Abstract
In a previous communication we employed the solution of the equation ∇
4
ψ
= 0 in bipolar co-ordinates defined by
α
+
iβ
= log
x
+
i
(
y
+
a
)/
x
+
i
(
y
-
a
) (1) to discuss the problem of the elastic equilibrium of a plate bounded by any two non-concentric circles. There is a well-known analogy between plain elastic stress and two-dimensional steady motion of a viscous fluid, for which the stream-function satisfies ∇
4
ψ
= 0. The boundary conditions are, however, different in the two cases, and the hydrodynamical problem has its own special difficulties.
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