386 THE MATHEMATICAL PRINCIPLES [BooK III. PHENOMENA, OR APPEARANCES, PHENOMENON I. That the circumjovial planets, by radii drawn to Jupiter's centre, de scribe areas proportional to the times of description ; and that their periodic times, the fixed stars being at rest, are in the sesquiplicate proportion of their distances from, its centre. This we know from astronomical observations. For the orbits of these planets differ but insensibly from circles concentric to Jupiter ; and their motions in those circles are found to be uniform. And all astronomers agree that their periodic times are in the sesquiplicate proportion of the semi-diameters of their orbits; and so it manifestly appears from the fol1 owing table. The periodic times of the satellites of Jupiter. H 18h. 27'. 34". 3d. 13h. 13' 42". 7d. 31'. 42' 36". 16d. 16h. 32' 9". The distances of the satellites from Jupiter's centre. From the observations of 1 2 3 4 Borelli 5$ 8