conception of matter in an indisputable position, but even
without this theory there is such an accumulation of electrical
and optical evidence in favour of the molecular conception of
matter that the tenability of this conception could not be
regarded as open to question.
The Scale of Molecular Structure.—Apart from speculation, the first definite evidence for the molecular structure of matter occurs when it is found that certain physical phenomena change their whole nature as soon as we deal with matter of which the linear dimensions are less than a certain amount. As a single instance of this may be mentioned some experiments of Lord Rayleigh (Proc. Roy. Soc., 1890, 47, p. 364), who found that a film of olive oil spread over the surface of water produced a perceptible effect on small floating pieces of camphor, at places at which the thickness of the film was 10·6×10−8 cms., but produced no perceptible effect at all at places where the thickness of the film was 8·1×10−8 cms. Thus a certain phenomenon, of the nature of capillary action, is seen to depend for its existence on the linear dimensions of the film of oil; the physical properties of a film of thickness 10·6×10−8 cms. are found to be in some way qualitatively different from those of a film of thickness 8·1×10−8 cms. Here is proof that the film of oil is not a continuous homogeneous structure, and we are led to suspect that the scale on which the structure is formed has a unit of length comparable with 8×10−8 cms. The probability of this conjecture is strengthened when it is discovered that in all phenomena of this type the critical length connected with the stage at which the phenomenon changes its nature is of the order of magnitude of 10−8 cms.
Lord Rayleigh (Phil. Mag. 1890 [5], 30, p. 474) has pointed out that the earliest known attempt to estimate the size of molecules, made by Thomas Young in 1805, was based upon the consideration of phenomena of the kind just mentioned. Discussing the theory of capillary attractions, Young[1] found that at a rough estimate “the extent of the cohesive force must be limited to about the 250-millionth of an inch” (＝10−8 cms.), and then argues that “within similar limits of uncertainty we may obtain something like a conjectural estimate of the mutual distance of the particles of vapours, and even of the actual magnitude of the elementary atoms of liquids. . . . It appears tolerably safe to conclude that, whatever errors may have affected the determination, the diameter or distance of the particles of water is between the two thousand and the ten thousand millionth of an inch” (＝between ·125×10−8 and ·025×10−8 cms.).
The best estimates which we now possess of the sizes of molecules are provided by calculations based upon the kinetic theory of gases. In the following table are given the values of the diameters of the molecules of six substances with which it is easy to experiment in the gaseous state, these values being calculated in different ways from formulae supplied by the kinetic theory.
| Gas | Diameter calculated by the kinetic theory of gases. | ||||
| From devia- tions from Boyle’s law. |
From co- efficient of viscosity. |
From co- efficient of conduction of heat. |
From co- efficient of conduction of diffusion. |
Mean value. | |
| Hydrogen | 2·05×10−8 | 2·05×10−8 | 1·99×10−8 | 2·02×10−8 | 2·03×10−8 |
| Carbon monoxide | — | 2·90×10−8 | 2·74×10−8 | 2·92×10−8 | 2·85×10−8 |
| Nitrogen | 3·12×10−8 | 2·90×10−8 | 2·74×10−8 | — | 2·92×10−8 |
| Air | 2·90×10−8 | 2·86×10−8 | 2·72×10−8 | — | 2·83×10−8 |
| Oxygen | — | 2·81×10−8 | 2·58×10−8 | 2·70×10−8 | 2·70×10−8 |
| Carbon dioxide | 3·00×10−8 | 3·47×10−8 | 3·58×10−8 | 3·28×10−8 | 3·33×10−8 |
The agreement of the values obtained for the same quantity by different methods provides valuable confirmation of the truth of the molecular theory and of the validity of the methods of the kinetic theory of gases. That. the results do not agree even better need not cause surprise when it is stated that the quantities are calculated on the hypothesis that the molecules are spherical in shape. This hypothesis is introduced for the sake of simplicity, but is known to be unjustifiable in fact. What is given by the formulae is accordingly the mean radius of an irregularly shaped solid (or, more probably, of the region in which the field of force surrounding such a solid is above a certain intensity), and the mean has to be taken in different ways in the different phenomena. This and the difficulty of obtaining accurate experimental results fully account for the differences inter se in the values of the quantities calculated.
Heat a Manifestation of Molecular Motion.—An essential feature of the modern view of the structure of matter is that the molecules are supposed to be in rapid motion relatively to one another. We are led to this conception by a number of experimental results, some of which will be mentioned later. We are compelled also to suppose that the motion assumes different forms in different substances. Roughly speaking, it is found that there are three main types of molecular motion corresponding to the three states of matter—solid, liquid and gaseous. That the distances traversed by the molecules of a solid are very small in extent is shown by innumerable facts of everyday observation, as for instance, the fact that the surface of a finely-carved metal (such as a plate used for steel engraving) will retain its exact shape for centuries, or again, the fact that when a metal body is coated with gold-leaf the molecules of the gold remain on its surface indefinitely: if they moved through any but the smallest distances they would soon become mixed with the molecules of the baser metal and diffused through its interior. Thus the molecules of a solid must make only small excursions about their mean positions. In a gas the state of things is very different; an odour is known to spread rapidly through great distances, even in the stillest air, and a gaseous poison or corrosive will attack not only those objects which are in contact with its source but also all those which can be reached by the motion of its molecules.
As a preliminary to examining further into the nature of molecular motion and the differences of character of this motion, let us try to picture the state of things which would exist in a mass of solid matter in which all the molecules are imagined to be at rest relatively to one another. The fact that a solid body in its natural state is capable both of compression and of dilatation indicates that the molecules of the body must not be supposed to be fixed rigidly in position relative to one another; the further fact that a motion of either compression or of dilatation is opposed by forces which are brought into play in the interior of the solid suggests that the position of rest is one in which the molecules are in stable equilibrium under their mutual forces. Such a mass of imaginary matter as we are now considering may be compared to a collection of heavy particles held in position relatively to one another by a system of light spiral springs, one spring being supposed to connect each pair of adjacent particles. Let two such masses of matter be suspended by strings from the same point, and then let one mass be drawn aside, pendulum-wise, and allowed to impinge on the other. After impact the two masses will rebound, and the process may be repeated any number of times, but ultimately the two masses will be found again hanging in contact side by side. At the first impact each layer of surface molecules which takes the shock of the impact will be thrust back upon the layer behind it: this layer will in this way be set into motion and so influence the layer still further behind; and so on indefinitely. The impact will accordingly result in all the molecules being set into motion, and by the time that the masses have ceased impinging on one another the molecules of which they are composed will be performing oscillations about their positions of equilibrium. The kinetic energy with which the moving mass originally impinged on that at rest is now represented by the energy, kinetic and, potential, of the small motions of the
- ↑ “On the Cohesions of Fluids,” Phil. Trans. (1805); Young’s Coll. Works, i. 461.
