We must, however, admit that the lessons as to the origin of the solar system, derived from the spiral nebulæ, must be received with due limitation. We may say at once that the _great_ spiral nebulæ do not appear to be evolving into systems like the sun and planets; their work is of a higher order of magnitude altogether. The great spiral nebulæ seem to be more analogous to galaxies, like the Milky Way (Fig. 32), than to solar systems. The spiral nebula instead of being described as a system, should perhaps be described as a system of systems. If the solar system were drawn to scale on the photograph of the Great Spiral (Fig. 28) the orbit of Neptune would not be larger than the smallest recognisable dot. ------------------------------------------------------------------------ CHAPTER XI. THE UNERRING GUIDE. The Solar System—Orbits nearly Plane—Satellites, Saturn’s Ring, Spiral Nebulæ—An Explanation of this Tendency of a System towards Flatness—The Energy of a System—Loss of Energy by Collision and Tidal Action—A System within a System—Movements of Translation and Movements of Rotation—The General Law of Conservation of Moment of Momentum—Illustrations of the Principle—The Conception of the Principal Plane—The Utility of this principle arises from its independence of Collisions or Friction—Nature does not do Things infinitely Improbable—The Decline of Energy and the Preservation of Moment of Momentum—Explanation of the Motions in one Plane and in the same Direction—The Satellites of Uranus—The Rotation of Uranus—Why the Orbits are not exactly in the same Plane—The Evolution of a Nebula—The Inevitable Tendency towards the Spiral—The Explanation of the Spiral. WE have to consider in this chapter the light which the laws of mathematics throw upon certain features which are possessed by a very large number of celestial objects. Let us first describe, as clearly as the circumstances will permit, the nature of these common features to which we now refer, and of which mathematics will suggest the explanation. We shall begin with our solar system, in which the earth describes an orbit around the sun. That orbit is contained within a plane, which plane passes through the centre of the sun. We may neglect for the present the earth’s occasional slight deviations from this plane which are caused by the attractions of the other planets. If we consider the other bodies of our system, such, for instance, as Venus or Jupiter, we find that the orbit of Venus also lies in a plane, and that plane also passes through the centre of the sun. The orbit of Jupiter is found to be contained within a plane, and it, too, passes through the sun’s centre. Each of the remaining planets in like manner is found to revolve in an orbit which is contained in a plane, and all these planes have one common point, that point being the centre of the sun.