Page:The American Cyclopædia (1879) Volume VI.djvu/496

488 ELASTIC CUEVE ELASTICITY the orbits ; teeth long, cylindrical, very sharp, and fitted for seizing the fish upon which it fed. It attained a length of 45 feet, and might well furnish a model for the modern sea ser- pent, which in the light of geology is not a zoological impossibility. ELASTIC CURVE, the curve assumed by a straight spring of uniform thickness when the ends are brought forcibly together. It em- braces a variety of appearances, simple waves, overlapping waves, a figure of eight, retro- grade loops or kinks, ordinary loops, and the circle. The fundamental law or equation of the curve is that the curvature of each point is directly proportional to its distance from a certain straight line on which the curvature is zero; so that when the curve crosses this line it reverses the direction of its curvature. ELASTICITY, the property in virtue of which a body tends to recover its form and dimen- sions on the removal of the forces by which these have been changed. A perfectly elastic body is defined by Thomson and Tait (1872) as one which " when brought to any one state of strain requires at all times the same stress to hold it in this state, however long it may be kept strained, or however rapidly its state may be al- tered from any other strain or from no strain to the strain in question." According to Maxwell (1872), a perfectly elastic body is one " which, subjected to a given stress at a given tempera- ture, experiences a strain of definite amount, which does not increase when the stress is pro- longed, and which disappears completely when the stress is removed." If the form of the body is found to be permanently altered, its state of stress just previous to the change is called the limit of perfect elasticity. If the stress increases until the body breaks, the value of the stress is called the strength of the mate- rial. If breaking takes place before there is any permanent alteration of form, the body is said to be brittle. If the stress, when it is main- tained constant, causes a displacement within the body which increases continually with the time, the substance is said to be viscous. Vis- cosity, whether in solids or fluids, is then inti- mately connected with their elasticity, and the preceding definitions of elasticity, although popularly associated with the behavior of solid bodies, are equally applicable to liquids and gases ; indeed, strictly interpreted, they have reference to the behavior of the molecules and ultimate atoms of which bodies are supposed to be composed. A perfect knowledge of the laws of elasticity is nothing less than a knowl- edge of the exact laws according to which atoms attract and repel each other, or, more generally, of the ultimate constitution of matter. In this broad sense this subject offers the most impor- tant and at the same time the most difficult field of study that can be cultivated by the physicist. The ultimate constitution of matter is in fact as truly the goal of the modern physi- cal and chemical sciences, as the constitution of the universe is the final problem of astrono- my. The tendency of modern physics is to look with distrust upon all theories of molecular action that assume the principle of action at a distance. When, however, we have attained to a correct knowledge of the internal constitution of bodies, it may be expected that the laws of elasticity will be deduced therefrom by mathe- matical processes. Until then the subject of our article must be treated inductively, except in so far as we assume the relative position of the particles of bodies to be disturbed only to an indefinitely small degree by the exterior forces ; in these cases the molecular motions may be deduced from the established general laws of mechanics, and have indeed been so investi- gated with great success by a host of scientists, beginning with Bernoulli, Young, Fresnel, and Green. The general investigation of the rela- tion between the strains and deformations of a solid has been shown by Green (1830) to de- pend upon the solution of a quadratic equation having 6 unknown quantities and 21 terms whose coefficients are essential for a complete theory of the dynamics of an elastic solid sub- jected to infinitely small strains. I. ELASTICI- TY OF MASSES. The elastic properties of homo- geneous bodies relate to the behavior either of the constituent molecules and sensible masses of the bodies or of their ultimate atoms to each other. In considering the latter class of rela- tions we have to do with chemical changes and the properties of heat, light, electricity, and magnetism. Considering the behavior of mo- lecules, we have to do with the laws of strength of materials, elasticity of springs, propagation of sound, &c. The latter class of phenomena will here first attract pur attention, and we shall treat in succession of solids, jellies, fluids, vapors, and gases, concluding with some of the relations between the molecular elastici- ties of these bodies and the agencies of heat, light, and electricity. Our first ideas as to the elasticity of solids are derived from the proper- ties of extension and compression under forces respectively of tension and pressure. In the second column of the following table is given for each substance the weight necessary to extend by T ^ part of its length (or one centi- metre) a bar whose section is one square milli- metre, and whose length is one metre : Modulus SUBSTANCE. Weight in kilogram- in kilo- grammes Modulus in pounds per Specific Modulus of length mes. per sq. mm. ,. inch. in metre?. Flint glass .... Brass 585-1 1,094-8 5,851 10,948 8.800,000 15,500,000 8-8 8-3 19,000 91,000 Copper 1,266-8 12.558 17,800,000 8-9 111,000 Cast iron 1,874-1 18,741 19,500,000 7-25 99,000 Wrought iron . 1,999-4 19.994 28.400,000 7-5 150,000 Steel 2,179-8 21,7H8 80,900,000 7-85 170,000 When the elongations are small they are, ac- cording to the law of Hooke, directly propor- tioned to the tension or the applied weight ; therefore in the preceding cases weights ten times as great as those in the second column