76. The laws of the resistance of materials depend on the manner in which the pieces are strained, and may be divided into three kinds.

First, When the force tends to pull the piece asunder in direction of its length, or the resistance to tension.

Secondly, When the force tends to break the piece across, or the resistance to cross strains.

Thirdly, When the force tends to compress the body in the direction of its length, or the resistance to compression.

77. Stiffness is that property of bodies by which they resist flexure or bending. Strength is that by which they resist fracture or breaking. This distinction must be carefully attended to, because the laws of strength and stiffness are not the same. For instance, the stiffness of a cylinder, exposed to a cross strain, increases as the fourth power of the diameter, but the strength increases only as the cube of the diameter. If the diameter of a cylinder be doubled, its stiffness will be sixteen times as great, but its strengh will only be increased eight times.

In carpentry the comparative stiffness is of much greater importance than the comparative strength, as timbers are seldom exposed to strains that break them.

78. All bodies may bo extended or compressed; and the extension or compression is assumed to be directly as the force producing it: that is, if a force of 100 lbs. produces an extension of one-tenth of an inch, 200 lbs. will produce an extension of two-tenths of an inch, and so on. It is on the truth of this principle that the greater part of the following inquiry depends; and it has been found by experiment to le practically true up to a certain point called the limit of elasticity, which, according to Barlow's experiments on the transverse strength of timber, would appear to be about one-third, and according to Kirkaldy's experiments on wrought iron, about one-half of the force required to produce rupture.

When this limit is exceeded, the alteration in length is no longer in proportion to the load, but increases as the ultimate strength of the material is approached; a permanent change then takes place, and when the load is removed the beam or bar will not quite return to its original state; this is called the set. The subject is still involved in obscurity, particularly as regards materials strained in the direction of their length. Barlow (' Essay on the Strength of Timber') states that he left more than three-fourths of the breaking weight hanging from a piece of timber for twenty-four hours without perceiving the least change in the state of the fibres or any diminution of the ultimate strength: in wrought iron a very decided change takes place under a corresponding application of the load, and Hodgkinson has shown that a permanent alteration takes place when a very small proportion of the breaking weight is applied.

Recent experiments on direct cohesion and on transverse strength seem to show that the theory of the resistance of materials is still in an unsatisfactory state.

It is probable, from observation and the few experiments we are in possession of, that the limit of elasticity is reduced by time; and it may be assumed in reference to a beam of timber submitted to a cross strain when loaded to within one-fifth of its breaking weight, that in the course of time the elasticity will be so impaired as to produce a permanent set.