Note N. 81 — SECTION III.

Note 81, p. 24. If each particle, &c. Let P, Pʹ, Pʺ, &c., fig. 21, be planets moving in their orbits about the centre of gravity of the system. Let P S M, Pʹ S Mʹ, &c., be portions of these orbits moved over by the radii vectores S P, S Pʹ, &c., in a given time, and let p S m, pʹ S mʹ, &c., be their shadows or projections on the invariable plane. Then, if the numbers which represent 444the masses of the planets P, Pʹ, &c., be respectively multiplied by the numbers representing the areas or spaces p S m, pʹ S mʹ, &c., the sum of the whole will be greater for the invariable plane than it would be for any plane that could pass through S, the centre of gravity of the system.