Page:The American Cyclopædia (1879) Volume VI.djvu/498

490 ELASTICITY the elasticity of the earth, considered as a whole, which is an important element in the theory of oceanic tides. Sir William Thom- son, who has given much attention to this problem, concludes (1871) that the earth has considerably more average rigidity than a globe of glass of the same size ; were it not so, the yielding of the solid earth to the tidal influence of the sun and moon would to a great degree annul the observed ocean tides. The elasticity of a body subjected to a severe strain is in general permanently injure^; and Messrs. Hodgkinson and Fairbairn (1837) concluded from their experiments on iron, &c., that the limit of perfect elasticity is much lower than was formerly conceived; that, indeed, a per- manent set takes place in ordinary cast iron on the application of even a very slight force; and that there is in general no clearly defined limit of perfect elasticity. This conclusion is probably applicable only to the metals as found in commerce, and not to chemically pure homo- geneous or crystalline masses. The ease with which a solid body receives a slight permanent set or deformation is expressed by the words soft and plastic, and the stress on a unit sec- tion exerted at the time the body breaks or crushes is the coefficient of rupture; at the limit of perfect elasticity the investigation of elasticity proper ceases, and the phenomena become those of viscosity, as previously de- fined, until the force applied causes a rupture of the body.* In connection with the elastic properties of solids there remain to be noticed the phenomena of impact. When two bodies strike each other, the portions in contact are forcibly compressed ; and as no body is per- fectly inelastic, they begin to separate as soon as the compression reaches its maximum value. Newton found that the relative velocity of separation after impact bears a proportion to the previous relative velocity of approach, which is constant for the same two bodies; this proportion is always less than unity, but approaches that limit the harder the bodies are. To this proportion the name coefficient of elasticity is frequently given ; this, however, is a misnomer, and Thomson and Tait suggest the more appropriate term coefficient of resti- tution, while others call it the coefficient of impact. The quantity of force, if any, that is apparently annulled on the collision of two bodies, is not destroyed, but is converted into the other forms of molecular elasticity, i. e., the vibrations of sound, heat, light, and actin- ism, which spread in all directions to indefinite distances from the place of their origin. Crys- talline bodies differ from homogeneous ones, so far as concerns their elastic properties, only in that the coefficient of elasticity varies with the direction of the external forces that produce the strain. Jellies form a class of solids dis- tinguished by a wide range of distortion possi- ble within the limits of perfect elasticity, or without producing permanent deformation. In solid bodies the limit of perfect, elasticity varies from something indefinitely small, as in most hard bodies, to a number as large as 1-1 or 1-2, as in the case of cork, and to 2 or 3 in the case of India rubber ; the latter is, in its pu- rest state, more properly allied to the class of jellies. In the vibration of solids it has been observed that a force generally called internal or molecular friction resists the vibrations and diminishes their amplitude ; this resisting force is probably nothing but the transformation of a portion of the vibratory movement of the mass into heat vibrations. The development of in- ternal friction is specially notable in the vibra- tions of jellies ; it is allied to, if not the same as, the property of viscosity in fluids. The distinctive property of a fluid is that its mole- cules can quickly, easily, and permanently change their relative positions ; a perfect fluid is a body incapable of resisting a change of shape, provided only that its volume be not altered. Fluids are divided into the two classes of liquids and gases, according to the relative values of their coefficients of elasticity and viscosity. The elasticity of liquids is generally known as their compressibility, which property has reference to the behavior of the interior of a mass of liquid ; the phenomena of capil- larity, on the other hand, depend on the pecu- liar elastic condition of the superficial film of a mass of liquid. "The coefficient of elas- ticity of a fluid is the ratio of any small in- crease of pressure to the cubical compression thereby produced. The elasticity however va- ries with certain conditions that may be im- posed, such as that the fluid be under a given pressure or exposed to a given temperature. Every substance has two elasticities, one cor- responding to a constant temperature, the other corresponding to the case where no heat is allowed to escape from the body during the process of compression. In the latter case the elasticity is always greater than in the case of uniform temperature." The following are the coefficients of compressibility of several liquids, or the fractions by which the original volume is diminished for an increase of pressure of one atmosphere or about 16 Ibs. to the square inch: Substance. Coefficient of elasticity. Mercury at a temperature of 82 Fahr 0-000008 Water " " 82 0-000050 107 0-000044 Alcohol u " 45 0-000084 Ether " " 82 0-000111 57 0-000140 The other and highly important property, the superficial elasticity of liquids, is commonly known as the phenomena of thin films, of capillarity, &c, and is well illustrated by the blowing of a soap bubble, which operation is but the forcible stretching of a superficial sheet of a highly elastic liquid membrane. The su- perficial tension of the latter may be measured in grammes weight per linear metre or other unit ; it is the same whether the globe be hollow or full ; it varies with different liquids and with the nature of the gas or other fluid