THE EQUILIBRIUM OF AN ISOTROPIC ELASTIC PLATE. 179 
permanent part of this function is then Ax(R)—By’x(R). We thus find for this part 
of the solution 
U 1 1 9 + i ny 1 2 9 atl , ) 
1D) 5 ms D) 2 
és a+ Mx —Eatyty) + g(x 
8h 2 4h\ 4 
te: 3(a+1)_, ee ) Tp an 73 — zi — iu “hid )e z 
Be (2x: 6° VX) * TA 12 10 vx 
, 1 Ie sp 1 5.4 ,5-a,, ——,, 
p= - 2 (x- oe'x) + (24 ge gat li? \y.x 
Sh 7D) 4h\ 4 
3(a+1), Ne. AiG ED B (GD ws app wear Ia, 
ae” (x-Zevx- Qhrzy x) = pal Pe — Be - hz \ew.x 
FS (2-2)v'x£2'v'x 
(83) 
When 2 is put equal to A in the above values of W’,, ¢’, 6 it will be found, with 
very little trouble, that they reduce to those of (48). . . . (51), multiplied by $(4+ 1). 
(Cf § 20.) As in § 20, the displacements due to the ambiguous terms in (83) are null 
ifR>0. But there is this difference in the present case, that they do not continue to 
vanish in the corresponding solution for am areal distribution of force on z= 2’. 
If the intensity of the distribution is X(qa, y, 2’) per unit area at (a, y), this solution 
is defined as in (79), W’, 6’, ¢’ being obtained from (82), (83) by multiplying by 
1 
xe n! , 7 Y day’ 
TE ACESN (i, y,2 de ay’, 
and integrating over the area within which X is finite. 
When this is done we find that the ambiguous terms lead to 
ae (64) 
In verification, we observe that these displacements are continuous above and below 
the plane z=z’, and that the corresponding stresses are also continuous with the excep- 
tion of zz, the value of which just below z=’ exceeds its value just above by X. The 
value of zz being --4X, we have for the contribution of (84) to the resultant | a zx Az, 
5, i 
sXx({ de | da) =4% (85) 
2 —h 2 
