194 
ME. L. N. G. FILON ON THE ELASTIC EQUILIBRIUM OF 
This gives 
, J)ac- Ea^c^ Yctc^ 
u,a + ^ + -5 + -Y- + -^ + -X 
+ S^-^I.- Si„U-i)- = o 
a’ 
ac~ 
+ I [(1 - r) - fc^] E - (I - y) E + T[t (1 + y) “ «^] E 
24 
+ ^ - Hi + y) E«c^ - (2y + 1) s E + N E i (_ I)n = 0 . 
N ow 
whei’e 
CO pT yy.i 
C= s 
n = l « 
24 
(2y +!)« + - (87 +1) 
1,2 - (87+ 4) Eh 
(94)- 
7.=r,r -I,M1 + 7=<‘) 
so that { is a known constant. 
1 ., 
We then find, putting in for N —: its value 71^90, 
= - E 
Tf now we write 
7 - ? 
12 
a 
‘ - 1 a°-c= + i (1 + y - A { 2 y + ]}) 
(95). 
/=(3y-l) +ic%=-U(2y+ l)c' 
?=A(i-r- 0«*-i«=n5 + Ui+y-A)% + O)c 4 . , (oe), 
L O -7 
A=-Be*y- ,p2y+l) + -h ' 
SO that /, g, h are known constants, then ecpiations (90), (93), (9.5) may be re-written 
as follows :— 
+ (k + 2g) w^^ -f- g /E = — Q ] 
'>-'■0 
+ ; 7 E = o 
2 (X -h /i) '>!() + X?f’„ -j- p/(E = 0 
(97). 
Solving, we have : 
gE = 
7(0 = 
— (27 — 1) 
(A+ ( 27 - 1 )/+2^(47-!)) ’ 
_ Qy (27 — 1) _ 
/A (/t + (27 — 1)/ -f 27 (47 — 1) I 
.(98), 
.(99). 
