192 
MR. L. X. G. FTLON ON THE ELASTIC EQEHLIBEIUM OF 
or 
X 
= -(- 1 ) 
/'3 
(27 + 1) « + -(87 + 1) 
a 
Ii-4I„(27 + 1) 
7a2V-(l F7a"MX 
• (92). 
AI and A., being known in terms of C, all the constants are now determined, 
except v^^, and E. 
§ 15. Determination of the Constants iVq, E. 
Let us now apply the condition that ; 
[ (19 { rzzdr = —vra'Q. 
-0 Jo 
II we write down the expression for 22 , using the expressions for Aj and A., in 
terms of C, we find : 
zz 2A.'?^q “h (X -h 2jU.)wQ 
+ 
-f (X A 2fi) 2 
'A + [\D + (X + 2/r)^,>2_p 
2EX + "^(X + 2p,) 
,.2,.3 
/ ^ 
+ K + 1 0 + (^ + 2^-) "^3 
AS 
2/.C 
7 h 
dll (d) - I 
u 
L 
— n 
nirz 
cos 
+ (2y + l) C-f ( -1)"X^ 
1 J-1 
16flc® iriiz 
COS — 
C 
— 2X'?<(j A (X A 2fji 
a- 
+ nEj .-ii“ + (-7-l)"7 >'"- + [0®-|t=(2y+l)]2=-'2)-2O 
i 
7n2y-l)n + -|(2y+l)2^ 
+ 
” 2/xO 
1 h 
fii ip) - 1, (p) \ 2 
COS 
nirz 
+ (2y+l)yEsi^h-l)-x X 
niTZ 
COS 
?r"7r’^ c 
