This general law of the decline of energy in an isolated system, is supplemented by another law often known as the conservation of moment of momentum. It may at first seem difficult to grasp the notion which this law involves. The effort is, however, worth making, for the law in question is of fundamental importance in the study of the mechanics of the universe. In the Appendix will be found an investigation by elementary geometry of the important mechanical principles which are involved in this subject.
Whatever may have been the origin of the primæval nebula, and whatever may have been the forces concerned in its production we may feel confident that it was not originally at rest. We do not indeed know any object which is at rest. Not one of the heavenly bodies is at rest, nothing on earth is at rest, for even the molecules of rigid matter are in rapid motion. Rest seems unknown in the universe. It would be, therefore, infinitely improbable that a primæval nebula, whatever may have been the agency by which it was started on that career which we are considering, was initially in a condition of absolute rest. We assume without hesitation that the nebula was to some extent in motion, and we may feel assured that the motions were of a highly complicated description. It is fortunate for us that our argument does not require us to know the precise character of the movements, as such knowledge would obviously be quite unattainable. We can, however, invoke the laws of mechanics as an unerring guide. They will tell us not indeed everything about those motions, but they will set forth certain characteristics which the movements must have had, and these characteristics suffice for our argument.
To illustrate the important principle on which we are now entering I must mention the famous problem of three bodies which has engaged the attention of the greatest mathematicians. Let there be a body A, and another B, and another C. We shall suppose that these bodies are so small that they may be regarded merely as points in comparison with the distances by which they are separated. We shall suppose that they are all moving in the same plane, and we shall suppose that each of them attracts the others, but that except these attractions there are no other forces in the system. To discover all about the motions of these bodies is so difficult a problem that mathematicians have never been able to solve it. But though we are not able to solve the problem completely, we can learn something with regard to it.