708 red heat, it is remarkably tough and ductile. "Vlieu heated to redness and cooled suddenly by being plunged in oil or water or mercury, it becomes exceedingly brittle and hard (glass-hard, as it is called), and to ordinary observation seems incapable of taking a permanent bend (though pro bably careful observation would prove it not quite so). The definition of steel used to be approximately pure iron capable of being tempered glass-hard, and again softened to different degrees by different degrees of heat. Now, the excellent qualities of iron made by Bessemer s and Siemens s processes are called steel, and are reckoned best when incapable of being tempered glass-hard, the possibility of brittleness supervening in the course of any treatment which the metal may meet with in its manufacture being an objection against the use of what was formerly called steel for ship s plates, ribs, stringers, &c., and for many applications of land engineering, even if the material could be had in sufficient abundance. 8. LIMITS OF ELASTICITY (CONTINUED) Elasticity of Bidk. If we reckon by the amount of pressure, there is probably no limit to the elasticity of bulk in the direction of increase of pressure for any solid or fluid ; but whether continued augmentation produces continued diminution of bulk towards zero without limit, or whether for any or every solid or fluid there is a limit towards which it may be reduced in bulk, but smaller than which no degree of pressure, however great, can condense it, is a question which cannot be answered in the present state of science. Would any pressure, however tremendous, give to gold a density greater than 19 6, or to copper a density greater than 9 - 0, after the pressure is removed (section 3 above)? But whether the body be fluid or a continuous non- porous solid, it probably recovers the same density, how ever tremendously it may have been pressed, and probably shows perfect elasticity of bulk (section 3 above) through the whole range of positive pressure from zero to infinity, provided the pressure has been equal in all directions like | fluid pressure. As for negative pressure, we have no know ledge of what limit, if any, there may be to the amount of force which can bs applied to a body pulling its surface out equally in all directions. The question of how to apply the negative pressure is inextricably involved with that of the body s power to resist, The upper part of the mercury of a barometer adhering to the glass above the level corre sponding to the atmospheric pressure is a familiar example of what is called negative pressure in liquids. Water and other transparent liquids show similar phenomena, another of which is the warming of water above its boiling point in an open glass or metal vessel varnished with shellac. Attempts to produce great degrees of this so-called negative pressure are baffled by what seems an instability of the equilibrium which supervenes when the negative pressure is too much augmented. It is a very interesting subject for experimental inquiry to find how high mercury or water or any other liquid can be got to stand above the level corre sponding to the atmospheric pressure in a tall hermetically sealed tube, and how many degrees a liquid can, with all precautions, be warmed above its boiling point. In each case it seems to be by a minute bubble forming and expanding somewhere at the boundary of the liquid, where it is in contact with the containing vessel, that the possible range of the negative pressure is limited, judging from what we see when we carefully examine a transparent liquid, or the surface of separation between mercury and glass, in any such experiment. The contrast of the amounts of negative pressure practically obtainable or obtained hitherto in such experiments on liquids (which are at the most those corresponding to the weight of a few metres of the substance), with that obtainable in the case of even the weakest solids, is remarkable ; and as for the strongest, consider for instance (sec. 22 below) 17 nautical miles of steel pianoforte wire hanging by one end. When a cord, or rod, or wire of any solid substance hangs vertically, the negative pressure (for example, 23,000 atmospheres in the case just cited) in any transverse section is equal to the weight of the part hanging below it. It is an interesting question not to be answered by any experiment easily made or even devised, How much would the longitudinal pull which can be applied to a cord, rod, or wire without break ing it be augmented (probably augmented, but possibly diminished) by lateral pull applied all round the sides so as to give equal negative pressure in all directions ] 9. LIMITS OF ELASTICITY (CONTINUED) Elasticity of Shape for Distortions not Uniform through the Substance, and for Compound Distortions ; and Elasticity wrespond- ing to Co-existent Distortion and Change of JJulk : Example 1. A round wire twisted, or a cylindrical shaft trans mitting revolutional motive in machinery, presents, as we shall see (sec. 64), an instance of simple distortion, bnt to different degrees in different parts of the substance, increasing from the axis where it is zero, uniformly to the surface where it is greatest. Example 2. Elongation of a wire or rod by direct pull, is (sec. 23) an instance of a compound distortion co-existing with a rarefaction of the substance, both distortion and rarefaction uniform throughout. Example 3. Shortening of a column by end pressure is an in stance of a similar compound distortion combined with condensa tion of the substance, both distortion and condensation uniform throughout. Example 4. Flexure of a round wire or of a liar, or beam, or girder, of any shape of normal section, by opposite bending couples applied at the two ends, is an instance in which one-half of the sub stance is stretched, and the other half shortened with exactly the same combination of distortions and changes of bulk as in examples 2 and 3. The strain is uniform along the length of the bar, but varies in the cross section in simple proportion to distance from a certain line (sec. 62) through the centre of gravity of the sectional nrea, which, in the case of a round bar, is the diameter perpendicular to the plane of curvature. The limits of elasticity in the cases of these four examples are subjects of vital importance in practical mechanics, and a vast amount of careful and accurate observation and experiment, which has given much valuable practical information regarding them, has been gone through by engineers, in their necessary dealings with questions regard ing strength of materials. Still there is great want of definite scientific information on the subject of limits of elasticity generally, and particularly on many elementary questions (section 21 below), which force themselves upon us when we endeavour to analyze the molecular actions concerned in such cases as the four examples now before us. Some principles of much importance for guidance in practical as well as theoretical deductions from observa tions and experiments on this subject were set forth twenty- nine years ago by Professor James Thomson, in an article published in the Cambridge and Dublin Mathematical Journal for November 1848. Nothing is to be gained either in clearness or brevity by any other way of dealing with it than reproducing it in extenso. It is accordingly given here, with a few changes made in it with its author s concurrence. It constitutes the following sections, 10-20. "On the strength of materials, as influenced by the existence or non- existence of certain mutual strains 1 among the particles cojn2)oswj them. By James Thomson, M.A., College, Glasgow. 10. "My principal object in the following paper is to show that the absolute strength of any material composed of a substance possess ing ductility (and few substances, if any, are entirely devoid of this property) may vary to a great extent, according to the state of tension or relaxation in which the particles have been made to exist when the material as a whole is subject to no external strain. 11. " Let, for instance, a round bar of malleable iron, or a piece of iron wire, be made red hot, and then be allowed to cool. Its 1 [Note added Nov. 1877.] More nearly what Is now called stress than what is now called strain is meant by "strain " in this article, which was written before Kankine s introduction of the word stress, and distinct definition of the word
strain (see chap. i. of Mathematical Theory below).