THE EQUILIBRIUM OF AN ISOTROPIC ELASTIC PLATE. 177 
These conditions are satisfied if 
ay aged de 79 
a dy’ pas da.” ; ; : = ek) 
and 
: diy at) dye 
(Eee Cae 
Q’ 2 =i) ail 
dd’ ap’ atl d /f Toes pot on zg= +h. 
zt de" qa) vada 
PO dp’ Bp a—1 Hi _ Che 
AD Es ae a 
We may take 
—2 »—1 co ; 
dz? 0 KZ 
1,,.-1 
Bor fa) { oFae-erd Renee | 
Ee ie eFKE-2)J Rd 
0 
upper or lower signs being taken, as all along, according as z>2’ or z<z’. We therefore 
determine provisional values of W’, 0’, d’, such that 
dy’ | SUE 
Wee aie eFee- 2 eR 
0 dp’ a’ a+ 1 
ge is 4 2 -(5 Dn +22 \eFde- 2) KR on z=+h 
PO Pd | dd’ a1 
de P2e = -(“> 2 i= a )oFet- ue 
These provisional values are easily found to be 
yn 8t cone 2) 
wee sinh xh sinh x2’ sinh xz} JykR 
K K. 
a + 1 , 
— —._—— cosh kh cosh xz’ cosh xz 
2x? sinh kh i . 
oe , 
co) = 52 cosh «(2 — 2’) 
Jock 
sinh xz F 1 . , 
P p Ixh — a) sinh Kz 
2(sinh Deh — Deh) | kz cosh xz + 5 (cosh 2h a) sinh x \ 
cosh Kz ite 1 ' } 
— a 0sh KZ 
sinh Inch + Deh) | Kz sinh xz’ + 5 (cosh 2«h + a) cosh xz 
’ 
6 =, cosh x(z— 2) — ~ sinh x(z- 7) 
K 
2K? 
sinh xz Pah : , 
| teenage ra Qh — 1 —442h2 a \ | I KR 
PiGmn Je) { xz’ cosh 2h cosh Kz + 5 (a cosh 2«h — 1 — 4x?h?) sinh xz i ok 
cosh? ‘ «2 cosh 2«h sinh xz’ + F(a cosh 2«h + 1 + 4«7h”) cosh xz’ ; 
~ (sinh 2h + 2h) a 
(80) 
28 
TRANS. ROY. SOC. EDIN., VOL. XLI. PART I. (NO. 8). 
