74. Two methods of obtaining the Law of Distribution of molecular velocities have now been given and also a comparison between them. These two methods have been limited to the consideration of molecules which may be treated as elastic spheres, exerting no forces on one another except when in actual collision. There is a more general way of treating the question, which permits of the molecules being dynamical systems of the most general type, capable of any kind of internal motion and exerting upon one another any forces we please. This method will be explained in the present chapter.

With a view to obtaining results which will be required later in the development of the subject, we shall not limit the discussion of the present chapter to the problem referred to above; we shall consider the “Statistical Mechanics” of a perfectly general dynamical system, not in the least limited to consisting of a gas. The special applications of the present chapter will be to a gas, while in later chapters we shall have occasion to apply the results to more general systems.

Degrees of Freedom.

75. The total number of independent quantities which need to be known before the configuration and position of any dynamical or other system can be fully known, is called the number of degrees of freedom of the system.