ic limit U of the
material, we have--T0 = U - t0. And for this value of T0, the
corresponding pressure inside the bore will be

R squared - r0 squared
P = (U - t0) ----------.
R squared + r0 squared

This pressure increases with the term (U - t0). With t0 positive,
i.e., when the internal stresses in the thickness of the hollow
cylinder are such that the metal of the layers nearest to the bore is
in a state of tension and that of the outer layers in a state of
compression, then the cylinder will have the least strength when t0
has the greatest numerical value. Such stresses are termed injurious
or detrimental stresses. With t0 negative, the strength of the
cylinder increases with the numerical value of t0, and those stresses
which cause compression in the layers nearest to the bore of the
cylinder and tension in the outer layers are termed beneficial or
useful stresses.

[Footnote 1: Lame holds that in a homogeneous tube subjected to
the action of two pressures, external and internal, the
difference between the tension and the compression developed at
any point of the thickness of the tube is a constant quantity,
and that the sum of these two stresses is inversely proportional
to the square of the radius of the layer under consideration. Let
r0, R, and r_x be the respective radii, p0, p