THIS Paper describes a series of experiments carried out by the Authors in the Fulton Engineering Laboratory of the University of Edinburgh, for the purpose of determining the behaviour, when tested to destruction under similar conditions, of hollow shafts, compared with that of solid shafts of equal strength as calculated by the usual, though incorrect, method. It has been considered possible, aft.er making certain assumptions, to determine the dimensions of two shafts of the same material, one hollow and one solid, which shall be of equal torsional strength, i.e., which shall require equal twisting-moments to produce fracture. The usual method is by a formula involving the assumption that the shafts remain perfectly elastic up to the point of fracture. This is not a fair assumption, because i t is well known that all materials used for shafts in engineering work lose their elasticity some time before fracture takes place, and become more or less plastic. It was, however, on this assumption that the Authors proportioned their torsion specimens. Let R be the radius of a solid shaft of a certain material, R, the external radius of a hollow shaft of the same material, R, the internal radius of the latter, f the maximum shear-stress in the shaft in question in pounds per square inch, T, the twistingmoment in inch-pounds necessary to fracture the solid shaft, and T, the twisting-moment in inch-pounds required to fracture the hollow shaft. From a right section of the shaft let an elementary ring be taken of width d r, and mean radius v. So long as the material remains elastic, the shearing-stress S on this ring will be proportional to U 2
