The theories which have been advanced and generally accepted, relative to the elastic resistance of hollow cylinders, are based on the assumption that the cylinder will be deformed only when one of the tensions or pressures acting on it equals the resistance of the metal at the elastic limit under traction or free compression.
According to the theory of Clavarino, however, the cylinder must be considered as having reached its limit of elasticity when, from the effects of all the forces acting upon any one of its fibres, it undergoes an elongation or a contraction equal to that which takes place at the elastic limit in the mechanical tests respectively of traction or compression.
To make this difference more clear, consider an elastic right prism submitted to the action of three forces, X, Y, and Z, at right angles to each other. Let ? be the elastic limit and ? the elongation at the elastic limit of the prism under simple traction, and let i1, e1, e1, be the changes of length in the three directions due to the force X, i2, e2, e2 those due to Y, and i3, e3, e3 3 those due to Z. Now the theory of Virgile asserts that the prism will take a permanent set in the direction of X only when X equals ?, regardless of the values of Y and Z, while the theory of Clavarino is that the prism will take a permanent set in the direction of X when i1 + e2 + e3 equals A, regardless of the value of X.
The tension at which wire must be wound in order that under a given internal pressure each layer may be at the same tension has been investigated in a previous paper ; it is now proposed to determine the tension of winding such that under the strain of firing each layer of wire may have the same extension.
(Additional formulas are available in the PDF.)