SEC. IX.] OF NATURAL PHILOSOPHY. 379 round the sun revolve in ellipses, having the sun in their common focus ; and by radii drawn to the sun describe areas proportional to the times. But now the parts of a vortex can never re volve with such a motion. Let AD, BE, CF, represent three orbits describ ed about the sun S, of which let the utmost circle CF be concentric to the sun ; and let the aphelia of the two in nermost be A, B j and their perihelia D, E. Therefore a body revolving in the orb CF, describing, by a radius drawn to the sun, areas proportional to the times, will move with an uniform motion. And, according to the laws of astronomy, the body revolving in the orb BE will move slower in its aphelion B, and swifter in its perihelion E ; whereas, according to the laws of mechanics, the matter of the vortex ought to move more swiftly in the narrow space between A and C than in the wide space between D and F ; that is, more swiftly in the aphelion than in the perihelion. Now these two conclusions contradict each other. So at the beginning of the sign of Virgo, where the aphelion of Mars is at present, the distance between the* orbits of Mars and Venus is to the distance between the same orbits, at the beginning of the sign of Pisces, as about 3 to 2 ; and therefore the matter of the vortex between those orbits ought to be swifter at the beginning of Pisces than at the beginning of Virgo in the ratio of 3 to 2 ; for the nar rower the space is through which the same quantity of matter passes in the same time of one revolution, the greater will be the velocity with which it passes through it. Therefore if the earth being relatively at rest in this celestial matter should be carried round by it, and revolve together with it about the sun, the velocity of the earth at the beginning of Pisces would be to its velocity at the beginning of Virgo in a sesquialteral ratio. Therefore the sun's apparent diurnal motion at the beginning of Virgo ought to be above 70 minutes, and at the beginning of Pisces less than 48 minutes; whereas, on the contrary, that apparent motion of the sun is really greater at the beginning of Pisces than at the beginning of Virgo; as experience testifies ; and therefore the earth is swifter at the beginning of Virgo than at the beginning of Pisces ; so that the hypothesis of vor tices is utterly irreconcileable with astronomical phenomena, and rather serves to perplex than explain the heavenly motions. How these mo tions are performed in free spaces without vortices, may be understood by the first Book j and I shall now more fully treat of it in the following Book.