form a clear idea of the most advantageous character for them to assume
both in homogeneous and in built-up hollow cylinders. In proof of this,
we can adduce the labors of Colonels Pashkevitch and Duchene, the former
of whom published an account of his investigations in the _Artillery
Journal_ for 1884--St. Petersburg--and the latter in a work entitled
"Basis of the Theory of Hooped Guns," from which we borrow some of the
following information.

The maximum resistance of a tube or hollow cylinder to external stresses
will be attained when all the layers are expanded simultaneously to the
elastic limit of the material employed. In that case, observing the same
notation as that already adopted, we have--

R - r0
P0 = T -------- (1)
r0

But since the initial internal stresses before firing, that is previous
to the action of the pressure inside the bore, should not exceed the
elastic limit,[2] the value of R will depend upon this condition.

[Footnote 2: We must, however, remark that in a built-up hollow
cylinder the compression of the metal at the surface of the bore
may exceed the elastic limit. This cannot occur in the case of
natural stresses.]

In a hollow cylinder which in a state of rest is free from initial
stresses, the fiber of which, under fire, will undergo the maximum
extension, will be that nearest to the internal surface, and the amount
of extension of all the remaining layers will decrease with the increase