with ideally perfect useful initial stresses. The work done by the
forces acting on a homogeneous cylinder is represented by the area _a b
c d_, and in a built-up cylinder by the two areas _a' b' c' d'_ and _a"
b" c" d"_. Calculation shows also that the resistance of the built-up
cylinder is only 3,262 atmospheres, or 72 per cent. of the resistance of
a homogeneous cylinder. By increasing the number of layers or rows of
hoops shrunk on, while the total thickness of metal and the caliber of
the gun remains the same, we also increase the number of layers
participating equally in the total resistance to the pressure in the
bore, and taking up strains which are not only equal throughout, but are
also the greatest possible. We see an endeavor to realize this idea in
the systems advocated by Longridge, Schultz, and others, either by
enveloping the inner tubes in numerous coils of wire, or, as in the
later imitations of this system, by constructing guns with a greater
number of thin hoops shrunk on in the customary manner. But in wire
guns, as well as in those with a larger number of hoops--from four to
six rows and more--the increase in strength anticipated is acknowledged
to be obtained in spite of a departure from one of the fundamental
principles of the theory of hooping, since in the majority of guns of
this type the initial compression of the metal at the surface of the
bore exceeds its elastic limit.[3] We have these examples of departure
from first principles, coupled with the assumption that initial stresses
do not exist in any form in the metal of the inner tube previous to the
hoops having been shrunk on; but if the tube happen to be under the
influence of the most advantageous initial stresses, and we proceed
either to hoop it or to envelope it with wire, according to the
principles at present in vogue, then, without doubt, we shall injure the
metal of the tube; its powers of resistance will be diminished instead
of increased, because the metal at the surface of the bore would be
compressed to an amount exceeding twice its elastic limit. An example of