Page:Encyclopædia Britannica, Ninth Edition, v. 7.djvu/828

804 ELASTICITY to the cause ; and the experiments on -which it is founded prove a perfect continuity from a pulling force to a smaller force in the same direction, and from the less force to zero, and from zero of pulling force to different degrees of push or positive pressure, or negative pull. Experimental proof merely of the continuity of the phenomena through zero of force suffices to show that, for infinitely small positive or negative pulls, positive or negative elongation is simply proportional to the positive or negative pull ; or, in other words, positive or negative contraction is proportional to the positive or negative pressure producing it. But now must be invoked minutely accurate experimental measurement to find how nearly the law of simple proportionality holds through finite ranges of contraction and elongation. The answer happily for mathematicians and engineers is that Ilooke s law is fulfilled, as accurately as any experiments hitherto made can tell, for all metals and hard solids each through the whole range within its limits of elasticity; and for woods, cork, india-rubber, jellies, when the elongation is not more than two or three per cent., or the angular dis tortion not more than a few hundredths of the radian (or not more than about two or three degrees). The same law holds for the condensation of liquids up to the highest pressures under which their compressibility has hitherto been accurately measured. [A decided but small deviation from Hooke s law has been found in steel pianoforte wire under combined influence of torsion and longitudinal pull by Mr M Farlane in experiments made for the present article after this section was in type. See section 81.] Boyle s law of the &quot; spring of air w shows that the augmentation of density of a gas is simply proportional to the augmentation of the pressure, through the very wide ranges of pressure through which that law is approximately enough fulfilled. Hence the infinitesimal diminution of volume produced by a given infinitesimal augmentation of pressure varies as the square of the volume, and the proportionate diminution of volume (that is to say, the ratio of the diminution of volume to the volume) is proportional to the volume, or inversely proportional to the density. Andrews s experiments on the compressibility of a fluid, such as carbonic acid, at temperatures slightly above the critical temperature, and of the gas and of liquids at tem peratures slightly below the critical temperature, are in tensely interesting, not merely in respect to the natural history of elasticity, but as opening vistas into the philoso phy of molecular action. We cannot expect to find any law of simple propor tionality between stress and change of dimensions, or pro portionate change of dimensions, in the case of any elastic or semi-elastic &quot; soft &quot; solids, such as cork on one hand or india-rubber or jellies on the other, when strained to large angular distortions, or to large proportionate changes of dimensions. The exceedingly imperfect elasticity of all these solids, and the want of definiteness of the substance of many of them, renders accurate experimenting unavail able for obtaining any very definite or consistent numerical results ; but it is interesting to observe roughly the forces required to produce some of the great strains of which they are capable without any total break down of elastic quality ; for instance, to hang weights successively on an india- rubber band and measure the elongations. This any one may readily do, and may be surprised to find the enormous increase of resistance to elongation presented by the attenu ated band before it breaks. 38. Homogeneousness defined. A body is called homo geneous when any two equal, similar parts of it, with corresponding lines parallel and turned towards the same parts, are un distinguishable from one another by any difference in quality. The perfect fulfilment of this condi tion, without any limit as to the smallness of the parts, though conceivable, is not generally regarded as probable, for any of the real solids or fluids known to us, however seemingly homogeneous. It is held by all naturalists that there is a molecular structure, according to which, in com pound bodies such as water, ice, rock-crystal, &c., the con stituent substances lie side by side, or arranged in groups of finite dimensions, and even in bodies called simple (that is those not known to be chemically resolvable into other substances) there is no ultimate homogeneousness. In other words, the prevailing belief is that every kind of matter with which we are acquainted has a more or less coarse-grained texture, whether (as great masses of solid brick-work or stone-building, or as natural sandstone or granite rocks) having visible molecules, or (as seemingly homogeneous metals, or continuous crystals, or liquids, or gases) having molecules too small to be directly visible, or measurable but not undiscoverably small, really, it is to be believed, of dimensions to be accurately determined in future advances of science. Practically the definition of homogeneousness may be applied on a very large scale to masses of building or coarse-grained conglomerate rock, or on a more moderate scale to blocks of common sandstone, or on a very small scale to seemingly homogeneous metals j 1 or on a scale of extreme, undiscovered fineness, to vitreous bodies, continuous crystals, solidified gums, as india-rubber, gum-arabic, &c., and fluids. 39. Isotropic and ^Eolotropic Substances defined. The substance of a homogeneous solid is called isotropic when a spherical portion of it, tested by any physical agency, exhibits no difference in quality however it is turned. Or, which amounts to the same, a cubical portion, cut from any position in an isotropic body, exhibits the same qualities relatively to each pair of parallel faces. Or two equal and similar portions cut from any positions in the body, not subject to the condition of parallelism (section 38),are undistingnishable from one another. A substance which is not isotropic, but exhibits differences of quality in different directions, is called ceolotrojric.- The remarks of section 38 relative to homogeneousness in the aggregate, and the supposed ultimately heterogeneous texture of all substances, however seemingly homogeneous, indicate cor responding limitations and non-rigorous practical interper- tations of isotropy and aeolotropy. 40. Isotropy and jEolotropy of di/erent sets of proper ties. The substance of a homogeneous solid may be iso tropic in one quality or class of qualities, but aeolotropic in others. Or a transparent substance may transmit light at different velocities in different directions through it (that is, be doubly -refracting], and yet a cube of it may (and does in many natural crystals) show no sensible difference in its absorption of white light transmitted across it perpendi cularly to any of its three pairs of faces. Or (as a crystal which exhibits dichroism) it may be sensibly asolotropic relatively to the absorption of light, but not sensibly double-refracting, or it may be dichroic and doubly-refract ing, and yet it may conduct heat equally in all directions. Still, as a rule, a homogeneous substance which is ceolotropic for one quality must be more than infinitesimally yeolotropic for every quality which has directional character admitting of a corresponding aeolotropy. 41. Moduluses of Elasticity. A modulus of elasticity is the number obtained by dividing the number expressing a stress 3 by the number expressing the strain 4 which it pro duces. A modulus is called a principal modulus when 1 Which, however, we know, as proved by Deville and Van Troost, are porous enough at high temperatures to allow very free percolation of gases. Hehnholtz and Root find percolation of platinum by hydro gen at ordinary temperature (tierl. Xitzungsbcricht). 2 Thomson and Tait s Natural Philosophy, section 676. 3 Mathematical Theory, below chap. i. * Ibid.