Text: It is thought to have been demonstrated, Section III, that for every point of the earth's orbit the centripetal force and that of repulsion, or the centrifugal, must be equal, and that the production of successive points of that orbit can only be by change of position of those forces relatively to each other. Having found the diagram of the ultimate effect of the co-operation of these two forces for any point of the orbit, it is shown: 1. That relatively to a center of force to which one is always directed, the resultant path must be that of a spiral closing upon that center, or a portion of the curve of an ellipse. 2. That by the very nature of their co-operation equal areas must, by the radius vector, be swept over in equal times. 3. That as these forces, by their co-operation, produce the curve of a spiral closing upon the sun, it must be by uniformly increased power to produce motion, resulting in uniformly increased velocity, which accords with the known obediences to that which is called the law of gravitation.

See Also: QUADRATURE

Source: 159