Page:The New International Encyclopædia 1st ed. v. 06.djvu/843

* ELASTICITY. 731 ELASTIN. the small parts of llie wire are altered; and therefore Young's modulus must depend upon both the hulk-modulus and the coefficient of rigidity, t'alliiij.' Young's modulus E, it may be sliown theoretically that 1 _ 1 1^ E ~" M + :U Solids differ greatly in their compressibility and in their rigidity; and they diller widely in llu- extent to whii-li they may be deformed and yet recover thoir former shape and size when released from the deforming forces. If the strain is too great, the body does not regain its former condition; the 'limits of elasticity' are said to have been passed. A body is called 'elastic' if these limits permit a large strain — e.g. glass, steel; while if these limits permit only small or minute strains, the body is said to he 'inelastic' If, however, the strain is small enough solids do return quite e.xactl,y to their former states; and for such small strains it is observed that the amount of the deformation produced varies directly as the deforming force. This is called 'Hooke's law,' from the name of the one wlio first proposed it, Robert Hooke. Man,v solids after being strained return to their previous condition slowly after the deforming force is removed: and nearly all take consider- able time to reach their permanent strain when a force is applied. There is therefore .a slight molecular 'slipping' in general in every deforma- tion of a solid : this necessarih" involves internal friction and the production of heat effects — in particular, rise in temperature. A 'perfect' solid might be defined as one in which there is no internal friction : while the more inelastic a body is, tile greater are the slipping and the in- ternal friction when there is a deformation. Since solids have, in general, elasticity both as to change in volume and as to change in shape, a solid medium can transmit two kinds of >vaves, compressional and transverse. (See Waves.) A solid rod, too, can vibrate in several wa.vs: longitudinally, if it is stroked length- wise; torsionally. if it is twisted; from side to side, like a tuning-fork, if it is bent. Fluids. A fluid is defined to he such a form of matter as will yield to a shearing force, how- ever small. Thus it is necessary to discuss the elasticity of fluids with reference to changes in volume only. As before, the definition of the coefficient of elasticity is ■ A/, k = Av where v is the original volume, and Af is the decrea.se in the volume accompanying an increase in the internal pressure of an amount Ap. For liquids k is very large, since they are so slightl.v compressible; for a gas, however, it is much smaller. When any portion of matter is com- pressed, the temperature is increased (except in most special eases) ; and this fact alters the value of the change of pressure corresponding to n definite change in volume. If the change in volume is to be due to the change in pressure alone, it is necessary to change the volume so slow- ly that the temperature remains practically con- stant. This fact is of particular importance in the case of gases, because they are so easily com- pressed and there is accordingly such a great rise in temperature unless care is taken. If -the Vol. VI —»7. gas is compressed so suddenly that the whole change in volume takes place before there is time for any loss of heat b,v radiation or con- duction, the temperature will rise greatly, and this will produce a nuirked increase in the pres- sure of the gas. tlius increasing the coefficient of elasticity for tlic gas. The eoellicient for a gas, when there is no change in temperature, ma.y be calculated from Bo.yle's law for a gas, which states that as long as the temperature of a gas does not change, the product of its pressure and volume remains con- stant, however the volume is altered. Thus, if r is the volume of the gas when the pi-essure is p, and r — Av. the volume when the pressure is increased to p + A/i, then pv = (p -- Ap)tv — Ac) = pi— II At- + ''^/>> if A/) and Av are so small that their product may be neglected. Hence pAv =: r A/» and therefore I: =■ Ac In words, the coefficient of elasticity for a gas at constant temperature numerically equals its pressure. If, however, the change in volume is made so rapidl,y that the heat produced has no time to escape, the coefficient equals ;//, where) ia a constant for any one gas, being equal to the ratio of the specific heat at constant pressure to that at constant volume. (See He.^t. I For air, hydro- gen, and oxygen y very nearly eqiuils 1.4. A fluid medium can transmit compressional waves onl.y; and in these the vilirations must be rapid, otherwise the fluid would flow round the vibrating l)od.y which is the cause of the waves. Therefore, the elasticit.v which is called into play is the one corresponding to no escape of heat. TABLES Srjlhh Glass 4.1X10" 2.4X10" Brass 10.6X10" 3.8X10" 11X10" Steel 18.8X10" 8.2X10" 20X10" Liquids Temperature AVater 8° C. 0.22X10" Sulphuric Ether 10° C. 0.07X10" Gaaes At pressure of 70 cm. iif mercury. 1.01 X 10" ELASTIC LIMIT. See Strength of Ma- TEIUAI.S. ELASTIC TISSUE. One of (he forms of fibrous tissue, known also as yellow filirous tissue. It derives its name from the reiuarkahle physical propert.y which it possesses of permitting its fibres to be ilrawu out to doulilc their length, and again returning to their original length. It occurs in various ligamentous and oHier struc- tures of the animal body in which elasticit.v is required, as. for example, in the vocal cords, the membranes connecting the cartilaginous rings of the trachea, the middle coat of the arteries, the skin. etc. ELASTIN (from elastic). . characteristic chemical constituent of the substance of all elastic fibres of the animal body. It may be pre- pared from the liganientvnii nuchie of an ox by