But the arca of any section of a cylinder whose radius is r being .74 w (r being the half circumference of a circle when the radius = 1) it is evident that r' sr will represent the lateral cohesion by which all the particles resist being separated by the force of detrusion. There fore the ratio between the force of detrusion and that of torsion will be as to — 4 ; • or as 4s. to r.
And since the strength under the latter strain depends on the radius, it is evident that a hollow cylinder must be stronger than a solid one ; the areas of the material in the transverse sections being equal to each other.
The preceding reasoning is entirely founded on the supposition that the sections of the various solids considered had but a small importance upon their resistance to the various forces considered; but this is far from being the case in practice, and especially in the ease of cast and wrought iron, the resistances of the upper and of the lower fibres of a rectangular beam differ to such an extent as to have rendered it necessary to carry out a long series of investigations into the real forms of solids of those particular materials presenting the greatest resistance. Mr. Iledgkinsen, after Tredgold and Barlow in our own
country, and Messrs. Morin and Love, after Navier, Coriolis, and Vicat, in France, have studied this complicated question ; and the results of their inquiries, so far as the practical arta of construction are con cerned, have been already alluded to under GIRDER, in which article also will be found enumerated the principal authors upon the subject it may be desirable for the student to consult. Very useful tables of the resistances of materials to efforts of compression, and of extension, may be found in Carr's Synopsis of Practical Philosophy,' 1843; Beardmore's Hydraulic, &c. Tables,'1852; lgoseley's Engineering and Architecture,' 1843; Willis'a edition of Barlow, on 'Materials and Construction,' 1851; and Claudel'e Formules it l'usage des Ingdnicurs; 1854.