the value of Young’s modulus. Applying these 
two equations specifically to crystal No. 2, first case (Table II), 
* we have 
ai = .0102 cm (mean of six edges) 
02 = .0130 cm (mean of six edges) 
c = .0102 cm 
e = .0028 cm 
Substituting in (7), 1.008 X 10~® cm^ (area X distance^). 
