STRENGTH OF MATERIALS 421 mining the resistance to rupture. The hard- est and most brittle materials break with a snap before any flow is perceptible, before the line of the diagram begins to deviate from the direction taken at the commencement, and be- fore the approach to the elastic limit is indica- ted. The elasticity of the material is deter- mined by relaxing the distorting force, and al- lowing the specimen to relieve itself from dis- tortion so far as its elasticity will permit. In such cases, the pencil traces a line e, O, re- sembling, in its general form and position in respect to the coordinates, that forming the initial portion of the diagram, but almost abso- lutely straight, and more nearly vertical. The degree of inclination of this line indicates the elasticity, precisely as the initial straight line gives a measure of the original stiffness of the test piece. The homogeneity of the material tested is hardly less important than its strength. The degree of depression of the line immedi- ately after passing the elastic limit exhibits the Cter or lesshomogeneousness of the material, resilience of the specimen is measured by the area included within the curve, this being the product of the mean force exerted into the distance through which it acts in producing rupture; i. e., it is proportional to the work done by the test piece in resisting fracture, and, taken up to the ordinate of the limit of elasticity, measures the capacity for resisting shock without serious distortion or injurious set. The ductility of the specimen is deduc'ed from the value of the total angle of torsion, and its measure is the elongation of a line of surface particles, originally parallel to the axis, which line assumes a helical form as the test piece yields, and finally parts at or near the point where the maximum resistance is ob- served. 29. The strain diagrams exhibit the characteristic differences of various materials. The woods have a structure which differs in a distinguishing degree, both in the distribution of the substance and in the action of those molec- ular forces capable of resisting rupture, from that of the metals, the latter being far more ho- mogeneous than the former. "Wood consists of an aggregation of strong fibres, lying parallel, or approximately so, and held together often by a comparatively feeble force of lateral cohe- sion. The metals, on the other hand, are nat- urally homogeneous, both in structure and in the distribution and intensity of the molecular forces. "Well worked and thoroughly annealed cast steel, as an example, is equally strong in all directions, is perfectly uniform in its struc- tural character, and is almost absolutely homo- geneous as to strain. "Wrought iron, as usually made, has a somewhat fibrous structure, which is produced by particles of cinder originally left in the mass by the imperfect work of the puddler while forming the ball of 'sponge in his furnace, which, not having been removed by the squeezers or by hammering the puddle ball, are, by the process of rolling, drawn out into long lines of non-cohering matter, and produce an effect upon the mass of metal which makes its behavior under stress some- what similar to that of the stronger and more thready kinds of wood. In the low steels also, in which, in consequence of the deficiency of manganese accompanying almost of necessity their low proportion of carbon, this fibrous structure is produced by cells and bubble holes in the ingot, refusing to weld up in work- ing, and drawing out into long microscopic, or less than microscopic, capillary openings. In consequence of this structure, a depression indicating this heterogeneousness of structure interrupts the regularity of their curves, im- mediately after passing the limit of elasticity. 30. The presence of internal strain constitutes an essential peculiarity of the metals which dis- tinguishes them from organic materials. The latter are built up by the action of molecular forces, and their particles assume naturally and invariably positions of equilibrium as to strain. The same is true of all naturally formed or- ganic substances. The metals, however, are given form by external and artificially produced forces. Their molecules are compelled to assume certain relative positions, and these positions may be those of equilibrium, or they may be such as to strain the cohesive forces to their very limit. This peculiar condition is of seri- ous importance where the metal is brittle, as is illustrated by the behavior of cast iron, and par- ticularly in ordnance. Even in ductile metals, it produces a reduction in the power of the material to resist external forces. This con- dition of internal strain may be relieved by annealing hammered and rolled metals, and by cooling castings very slowly, so that the par- ticles may naturally assume positions of equi- librium, "in tough and ductile metals, internal strain may be removed by heating to a high temperature and then cooling under the action of a force approximately equal to the elastic re- sistance of the substance. This process, called " thermo-tension," was first used by Prof. W. R. Johnson in 1836. The cause of this, which he terms an anomalous condition of the metal, was not then discovered. Ductile metals may be strengthened in a considerable degree by this relief of internal strain, and also by sim- ply straining them while cold to the elastic limit, and thus dragging all their particles into extreme positions of tension, from which when released from strain they may all spring back into their natural and unstrained posi- tions of equilibrium. This fact was noted by Prof. Thurston, and soon after independently by Commander Beardslee, U. S. K _ It has an important bearing upon the resisting power of materials, and upon the character of all formulas in which it may be attempted to embody accurately the law of resistance of such materials to distorting or breaking strain. The initial portion of the diagram, when the material is free from internal strain, is a straight line up to the limit of elasticity. This line, with strained materials, becomes con-
