190 
ME. L. X. G. FILON ON THE ELASTIC EQUILIBPJUM OF 
The first term is zero in virtue of equation (86), and using the relations (87) 
we find 
XEx(2y+l), 
n-^TT' 
whence, comparing coefficients 
A ■ A 2C «Ia , _, 16«(r^ , . 
A. + V + ^^ = (-l)«-,-,^,(2y+l)E 
( 88 ). 
This gives us rz consistently zero right up to the plane end. 
Next we have 
( rr = 2 (X + p,) Wq + X^(q 
+ 0 
D' 
I (2^ + S/a) ^ 
-I- z~ D(X -|- p) D -j- XiC]] 
.O 0 
a-z- 
+ "7 [(IX + C,.) E + 3XE'] + a* 
+ £* ’X±eF + X?(’, 
fi- (X + 2p) 
jr = n 
^ r = « 
Hence we have to make 
i^[(i + y)^i + (1 ~ y)-^2]lo + 2p 
A T ■ 
nirz 
COS 
= — 2(X + p)7/o — Xa’o 
a~ 
1(2^ + 3p) ?q + 
■■ |(^ “k 1^^)^ + X??;^ + — [(4X+ 6p)E A 3XE ] 
A 
A. -1- p 
F + \iu„ 
(89). 
Now we have 
— o + 
4C"(— 1)" llTTZ 
S' 
^ 0 o 
] n-iT- 
cos 
..4 _ 
^ 1 / X / 1 6 \ niTZ 
y + t^c\— 1 ” Hr o — TAH^® 
5 1 \ 77 ' 7 r“ n^TT^I c 
Hence if the right-hand side of equation (89) he expanded in the form 
S l>„ cos 
niTZ 
