A body in which change of volume calls into play a stress is said to have volume elasticity.

A body in which change of shape, without change of volume, calls into play a stress is said to possess rigidity.

The elasticity of a body is measured by the ratio of the stress produced by a given strain to that strain, or

The question as to how the strain and stress have to be measured in different cases is postponed till we come to consider in greater detail the properties of the various forms of matter.

123. States of Matter.-For the purposes of subdivision we may say that matter exists in three distinct states, the solid, the liquid, and the gaseous. In addition, however, to states which fulfil the definitions of a solid, a liquid, or a gas, which we shall give later on, it will be found that there are intermediate states which bridge over the intervals between the solid and the liquid, and the liquid and the gas. As an example of the kind of gradation which exists, we may take the following: steel, lead, wax, cobbler's-wax (which will flow like a liquid if allowed sufficient time), treacle, water, ether, liquefied carbon dioxide, steam, sulphur dioxide, air, hydrogen. In addition there is the critical state when a substance is to all intents and purposes both a liquid and a gas, and the state of extreme rarefication of a gas which is sometimes called the radiant state or "fourth state" of matter.

We may define a solid as a portion of matter which is able to support a steady longitudinal stress without lateral support. In contradistinction, a portion of matter which is unable to support a steady longitudinal stress without lateral support is called a fluid.

If we take a solid body, say a lead-pencil, then we may apply a deforming force, either of compression or extension, in any direction to the pencil, and there will be a certain amount of strain, either elongation, compression, or bending produced, which will call into play a stress that, so long as the deforming force is not too great, will be in equilibrium with this force, and this stress will be produced without the body being supported in any way in a direction at right angles to that along which the stress acts. In the case of a fluid, such as water or air, we are unable to exert a stress on it, and hence produce a corresponding strain, unless we supply some constraining boundary which shall prevent the fluid swelling out at right angles to the line of action of the stress. Thus if we have a fluid enclosed in a cylindrical tube between two pistons, then we may apply a deforming force to the fluid either by forcing the pistons towards one another, or by pulling them apart, in one case producing a compression, and in the other a tension in the direction of the axis of the tube, and a stress will in both cases be produced in an opposite direction to

the applied force. If, however, part of the wall of the tube between the pistons is removed, and we then attempt to apply stress to the liquid, we shall not succeed, for either the liquid will flow out through the gap in the tube, or air will be sucked into the tube through this opening, and the fluid will remain unstrained. It is only, therefore, when the column of fluid is laterally supported by the walls of the tube that it is capable of exerting a longitudinal stress.

Fluids are divided into liquids and gases. A liquid is a fluid such that when a certain volume is introduced into a vessel of greater volume it only occupies a portion of the vessel equal to its own volume. A gas is a fluid such that if a certain volume is introduced into a vessel, then, whatever the volume of the vessel may be, the gas will distribute itself throughout the vessel.

124. The Constitution of Matter.-The question as to the finite divisibility of matter has been referred to in § 121. The theory that matter is not infinitely divisible, but that every body is made up of small indivisible parts called atoms (from aroμos) is one of extreme antiquity. At the present day this theory is generally accepted, and we are hence led to consider what is the nature of these atoms. In chemistry it is usual to apply the term molecule to the smallest portion of any kind of matter which can exist alone and still preserve the character of that kind of matter, and to restrict the term atom to the smallest portion of any element which can take part in a chemical reaction. In the case of such a substance as chalk, the molecule is the smallest portion of chalk which can exist.

The molecule of chalk can, by certain processes, be further subdivided, but the parts have no longer any of the attributes of chalk; they may be carbon dioxide, and lime. These again can be split up into carbon, oxygen, and calcium, but further than this it has up to now been impossible to go. For this reason chalk or carbonate of lime, carbon dioxide, and lime are called compounds, since the molecule of these bodies can be further subdivided, losing, however, in the process their essential properties as chalk, carbon dioxide, &c. On the other hand carbon, oxygen, and calcium are called elements, since the molecule of these bodies cannot by any known means be split up into any simpler bodies. For the purposes of the physicist, as distinct from the chemist, it is generally unnecessary to distinguish between the smallest particle which can exist of a compound or of an element. For our purposes, in considering the structure of matter, we shall call the ultimate particle a molecule, and shall not, in most cases, further consider the question whether it might not be split up into more elementary molecules.

The original conception of a molecule was that it consisted of a hard sphere, and that bodies were built up of such spheres, which were not necessarily in contact with one another. This conception was further extended by Boscovich, who did away with the consideration that the molecule is a material body occupying a certain space. He considered

the molecule to be a mere mathematical point towards or from which certain forces act. He further supposed that any two molecules attract each other with a force which for considerable distances varies inversely as the square of the distance, but which for small distances becomes changed into a repulsion, which increases as the molecules come nearer and nearer together. The chief difficulty in this theory is that it does not seem capable of explaining the inertia of matter.

One of the most recent theories, and one which very powerfully appeals to the imagination, is Lord Kelvin's vortex atom theory. By vortex motion is meant a form of motion such as occurs in a smokering. The path of the particles of air in such a smoke-ring is indicated by the arrows in Fig. 95, where the curved arrows show the direction in which the air particles, which are simply rendered visible by the smoke, rotate, while the straight arrow shows the direction in which the ring, as a whole, moves. There is a very important difference between this form of motion and a wave motion. In the latter, although the waves travel onwards, the individual particles of the medium in which the wave is being propagated only move through a comparatively small distance from their original position, the motion being handed on from one particle to the next. In vortex motion, however, the particles of the medium themselves move forward, so that in a smoke-ring the particles of air originally forming the ring move on with the ring.

FIG. 95.

The properties of vortex motion were first examined by rigid mathematical methods by von Helmholtz, who found that if the fluid in which this form of motion exists is frictionless, incompressible, and homogeneous, then: (1) A vortex can never be produced, nor if one exists can it be destroyed, so that the number of vortices existing is fixed. This corresponds to the indestructible property of matter. (2) The rotating portions of the fluid forming the vortex maintain their identity, and are permanently differentiated from the non-rotating portions of the fluid. (3) These vortex motions must consist of an endless filament in which the fluid is everywhere rotating at right angles to the axis of the filament, unless the filament stretches to the bounding surface of the fluid. (4) A vortex behaves as a perfectly elastic substance. (5) Two vortices cannot intersect each other, neither can a vortex intersect itself.

On the basis of these results of von Helmholtz, Lord Kelvin has founded a theory as to the constitution of matter. He supposes that all space is filled with a frictionless, incompressible, and homogeneous fluid (the ether), and that an atom is simply a vortex in this medium. The existence of different kinds of atoms may be accounted for by the fact that a vortex need not necessarily be a simple ring, as shown in Fig. 95,

K

but might have such a form as that shown in Fig. 96. Since a vortex can never intersect itself, it follows that the number of times such a vortex

is linked with itself must always remain the same. Hence we may suppose that the atoms of the different elements are distinguished from one another by the number of times they are linked.

125. The Size of Molecules.-Until more is known of the nature of molecules, no very definite statement as to what is meant by the size of a molecule is possible. Since, however, the methods of deducing the size of FIG. 96. the molecules at present known only give at the most a rough estimate of the "magnitude" of this quantity, the difficulty of defining what is meant by the size is not very important. For the present it is usual to consider that a molecule consists of a solid sphere, though of course these spheres need not fill even a small fraction of the total space which the body apparently occupies.

The methods by which the following estimates of molecular magnitude have been made cannot be described till the physical phenomena from which they are deduced have been considered.

In the following table the diameters of the molecules of some gases, supposed to be spherical, are given, as well as the mass of a single molecule. Knowing the mass of a molecule and the density, that is, the mass of unit volume at standard temperature and pressure, we may calculate the number of molecules contained in unit volume. Thus if m is the mass of each molecule, and there are n molecules in unit volume, the mass of unit volume, that is, the density d, is given by

d=nm.

Substituting the values of m from the first column of the table, and the values of the density as given in the table on page 150, it will be found that in each case the value found for n is about 2 × 1019.

As a help to the realisation of what the above numbers mean, we may say that seventeen millions of hydrogen molecules, if placed in a row so that one touched the next, would form a row about one centimetre in length. Another illustration has been given by Lord Kelvin, namely: if a drop of water were magnified till it was equal in size to the earth, the molecules would be about the size of cricket-balls.

CHAPTER XVI

PROPERTIES OF GASES

WE commence our study of the general characteristics of the different states of matter with that of the gaseous state, for in this condition we are able to account for most of the observed facts by dynamical reasoning, based on what is known as the kinetic theory of gases. On the other hand, in the case of solids and liquids we are very far from possessing even an approximate dynamical theory to account for the observed properties. The structure of a gas being so much more simple than that of a liquid or solid, it is best to begin by the study of the gaseous state, and then to proceed to that of the liquid and solid states.

Before, however, commencing the study of the special properties of gases it will be convenient to consider some of the general properties of fluids, since these properties are common to both gases and liquids.

126. Pressure Exerted by a Fluid.-Since a fluid cannot resist a stress unless it is supported on all sides, or in other words it has only elasticity of volume, it can offer no resistance to forces which tend only to change its shape and not its bulk.

It follows, from this mobility of fluids, that in the case of a fluid at rest the force it exerts on any surface in contact with it must be perpendicular to the surface. If the force did not act perpendicular to the surface, then it could be resolved into two components, one acting perpendicular to the surface, and the other acting parallel to the surface. This latter component would, if it existed, cause the fluid to move parallel to the surface. Since by supposition the fluid is at rest, and therefore no such tangential motion exists, there can be no tangential component of the force, so that the force exerted by the fluid on the surface is perpendicular to the surface. The magnitude of a force exerted by a fluid is measured by the force exerted on the unit of surface, and is called the pressure.

Hence in the c.g.s. system the unit of pressure is a dyne per square centimetre. The dimensions of pressure are [Force]÷[Areal, or [L1MT-"]÷[L3], or [L-1MT-2].

If the pressure over a surface is not uniform, then we measure the pressure at a point by considering the force exerted on an element of area, taken round the given point, so small that the pressure is practically constant over this area, and divide the force by the area; a process exactly analogous to that adopted in the case of a variable speed in § 31.