Let us see whether mathematics can provide any suggestion as to the cause of this tendency towards flatness which seems to affect those systems in the universe which are sufficiently isolated to escape from any large disturbance of their parts by outside interference. We must begin by putting, as it were, the problem into shape, and by enumerating certain conditions which, though they may not be absolutely fulfilled in nature, are often so very nearly fulfilled that we make no appreciable error by supposing them to be so. Let us suppose that a myriad bodies of various sizes, shapes, materials and masses, are launched in space in any order whatever, at any distances from each other, and that they are started with very different movements. Some may be going very fast, some going slowly, or not at all; some may be moving up or down or to the right or to the left—there may be, in fact, every variety in their distances and their velocities, and in the directions in which they are started. We assume that each pair of masses attract each other by the well-known law of gravitation, which expresses that the force between any two bodies is proportional directly to the product of their masses and inversely to the square of their distance. We have one further supposition to make, and it is an important one. We shall assume that though each one of the bodies which we are considering is affecting all the others, and is in turn affected by them, yet that they are subjected to no appreciable disturbing influence from other bodies not included in the system to which they belong. This may seem at first to make the problem we are about to consider a purely imaginary one, such as could only be applicable to systems different from those which are actually presented to us in nature. It must be admitted that the condition we have inferred can only be approximately fulfilled. But a little consideration will show that the supposition is not an unreasonable one. Take, for instance, the solar system, consisting of the sun, the planets, and their satellites. Every one of these bodies attracts every other body, and the movement of each of the bodies is produced by the joint effects of the forces exerted upon it by all the others. Assuredly this gives a problem quite difficult enough for all the resources that are at our command. But in such investigations we omit altogether the influence of the stars. Sirius, for example, does exercise some attraction on the bodies of our system, but owing to its enormous distance, in comparison with the distances in our solar system, the effect of the disturbance of Sirius on the relative movements of the planets is wholly inappreciable. Indeed, we may add that the disturbances in the solar system produced by all the stars, even including the myriads of the Milky Way, are absolutely negligible. The movements in our solar system, so far as our observations reveal them,