203. So far our molecules have been treated either as elastic spheres, exerting no forces on one another except when in actual collision, or else as point centres of force, attracting or repelling according to comparatively simple laws. The time has now come to discard all such restrictions, and treat the question in a more general way, regarding the molecules as general mechanical structures, which may be as complicated as we please, consisting of any number of parts, capable of any kind of internal motion and exerting upon one another forces of any type.

Degrees of Freedom

204. The total number of independent quantities which are needed to specify the configuration of any mechanical system is called the number of degrees of freedom of the system. This number does not depend on the motions, but on the capacities for motion, of the various parts of the system; it is therefore related to the geometrical or kinematical, and not to the mechanical, properties of the system.

For example, if a point is free to move in space, its position can be specified by three quantities, as for instance x, y, z, the rectangular coordinates of the point, so that a point which is free to move in space has three degrees of freedom.

I have intended that the present book shall provide such knowledge of the Kinetic Theory as is required by the average serious student of physics and physical chemistry. I hope it will also give the mathematical student the equipment he should have before undertaking the study of specialist monographs, such, for instance, as the recent books of Chapman and Cowling (The Mathematical Theory of Non-uniform Gases) and R. H. Fowler (Statistical Thermodynamics).

Inevitably the book covers a good deal of the same ground as my earlier book, The Dynamical Theory of Gases, but it is covered in a simpler and more physical manner. Primarily I have kept before me the physicist's need for clearness and directness of treatment rather than the mathematician's need for rigorous general proofs. This does not mean that many subjects will not be found treated in the same way–and often in the same words–in the two books; I have tried to retain all that was of physical interest in the old book, while discarding much of which the interest was mainly mathematical.

It is a pleasure to thank Professor E. N. da C. Andrade for reading my proofs, and suggesting many improvements which have greatly enhanced the value of the book. I am also greatly indebted to W. F. Sedgwick, sometime of Trinity College, Cambridge, for checking all the numerical calculations in the latest edition of my old book, and suggesting many improvements.

In this chapter we shall discuss some of the secondary effects accompanying the emission of αparticles, including the emission of delta rays, the recoil accompanjdng the ejection of an α particle, the heating effect produced by the absorption of α particles, and the production of helium due to the accumulated α particles.

§ 29. Emission of delta rays. When a stream of α particles passes through a thin sheet of matter in a vacuum, a number of electrons are observed to be emitted from both sides of the plate. The energy of the great majority of these electrons is only a few volts, but the total number from each surface of the plate is of the order of 10 times the number of incident α particles. J. J. Thomson, who first studied this emission of electrons from a polonium plate, gave them the name of 8 (delta) rays. A large amount of work has been done to determine the factors involved in the liberation of these electrons, including the effect of velocity of the α particle, the nature of the bombarded material, the state of its surface, and the distribution with velocity of the escaping electrons. Before discussing these data, it is desirable to consider the origin of these electrons. It is clear that the escape of electrons, whether from a radioactive surface or a bombarded plate, is in a sense a secondary effect connected with the absorption of energy of the α rays in their passage through matter.

In fact, on modern views, the emission of δ rays is a necessary and inevitable consequence of the passage of α rays through matter.

§ 56. In the previous chapter those experiments on the scattering of α particles in passing through matter were described which confirm the essential assumption of the present theory of atomic structure, that the atoms of matter contain a positively charged nucleus having practically the whole mass of the atom associated with it. The experiments showed that the magnitude of the positive charge of the nucleus was fixed by the atomic number of the atom, or its position in the ascending series of the chemical elements. In the collisions examined in these experiments, in which no elements of smaller atomic number than copper were investigated, the atomic nucleus and the α particle behaved as point charges repelling each other with a force varying inversely as the square of the distance between them.

It is to be anticipated that divergences from the Coulomb law of force would appear when the collisions between the atomic nucleus and the α particle are sufficiently close, for the nuclei are generally supposed to have a complex structure and to be built up in some way from two common units, the electron and the hydrogen nucleus or proton. Since the closest distance of approach to a nucleus of an α particle of given energy is proportional to the charge of the nucleus, it is in the collisions of fast α particles with the nuclei of the lighter elements that deviations from the normal law of force might be expected to be most readily discovered.

§ 119. In previous chapters we have discussed some of the properties of radioactive nuclei and the types of radiation which accompany their transformations. The instability of these nuclei has given us important information on their structure, but unfortunately such information is not available in the case of the ordinary non-radioactive elements. Apart from their instability, there is no reason to believe that the nuclei of the radioactive elements differ in any marked way in their general type of structure from ordinary elements of high atomic weight. It is thus important to examine the properties of atomic nuclei in general to see whether we can obtain evidence to throw light on their structure and their connection with one another. In particular, it is of great interest to see whether any definite evidence can be obtained of the reasons why the property of radioactivity only manifests itself in any marked degree in the two elements of highest atomic weight, thorium and uranium, and their products of transformation.

In chapter vn an account has been given of the genesis of the nuclear theory of the atom and the evidence in its support. On this theory, the ordinary physical and chemical properties of the atom, excluding its mass, depend on the magnitude of the nuclear charge, for on this depends the number and distribution of the outer electrons.