The materials of which structures and works of art are composed are liable to so many and so considerable inequalities of texture, that any rule which can be deduced, even by the most extensive series of experiments, must be regarded as a mean result, from which individual examples will be found to vary in so great a degree, that more than usual caution must be observed in its practical application. The details of this subject belong to engineering, more properly than to the elements of mechanics. Nevertheless, a general view of the most important principles which have been established respecting the strength of materials will not be misplaced in this treatise. A piece of solid matter may be submitted to the action of a force tending to separate its parts in several ways; the principal of which are,-- 1. To a _direct pull_,--as when a rope or wire is stretched by a weight. When a tie-beam resists the separation of the sides of a structure, &c. 2. To a direct pressure or thrust,--as when a weight rests upon a pillar. 3. To a transverse strain,--as when weights on the ends of a lever press it on the fulcrum. (331.) If a solid be submitted to a force which draws it in the direction of its length, having a tendency to pull its ends in opposite directions, its strength or power to resist such a force is proportional to the magnitude of its transverse section. Thus, suppose a square rod of metal A B, _fig. 185._, of the breadth and thickness of one inch, be pulled by a force in the direction A B, and that a certain force is found sufficient to tear it; a rod of the same metal of twice the breadth and the same thickness will require double the force to break it; one of treble the breadth and the same thickness will require treble the force to break it, and so on. The reason of this is evident. A rod of double or treble the thickness, in this case, is equivalent to two or three equal and similar rods which equally and separately resist the drawing force, and therefore possess a degree of strength proportionate to their number. It will easily be perceived, that whatever be the section, the same reasoning will be applicable, and the power of resistance will, in general, be proportional to its magnitude or area. If the material were perfectly uniform throughout its dimensions, the resistance to a direct pull would not be affected by the length of the rod. In practice, however, the increase of length is found to lessen the strength. This is to be attributed to the increased chance of inequality.