Page:Harper's New Monthly Magazine - v108.djvu/140

130 the axis of rotation. Now the amount of rotation will increase even with a diminished rate of spin, provided the mass is placed at a greater distance from the axis. The real effect of contraction in cooling is to increase the amount of rotation in this new sense. In the case of the planetary body the amount of rotation increases because both factors increase, but for the ellipsoidal and pear-shaped bodies it increases because the second factor increases very rapidly while the first diminishes slowly. It seemed necessary to refer to this rather recondite point, and those readers who do not follow the argument must be asked to believe that cooling and contraction are competent to produce the required acceleration of spinning at first and the subsequent retardation.

In this discussion we have only considered a liquid of uniform density, but all celestial bodies must really have a great condensation produced by pressure throughout the central portions. The parallel discussion of the changes of a body with central condensation and density diminishing towards the outside as yet transcends the powers of the mathematician. How far the conclusions would be changed must at present remain uncertain, but I cannot help seeing in our results the counterpart of one form of the birth of a satellite. In looking at these figures one can hardly fail to be reminded of the protrusion of a filament of protoplasm by a living body, and we might regard this kind of process as a crisis in the life of a planet and the beginning of the life of its infant daughter.