HOOK. III.] OF NATURAL PHILOSOPHY 387 which two satellites, the first and the third, passed over Jupiter's body, were observed, from the beginning of the ingress to the beginning of the egress, and from the complete ingress to the complete egress, with the long tele scope. And from the transit of the first satellite, the diameter of Jupiter at its mean distance from the earth came forth 37 J-". and from the transit of the third 371". There was observed also the time in which the shadow of the first satellite passed over Jupiter's body, and thence the diameter of Jupiter at its mean distance from the earth came out about 37". Let us suppose its diameter to be 37}" very nearly, and then the greatest elonga tions of the first, second, third, and fourth satellite will be respectively equal to 5,965, 9,494, 15,141, and 26,63 semi-diameters of Jupiter. PHENOMENON II. Tkat the. circumsalurnal planets, by radii drawn, to Saturtfs centre, de scribe areas proportional to the times of description ; and that their periodic times, the fixed stars being at rest, are in the sesqniplicata proportion uf their distances from its centre. For, as Cassiui from his own observations has determined, theii distan ces from Saturn's centre and their periodic times are as follow. The periodic times of the satellites of Saturn. ld. 2lh. IS' 27". 2d. 17h. 41' 22". 4d. 12". 25' 12". 15d. 22^. 41' 14", 79'1. 71'. 48' 00". The distances of the satellites from Saturn's centre, in semi-diameters oj itv ring'. From observations li-». 2f 3