218 
wliere 
MR. L. N. G. FILOX OX THE ELASTIC EQUILIBRIUM OF 
_ 1(1 _y)I) I 
> . 
— — yl) J 
A, - A, = 20/^1 
A.2 + Aj = 
where 
Also 
and 
-i:' I ( _ I Y 
(119), 
( 120 ), 
1 ) 
C=- ( - 1) 
Wo = D 
/,. 
1(1 - y)a- - 
1-7 
k = mrjc. 
, (^7 + 1 ) — 7^'do («) 
7 A (1,3 («) - ly («) ) - lU («) 
ur 
(d- 1 ). 
where 
and 
) ) = - ‘^ 
3 (1 - 7 ) 
27 — 1 
U+y-i) 
(122). 
'' 4*- .1 ‘-[?(n-i) + 07-i)] 
-I O 
/ _ „ '' ^ J_ 1 Jc(-l7 + 1 ) - ^-hih 
^ 7r3 T vd ly 
The method by Avhich the constants are obtained is precisely die same as that 
used in §§ 14, 1 5. 
The ex^ji-essions for the stresses are given below : 
rr 
= I) 
i(i + y)(«"--0 + 2yU-T) + 
2 rtc« ( - I p 
di ip) i(,(pV 
7r 7 
COS 
mr: 
+ 
2C 
7 A' 
u\ 
l + ^jIo(F) 
^h ) 1 
u ^"7 
h (p) 
- P Ii {P) 
utt: 
COS 
. (123), 
(pcf) 
p- 
L) 
T (1 + y) + 2y ( 2 '- - TV) - i (3y - 1) P' - S ^ cos 
« 2 C 
+ ?tl 
Ml / 1 J_ _L 
P J 
2 pc “ ( — 1 )'^ 1 ] ip) ^ nirr. 
TT 7 w pTi («) 
?i7r:i 
COS 
(124), 
J'.S + 
P 
= T) 
gw 27 - In 
3 4 
2 „ 27 — 1 ,, , 2(7c * (- 1 )" I„(p) niTX 
~ — Z- -- y- + — X --y- cos- 
2 TT I n iU*) ^ 
00 on 
I < “2 
i- 
2-“['^)Io(p)+Ai (P) 
lllTZ 
COS 
(125), 
- = D 
2«c “ ( — ly Ii(p) . n-Kz 
rz -\ -X- sin 
a 1 n 111®!) r 
+ 
® 2C / , , . \ «lri\ • 
( 126 ). 
