Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/318

 quares of the ditances from that great body; epecially if the inequality of this proportion be greater than the inequality of the proportion of the ditances from the great body. For if the accelerative force, acting in parallel directions and equally, caues no perturbation in the motions of the parts of the ytem, it mut of coure, when it acts unequally, caue a perturbation omewhere, which will be greater or les as the inequality is greater or les. The exces of the greater impules acting upon ome bodies, and not acting upon others, mut necearily change their ituation among themelves. And this perturbation, added to the perturbation ariing from the inequality and inclination of the lines, makes the whole perturbation greater.

Hence if the parts of this ytem move in ellipes or circles without any remarkable perturbation; it is manifet, that if they are at all impelled by accelerative forces tending to any other bodies, the impule is very weak, or ele is impreed very near equally and in parallel directions upon all of them,

If three bodies whoe forces decreae in a duplicate ratio of the ditances, attract each other mutually; and the accelerative attractions of any two towards the third be between themelves reciprocally as the quares of the ditances and the two leas revolve