CONSTITUTION OF BODIES. The question whether the smallest parts of which bodies are composed are finite in number, or whether, on the other hand, bodies are infinitely divisible, relates to the 'ultimate constitution of bodies, and is treated of in the article ATOM.
The mode in which elementary substances combine to form compound substances is called the chemical constitu-tion of bodies, and is treated of in CHEMISTRY.
The mode in which sensible quantities of matter, whether elementary or compound, are aggregated together so as to form a mass having certain observed properties, is called the physical constitution of bodies.
Bodies may be classed in relation to their physical con-stitution by considering the effects of internal stress in changing their dimensions. When a body can exist in equilibrium under the action of a stress which is not uniform in all directions it is said to be solid.
When a body is such that it cannot be in equilibrium unless the stress at every point is uniform in all directions, it is said to be fluid.
There are certain fluids, any portion of which, however small, is capable of expanding indefinitely, so as to fill any vessel, however large. These are called gases. There are

other fluids, a small portion of which, when placed in a large vessel, does not at once expand so as to fill the vessel uniformly, but remains in a collected mass at the bottom, even when the pressure is removed. These fluids are called liquids.
When a liquid is placed in a vessel so large that it only occupies a part of it, part of the liquid begins to evaporate, or in other words it passes into the state of a gas, and this process goes on either till the whole of the liquid is evapor-ated, or till the density of the gaseous part of the substance has reached a certain limit. The liquid and the gaseous portions of the substance are then in equilibrium. If the volume of the vessel be now made smaller, part of the gas will be condensed as a liquid, and if it be made larger, part of the liquid will be evaporated as a gas.
The processes of evaporation and condensation, by which the substance passes from the liquid to the gaseous, and from the gaseous to the liquid state, are discontinuous processes, that is to say, the properties of the substance are very different just before and just after the change has been effected. But this difference is less in all respects the higher the temperature at which the change takes place, and Caguiard de la Tour in 1822 first showed that several substances, such as ether, alcohol, bisulphide of carbon, and water, when heated to a temperature sufficiently high, pass into a state which differs from the ordinary gaseous state as much as from the liquid state. Dr Andrews has since made a complete investigation of the properties of carbonic acid both below and above the temperature at which the phenomena of condensation and evaporation cease to take place, and has thus explored as well as established the continuity of the liquid and gaseous states of matter.
For carbonic acid at a temperature, say of 0° C, and at the ordinary pressure of the atmosphere, is a gas. If the gas be compressed till the pressure rises to about 40 atmo-spheres, condensation takes place, that is to say, the sub-stance passes in successive portions from the gaseous to the liquid condition.
If we examine the substance when part of it is condensed, we find that the liquid carbonic acid at the bottom of the vessel has all the properties of a liquid, and is separated by a distinct surface from the gaseous carbonic acid which occupies the upper part of the vessel.
But we may transform gaseous carbonic acid at 0° C. into liquid carbonic acid at 0° C. without any abrupt change, by first raising the temperature of the gas above 30°.92 C. which is the critical temperature, then raising the pressure to about 80 atmospheres, and then cooling the substance, still at high pressure, to zero.
During the whole of this process the substance remains perfectly homogeneous. There is no surface of separation between two forms of the substance, nor can any sudden change be observed like that which takes place when the gas is condensed into a liquid at low temperatures ; but at the end of the process the substance is undoubtedly in the liquid state, for if we now diminish the pressure to some-what less than 40 atmospheres the substance will exhibit the ordinary distinction between the liquid and the gaseous state, that is to say, part of it will evaporate, leaving the rest at the bottom of the vessel, with a distinct surface of separation between the gaseous and the liquid parts.
The passage of a substance between the liquid and the solid state takes place with various degrees of abruptness. Some substances, such as some of the more crystalline metals, seem to pass from a completely fluid to a completely solid state very suddenly. In some cases the melted matter appears to become thicker before it solidifies, but this may arise from a multitude of solid crystals being formed in the still liquid mass, so that the consistency of the mass becomes like that of a mixture of sand and water, till the melted matter in which the crystals are swimming becomes all solid.
There are other substances, most of them colloidal, such that when the melted substance cools it becomes more and more viscous, passing into the solid state with hardly any discontinuity. This is the case with pitch.
The theory of the consistency of solid bodies will be discussed in the article ELASTICITY, but the manner in which a solid behaves when acted on by stress furnishes us with a system of names of different degrees and kinds of solidity.
A fluid, as we have seen, can support a stress only when it is uniform in all directions, that is to say, when it is of the nature of a hydrostatic pressure.
There are a great many substances which so far corre-spond to this definition of a fluid that they cannot remain in permanent equilibrium if the stress within them is not uniform in all directions.
In all existing fluids, however, when their motion is such that the shape of any small portion is continually changing, the internal stress is not uniform in all directions, but is of such a kind as to tend to check the relative motion of the parts of the fluid.
This capacity of having inequality of stress called into play by inequality of motion is called viscosity. All real fluids are viscous, from treacle and tar to water and ether and air and hydrogen.
When the viscosity is very small the fluid is said to be mobile, like water and ether.
When the viscosity is so great that a considerable inequality of stress, though it produces a continuously increasing displacement, produces it so slowly that we can hardly see it, we are often inclined to call the substance a solid, and even a hard solid. Thus the viscosity of cold pitch or of asphalt is so great that the substance will break rather than yield to any sudden blow, and yet if it is left for a sufficient time it will be found unable to remain in equilibrium under the slight inequality of stress produced by its own weight, but will flow like a fluid till its surface becomes level.
If, therefore, we define a fluid as a substance which cannot remain in permanent equilibrium under a stress not equal in all directions, we must call these substances fluids, though they are so viscous that we can walk on them without leaving any footprints.
If a body, after having its form altered by the applica-tion of stress, tends to recover its original form when the stress is removed, the body is said to be elastic.
The ratio of the numerical value of the stress to the numerical value of the strain produced by it is called the coefficient of elasticity, and the ratio of the strain to the stress is called the coefficient of pliability.
There are as many kinds of these coefficients as there are kinds of stress and of strains or components of strains produced by them.
If, then, the values of the coefficients of elasticity were to increase without limit, the body would approximate to the condition of a rigid body.
We may form an elastic body of great pliability by dissolving gelatine or isinglass in hot water and allowing the solution to cool into a jelly. By diminishing the proportion of gelatine the coefficient of elasticity of the jelly may be diminished, so that a very small force is required to produce a large change of form in the substance.
When the deformation of an elastic body is pushed | beyond certain limits depending on the nature of the sub-

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 force 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 permanent 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 (Pogg. 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. Boltzmann (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 speaks 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 has 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 Leydenjar which has been charged positively for a day, negatively for an hour, and positively again for a minute.
The effects of successive magnetization on iron and steel are also in many respects analogous to those of strain and electrification.
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, 6m, but of the strains to which the body has been subjected during all previous time.
His equation is of the form
/
to il/(w)8t-wdo:, o

where o> is the interval of time reckoned backwards from the actual time t to the time t-u>, when the strain #£_w existed, and y>(co) is some function of that interval.
We may describe this method of deducing the actual state from the previous states as the historical method, be-cause it involves a knowledge of the previous history of the body. But this method may be transformed into another, in which the present state is not regarded as in-fluenced by any state which has ceased to exist. For if we expand 6t-u by Taylor's theorem,


and if we also write
/o» RX /-EO ID"
\— di[a>)da} , B = / u>^i(a>)doi , C = / -JTS i|<(a>)<Zei>, &C.,
then equation (1) becomes
L=(KA)9 + B^-C^+&c.,
where no symbols of time are subscribed, because all the quantities refer to the present time.
This expression of Boltzmann's, however, is not ill any sense a physical theory of the phenomena; it is merely a mathematical formula which, though it represents some of the observed phenomena, fails to express the phenomenon of permanent deformation. Now we know that several substances, such as gutta-percha, India-rubber, &c, may be permanently stretched when cold, and yet when afterwards heated to a certain temperature they recover their original form. Gelatine also may be dried when in a state of strain, and may recover its form by absorbing water.
We know that the molecules of all bodies are in motion. In gases and liquids the motion is such that there is nothing to prevent any molecule from passing from any part of the mass to any other part; but in solids we must suppose that some, at least, of the molecules merely oscillate about a certain mean position, so that, if we consider a certain group of molecules, its configuration is never very different from a certain stable configuration, about which it oscillates.
This will be the case even when the solid is in a state of strain, provided the amplitude of the oscillations does not exceed a certain limit, but if it exceeds this limit the group does not tend to return to its former configuration, but begins to oscillate about a new configuration of stability, the strain in which is either zero, or at least less than in the original configuration.
The condition of this breaking up of a configuration must depend partly on the amplitude of the oscillations, and partly on the amount of strain in the original configura-tion ; and we may suppose that different groups of molecules, even in a homogeneous solid, are not in similar circumstances in this respect.
Thus we may suppose that in a certain number of groups the ordinary agitation of the molecules is liable to accumulate so much that every now and then the con-figuration of one of the groups breaks up, and this whether it is in a state of strain or not. We may in this case assume that in every second a certain proportion of these groups break up, and assume configurations corresponding to a strain uniform in all directions.
If all the groups were of this kind, the medium would be a viscous fluid.
But we may suppose that there are other groups, the configuration of which is so stable that they will not break up under the ordinary agitation of the molecules unless the average strain exceeds a certain limit, and this limit may be different for different systems of these groups.
Now if such groups of greater stability are disseminated through the substance in such abundance as to build up a solid framework, the substance will be a solid, which will not be permanently deformed except by a stress greater than a certain given stress.
But if the solid also contains groups of smaller stability and also groups of the first kind which break up of them-selves, then when a strain is applied the resistance to it will gradually diminish as the groups of the first kind break up, and this will go on till the stress is reduced to that due to the more permanent groups. If the body is now left to itself, it will not at once return to its original form, but will only do so when the groups of the first kind have broken up so often as to get back to their original state of strain.
This view of the constitution of a solid, as consisting of groups of molecules some of which are in different circum-stances from others, also helps to explain the state of the solid after a permanent deformation has been given to it. In this case some of the less stable groups have broken up and assumed new configurations, but it is quite possible that others, more stable, may still retain their original configurations, so that the form of the body is determined by the equilibrium between these two sets of groups; but if, on account of rise of temperature, increase of moisture, violent vibration, or any other cause, the breaking up of the less stable groups is facilitated, the more stable groups may again assert their swav, and tend to restore the body to the shape it had before its deformation. (J. c. M.)


Footnotes

Annates de Chimie, 2rne .série, xxi et xxii.
8 Phil. Trans. 1869, p. 575.

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.