due to such pressure, and which acts tangentially to the circumference,
will increase the stress, already excessive, in the layers of the
cylinder; and this will occur, notwithstanding the circumstance that the
metal, according to the indications of test pieces taken from the bore,
possessed the high elastic limit of 3,000 atmospheres.

[Illustration: Fig. 1]

In order to understand more thoroughly the difference of the law of
distribution of useful internal stresses as applied to homogeneous or to
built-up cylinders, let us imagine the latter having the external and
internal radii of the same length as in the first case, but as being
composed of two layers--that is to say, made up of a tube with one hoop
shrunk on under the most favorable conditions--when the internal radius
of the hoop = sqrt(R v0) or 118.7 mm., Fig. 2, has been traced,
after calculating, by means of the usual well known formulæ, the amount
of pressure exerted by the hoop on the tube, as well as the stresses and
pressures inside the tube and the hoop, before and after firing. A
comparison of these curves with those on Fig. 1 will show the difference
between the internal stresses in a homogeneous and in a built-up
cylinder. In the case of the hooped gun, the stresses in the layers
before firing, both in the tube and in the hoop, diminish in intensity
from the inside of the bore outward; but this decrease is comparatively
small. In the first place, the layer in which the stresses are = 0 when
the gun is in a state of rest does not exist. Secondly, under the
pressure produced by the discharge, all the layers do not acquire
simultaneously a strain equal to the elastic limit. Only two of them,
situated on the internal radii of the tube and hoop, reach such a
stress; whence it follows that a cylinder so constructed possesses less
resistance than one which is homogeneous and at the same time endowed