Page:Encyclopædia Britannica, Ninth Edition, v. 7.djvu/821

797 ELASTICITY 797 4. The elasticity of shape of many solids is not perfect : it is not known whether it is perfect for any. It might be expected to be perfect for glass and rock crystal and diamond and other hard, brittle, homogeneous substances; but experiment proves that at all events for glass it is not so, and shows on the contrary a notable degree of imperfec tion in the torsional elasticity of glass fibres. It might be expected that in copper and soft iron and other plastic metals the elasticity of shape would be very imperfect ; experiment shows, on the contrary, that in copper, brass, soft iron, steel, platinum, provided the distortion does not exceed a certain limit in each case, elasticity of shape is remarkably perfect, much more perfect than in glass. It is quite probable that even in the softer metals zinc, tin, lead, cadmium, potassium, sodium, &c. the elasticity of shape may be as perfect as in the metals mentioned above, but within narrower limits as to degree of distortion. Accurate experiment is utterly wanting, to discover what is the degree of imperfection, if any, of the elasticity of any metal or alloy, when tested within sufficiently narrow limits of distortion. 5. The &quot; viscosity of metals&quot; described below (sections 21- 25) does not demonstrate any imperfectness of elasticity according to the definition of section 1, which is purely statical. The viscosity of solids may (for all we yet know by experiment) depend, as does the viscosity of fluids, upon a resistance varying with the velocity of the change, and vanishing ivhen the velocity of the change is zero, that is to say, when the body is at rest in any configuration ; if so, the elasticity of the substance concerned is perfect within the limits of the experiment in question. If, on the other hand (as the discovery of elastic fatigue described below seems to indicate may be to some degree the case), the loss of energy from the vibrations in the experiments described is due to a dependence of the elastic resilient force upon previous conditions of the substance in respect to strain, the &quot; viscosity &quot; would be continuous with a true imperfect- ness of static elasticity. Here, then, we have a definite question which can be answered by experiment only : Con sider a certain definite stress applied to a solid substance ; as, for example, a certain &quot; couple &quot; twisting a wire or rod ; or a certain weight pulling it out, or compressing it lengthwise ; or a certain weight placed on the middle of a beam supported by trestles under its ends. Let it be applied and removed a great many times, and suppose it to be .seen that after each application and removal of ths stress the body comes to rest in exactly the same configuration as after the previous application or removal of the stress. If now the body be left to itself with the stress removed, and if it be found to remain at rest in the same configuration for minutes, or hours, or days, or years after the removal of the stress, a part of the definition of perfect elasticity is fulfilled. Or, again, if the stress be applied, and kept applied with absolute constancy, and if the body remain permanently in a constant con figuration, another item of the definition of perfect elasticity is proved. When any such experiment is made on any metal, unless some of the softer metals (section 4) is to be excepted, there is certainly very little if any change of con figuration in the circumstances now supposed. The writer believes, indeed, that nothing of the kind has hitherto been discovered by experiment, provided the stress has been considerably less than that which would break or give a notable permanent twist, or elongation, or bend, to the body, that is to say, provided the action has been kept decidedly within the limits of the body s elasticity as commonly understood (sections 7-20). Mr J. T. Bottornley, with the assistance of a grant of money from tho British Association, has commenced making arrangements for secular experi ments on the elasticity of metals, in the tower of the university of Glasgow, to answer this question in re spect to permanence or non-permanence through minutes, or hours, or days, or years, or centuries. If several gold wires are hung side by side, one of them bearing the smallest weight that will keep it approximately straight, another wire -^ of the breaking weight, another wire -/$ of the breaking weight, and so on ; the one of them bearing -| of the breaking weight will probably, in the course of a few hours or days, show very sensible elongation. Will it go on becoming longer and longer till it breaks, or will the time-curve of its elongation be asymptotic 1 Even with considerably less than -j-g- of the breaking weight there will probably be a continually augmenting elongation, but with asymptotic time-curve indicating a limit beyond which the elongation never goes, but which it infinitely nearly reaches in an infinite time. It is not probable that a gold wire stretched by -^ of its present breaking weight, or by ^ of its present breaking weight, or even by ^ of its present breaking weight, would break in a thousand or in a million years. The existence of gold ornaments which have been fouud in ancient tombs and cities, and have preserved their shapes for thousands of years without running down glacier-wise (as does brittle pitch or sealing-wax in the course of a few years in moderately warm climates), seems to prove that for gold (and therefore leaves no doubt also for many other metals) the time-curve is asymptotic, if indeed there is any slow change of shape at all after the application of a moderate stress well within the limits of elasticity. Egyptian and Greek statues, Etruscan vases, Egyptian obelisks, and other stone monuments with their engraved hieroglyphics, flint implements and boulders, and mountains with the geological evidence we have of their antiquity, prove for stones, and pottery, and rocks of vari ous kinds, a permanence for thousands and milliocs of years of resistance to distorting stress. 6. The complete fulfilment of the definition of perfect elasticity is not proved by mere permanence of the extreme configurations assumed by the substance when a stated amount of the stress is alternately applied and removed. This condition might be fulfilled, and yet the amount of elastic force might be different with the same palpable configuration of the body during gradual augmentation and during gradual diminution of the stress. That it is so in fact is proved by the discovery of viscosity referred to below ; but it is not yet proved that if, after increasing the stress to a certain definite amount, the body is brought to rest in the same palpable configuration as before, the amounts of stress required to hold it in this configuration are different in the two cases. If they are (section 1) the elasticity is imperfect ; if they are not the elasticity is perfect within the limits of the experiment (compare section 36 below). 7. LIMITS OF ELASTICITY Elasticity of Shape. The degree of distortion within which elasticity of shape is fouud is essentially limited in every solid. Within sufficiently narrow limits of distortion every solid shows elasticity of shape to some degree some solids to perfec tion, so far as we know at present. When the distortion is too great, the body either breaks or receives a permanent; bend (that is, such a molecular disturbance that it does not return to its original figure when the bending force is removed). If the first notable dereliction from perfectness of elasticity is a breakage, the body is called brittle, if a permanent bend, plastic or malleable or ductile. The metals are generally ductile; some metals and metallic alloys and compounds of metals with small proportions of other substances, are brittle ; some of them brittle only in certain states of temper, others it seems essentially brittle. The steel of before the days of Bessemer and Siemens is a remarkable instance. When slowly cooled from a bright