ELASTICITY 801 Fig. 2. where the continuous lines represent a portion of the unpulled wire, and the dotted lines the same portion of the wire when pulled. The change in each of the angles would be -^ of the radian in virtue of the elongation were there no lateral shrinking, and about -g^ of the radian in virtue of the lateral shrink ing were there no elongation. Thewhole change experienced by each of the right angles is therefore actually (section 37) sV + ir3T7> or about ^ of the radian, or 0* 84. This is an extreme cass. In all other cases of metals, stones, glasses, crystals, the substance either breaks or takes a permanent bend, probably be fore it experiences any so great angular distortion as a degree ; and except in the case of steel we may roughly regard the limits of elasticity as being some thing between y^o" and --^ in respect to the linear elongation or contraction, and from J^ of a degree to half a de gree in respect to angular distortion. 24. On the other hand, gelatinous substances, such as india-rubber and elastic jellies, have very wide limits of elasticity. A vulcanized india-rubber band, for instance, is capable of being stretched, again and again, to eight times its length, and returning always to nearly its previous condition when the stress is removed. A shape of transparent jelly presents a beautiful instance of great degrees of distortion with seemingly very perfect elasticity. All these instances, india-rubber and jellies, show with great changes of shape but slight changes of bulk. They have, in fact, all, as nearly as experiment has hitherto been able to determine, the same compressibility as water. 25. Cork, another body with very wide limits of elasticity (very imperfect elasticity it is true) is singular, among bodies seemingly homogeneous to the eye, in its remarkably easy compressibility. It is, in fact, the only seemingly homogeneous solid which shows to the unaided eye any sensible change of bulk under any practically applicable forces. A small homogeneous piece torn out of a cork may, by merely pressing it between the fingers, be readily com pressed to half its bulk, and a large slab of cork in a Brarnah press may be compressed to -^ of its bulk. An ordinary bottle cork loaded with a small piece of metal presents a very interesting appearance in an Oersted glass compressing vessel; first floating, and when compressed to 20 or 30 atmospheres sinking, and shrivelling in bulk very curiously; then on the pressure being removed, expanding again, but not quite to previous bulk, and floating up or remaining down according to the amount of its load. The divergencies presented by cork and gelatinous bodies in opposite directions from the regular elasticity of hard solids form an interesting subject, to which we shall return later (section 48). 26. Liquids. In respect to liquids, there are no limits of elasticity so far as regards the magnitude of the positive pressure applied or conceivably applicable; but in respect to the magnitude of negative pressure, and in respect to the magnitude of the change of bulk, whether by negative or positive pressure, there are probably very decided and not very wide limits. Thus water, though condensed r *- of its bulk by 2000 atmospheres in Per kins s 1 experiments corrected roughly for the compres- 1 Transactions of Royal Society, June 1826, "On the Progressive Compression of Water by high degrees of force, with some trials of its effects on othej- liquids," by J . Perkins. Communicate-l by W. H. Wollaston, M.D., V.P.B.S. sion of his glass " piezometer," which is very nearly at the rate of ^-y^ny per atmosphere found (section 75 below) more accurately by subsequent experiments for moderate pressures up to 20 or 30 atmospheres, may be expected to be compressed by much less than ^ of its volume under a pressure of 7000 atmospheres. How much it or any other liquid is condensed by a pressure of 10,000 atmospheres, or by 20,000 atmospheres, is an interesting subject for experimental investigation. 27. Gases. In respect to rarefaction, and in respect to proportionate condensation, gases present enormously wider limits of elasticity than any liquids or solids, in fact no limit in respect to dilatation, and in respect to condensation a definite limit only when the gas is below Andrews s "critical temperature." If the gas be kept at any temperature above that critical temperature, it remains homogeneous, however much it be condensed; and therefore for a fluid above the critical temperature there is, in respect to magnitude of pressure, no superior limit to its elasticity. On the other hand, if a fluid be kept at any constant temperature less than its critical temperature, it remains homogeneous, and presents an increasing pressure until a certain density is reached; when its bulk is further diminished it divides into two parts of less and greater density (the part of less density being called vapour, that of greater density being called liquid, if it is not solid) and presents no further increase of pressure until the vaporous part shrinks to nothing, and the whole becomes liquid (that is to say, homo geneous fluid at the greater of the two densities) or else becomes solid the question whether the more dense part is liquid or solid depending on the particular temperature below the critical temperature at which the whole substance is kept during the supposed experiment. 28. The thermo-dynamic reasoning of Professor James Thomson, which showed the effect of change of pressure in altering the freezing point of a liquid, leads to analogous considerations regarding the eft ect of continuous increase or continuous decrease of pressure upon a mass consisting of the same substance partly in the liquid and partly in the solid state at one temperature. The three cases of transi tion from gas to liquid, from gas to solid, and from liquid to solid, present us with perfectly definite limits of elasticity, the only perfectly definite limits of elasticity in nature of which we have any certain knowledge. 29. Viscosity of Fluids and Solids. Closely connected with limits of elasticitj , and with imperfectness of elasticity, is viscosity, that is to say, resistance to change of shape depending on the velocity of the change. The full dis covery of the viscosity of liquids and gases is due originally to Stokes ; and his hypothesis that in fluids the force of resistance is in simple proportion to the velocity cf change of shape has been subsequently confirmed by the experi mental investigations of Helmholtz, Maxwell, Meyer, Kundt, and Warburg. The definition of a fluid given in section 2 above may, by section 1, be transformed into the following: A fluid is a body which requires no force to keep it in any particular shape, or A fluid is a body which exercises no permanent resistance to a change of shape. The resistance to a change of shape presented by a fluid, evanescent as it is when the shape is not being changed (or vanishing when the velocity of the change vanishes), is essentially different from that permanent resistance to change of shape, the manifestation of which in solids constitutes elasticity of shape as defined in section 1. Maxwell s admirable kiretic theory of the viscosity cf gases points to a full explanation of viscosity, whether of gases, liquids, or solids, in the consideration of configura tions and arrangements of relative motions of molecules, permanent in a solid under distorting stress, and temporary in fluids or solids while the shape is being changed, in
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