1887. ] deformation of elastic plates. 153 
Again, 
.: =— k,[2+w,— tr.v + K,2y + FK,Y', 
ya Leb, Pet + may + ey] + oy 
ox) Ov 
The condition —— nau ae a a 8 gives 
— K, («2 + Ky) = =—«,(—A,e + KY), 
so that «,,+«, = 0 as before. 
Hence 
V= 0) — K20 — KyYZ + OLY — Wy (K,0 + KY) + EAH, — $4, "y"... (14), 
where v, is a function of z. 
If w, and vy, denote now known functions of z (determined by 
the equations S, 7, R=0 and a= - b= I we shall have 
ow 
aries —V, (w+ u— KyZ + r,20 + 0,4 + wy) 
+k, (YU — KYZ — Kz" + oY), 
ow 
ayn (@ + Uy, — KYZ+X,20 + 0," + wy) 
4+ «,(Y +0, — KYyZ — K,20 + oy) —[K,(6,—0,) +2,@] @. 
The condition my wh 
Ou dy Oy ea 
=w,—$r,0' + «,2y + hn,’ —«,(«, —2,) 2yZ 
is identically satisfied, and we obtain 
—4h OP + «20? —4$ (kK +4) zy — tore + $o,K,y° — Away 
= (Ap — KyUp) BAR (Ky Uy tH yUp) Y vec cec ere cere ee ew tees seen noes (15), 
where w, is a function of z. 
We find for the six strains 
e=AZto,+WA,—-Fyw 
Us Sa Oe OUNCE oe 2 Kgy. 
ae D5 4, OMe «, 2) Oty 2 
I~ oe ( 10z 26 +y(« 192 | 8 Oz, 
SUN des r,) ay — (ry + Ky) & —4(K+«,)y’. 
