Page:The evolution of worlds - Lowell.djvu/174

142 is least when they all move in one plane. This is evident at once because the components of motion at right angles to the principal plane add nothing to the moment of momentum of the system. It is also least when the bodies all revolve in circles about the centre of gravity. The circle has some interesting properties which almost justify the regard paid to it by the ancients as the only perfect figure. It encloses the maximum area for a given periphery, so that according to the old legends, if one were given as much land as he could enclose with a certain bull's hide, he should, after cutting the hide into strips, arrange these along the circumference of a circle. Now this property of the circle is intimately connected with the fact that a body revolving in a circle has the greatest moment of momentum for the least expenditure of energy. For under the same central force all ellipses of the same longest diameters—major axes these are technically called—are described in the same time, and with the same energy, and of all such, the circle encloses the greatest area, which area measures the moment of momentum.$6$

Given a certain moment of momentum, then the energy is least when the bodies all move in one plane and all travel in circles in that plane. As energy is constantly being dissipated while any alteration among the bodies is going on, to coplanarity and circularity of path all the bodies must tend, if by collision they be