THE EQUILIBRIUM OF AN ISOTROPIC: ELASTIC PLATE. 223 
where 
and ¥,, has the edge value 9,F. 
Thus 
dy _ dy aaa) 
woe = Say ) i pie 
oe ers ite = — et sin | a 
the principal value of which is 
lors eae Ne amen mes 
= =H oF (sin an 3B sin ah > 5g IN + | 
Let 
UG eae No Bae? le Dae 
B(z/h) =, = gp 8S + gg8in— wae 3) ; (11) 
then 
_- — 12 B(2/h) IF ; : 2 i) 
and 
ig oe — Pat ( eae ary .) 8 
a 7 Be Sy 
2 
ey > (13) 
T 
i = AT ge 
if Fy Bias Rant ae 
Now multiply (8) by z, and integrate from —/, to h. 
Hence 
ie = ysh-f 8 ae as 
_ and 
Dig N (xe) = | 2h? B(aih) — 384y<hz/m" Ve one nao) 
This, and equation (7), define g, . 
As we do not require g,’, we will eliminate it from (10) at once by integrating. 
Thus 
Multiply (9) by z and integrate. Then 
av _ 23 / | a 
ae dz= eee = 
-2f dn 3 vee v 
and from this with the last 
dj2[ dy me ( ee ) 
— —_— 4S dz => Y, — SY) i 
ds ' p fie? ‘ 3 eel Pas os 
eed 384d 
Wie OR i d ; 
SF + 7_9.F fap IAF ) (16) 
or, from (13), 
| (14) and (16) give F’, and ¥ may be found from (9). 
