CONSTITUTION OF BODIES stance, it is found that when the stress is removed it does not return exactly to its original shape, but remains per manently deformed. These limits of the different kinds of strain are called the limits of perfect elasticity. There are other limits which may be called the limits of cohesion or of tenacity, such that when the deformation of the body reaches these limits the body breaks, tears asunder, or otherwise gives way, and the continuity of its substance is destroyed, A body which can have its form permanently changed without any flaw or break taking place is called mild. "When the fores required is small the body is said to be soft ; when it is great the body is said to be tough. A body which becomes flawed or broken before it can be permanently deformed is called brittle. When the force required is great the body is said to be hard. The stiffness of a body is measured by the force required to produce a given amount of deformation. Its strength is measured by the force required to break or crush it. We may conceive a solid body to approximate to the condition of a fluid in several different ways. If we knead fine clay with water, the more water we add the softer does the mixture become till at last we have water with particles of clay slowly subsiding through it. This is an instance of a mechanical mixture the constituents of which separate of themselves. But if we mix bees wax with oil, or rosin with turpentine, we may form per manent mixtures of all degrees of softness, and so pass from the solid to the fluid state through all degrees of viscosity. We may also begin with an elastic and somewhat brittle substance like gelatine, and add more and more water till we form a very weak jelly which opposes a very feeble resistance to the motion of a solid body, such as a spoon, through it. But even such a weak jelly may not be a true fluid, for it may be able to withstand a very small force, such as the weight of a small mote. If a small mote or seed is enclosed in the jelly, and if its specific gravity is different from that of the jelly, it will tend to rise to the top or sink to the bottom. If it does not do so we con clude that the jelly is not a fluid but a solid body, very weak, indeed, but able to sustain the force with which the mote tends to move. It appears, therefore, that the passage from the solid to the fluid state may be conceived to take place by the diminution without limit either of the coefficient of rigidity, or of the ultimate strength against rupture, as well as by the diminution of the viscosity. But whereas the body is not a true fluid till the ultimate strength, or the coefficient of rigidity, are reduced to zero, it is not a true solid as long as the viscosity is not infinite. Solids, however, which are not viscous in the sense of being capable of an unlimited amount of change of form, are yet subject to alterations depending on the time during which stress has acted on them. In other words, the stress at any given instant depends, not only on the strain at that instant, but on the previous history of the body. Thus the stress is somewhat greater when the strain is increasing than when it is diminishing, and if the strain is continued for a long time, the body, when left to itself, does not at once return to its original shape, but appears to have taken a set, which, however, is not a permanent set, for the body slowly creeps back towards its original shape with a motion which may be observed to go on for hours and even weeks after the body is left to itself. Phenomena of this kind were pointed out by Weber and Kohlrausch (P<*jg. Ann, Bd. 54, 119 and 128), and have been described by O. E. Meyer (Pogg. Ann. Bd. 131, 108), and by Maxwell (Phil. Trans. 1866, p. 249), and a theory of the phenomena has been proposed by Dr L. Boltzmaun (Wiener Sitzungsberichte, 8th October 1874). The German writers refer to the phenomena by the name of " elastische Nachwirkung," which might be translated " elastic reaction " if the word reaction were not already used in a different sense. Sir W. Thomson Vpeaks of the viscosity of elastic bodies. The phenomena are most easily observed by twisting a fine wire suspended from a fixed support, and having a small mirror suspended from the lower end, the position of which can be observed .in the usual way by means of a telescope and scale. If the lower end of the wire is turned round through an angle not too great, and then left to itself, the mirror makes oscillations, the extent of which may be read off on the scale. These oscillations decay much more rapidly than if the only retarding force were the resistance of the air, showing that the force of torsion in the wire must be greater when the twist is increasing than when it is diminishing. This is the phenomenon described by Sir W. Thomson under the name of the viscosity of elastic solids. But we may also ascertain the middle point of these oscillations, or the point of temporary equilibrium when the oscillations have subsided, and trace the variations of its position. If we begin by keeping the wire twisted, say for a minute or an hour, and then leave it to itself, we find that the point of temporary equilibrium is displaced in the direction of twisting, and that this displacement is greater the longer the wire has been kept twisted. But this dis placement of the point of equilibrium is not of the nature of a permanent set, for the wire, if left to itself, creeps back towards its original position, but always slower and slower. This slow motion Las been observed by the writer going on for more than a week, and he also found that if the wire was set in vibration the motion of the point of equilibrium was more rapid than when the wire was not in vibration. We may produce a very complicated series of motions of the lower end of the wire by previously subjecting the wire to a series of twists. For instance, we may first twist it in the positive direction, and keep it twisted for a day, then in the negative direction for an hour, and then in the positive direction for a minute. When the wire is left to itself the displacement, at first positive, becomes negative in a few seconds, and this negative displacement increases for some time. It then diminishes, and the displacement becomes positive, and lasts a longer time, till it too finally dies away. The phenomena are in some respects analogous to the variations of the surface temperature of a very large ball of iron which has been heated in a furnace for a day, then placed in melting ice for an hour, then in boiling water for a minute, and then exposed to the air ; but a still more perfect analogy may be found in the variations of potential of a Leyden jar which has been charged positively for a day. negatively for an hour, and positively .again for a minute. 1 The effects of successive magnetization on iron and steel are also in many respects analogous to those of strain and electrification. 2 The method proposed by Boltzmann for representing such phenomena mathematically is to express the actual stress, L//), in terms not only of the actual strain, 0), but of the strains to which the body lias been subjected during all previous time. His equation is of the form /OD o 1 See Dr Hopkinson, " On the Residual Charge of the Leyden Jar," Proc. R. S., xxiv. 408, March 30, 1876.
- See Wiedemann s Galvanismus, vol. ii. p. 567.
