.BOOK II1.J OF NATURAL PHILOSOPHY. 39(.* planets; for their quantities of matter are as the forces of gravity at equai distances from their centres; that is, in the sun, Jupiter, Saturn, and the earth, as 1, TO'FTJ a-oVr? anc^ TeVaja respectively. If the parallax of the sun be taken greater or less than 10" 30'", the quantity of matter in the earth must be augmented or diminished in the triplicate of that pro portion. COR. 3. Hence also we find the densities of the planets ; for (by Prop. LXXII, Book I) the weights of equal and similar bodies towards similar spheres are, at the surfaces of those spheres, as the diameters of the spheres 5 and therefore the densities of dissimilar spheres are as those weights applied to the diameters of the spheres. But the true diameters of the Sun, .Jupi ter, Saturn, and the earth, were one to another as 10000, 997, 791, arid 109; and the weights towards the same as 10000, 943, 529, and 435 re spectively ; and therefore their densities are as 100. 94