BOOK III.] OF NATURAL PHILOSOPHY. 4()£ in his Astronomy, published at the beginning of the year 1676. explained more fully out of the letters I sent him. The utmost satellite of Saturn eeems to revolve about its axis with a motion like this of the moon, respect ing Saturn continually with the same face; for in its revolution round Saturn, as often as it comes to the eastern part of its orbit, it is scarcel) visible, and generally quite disappears ; which is like to be occasioned by some spots in that part of its body, which is then turned towards the earth, as M. Cassini has observed. So also the utmost satellite of Jupiter seema to revolve about its axis with a like motion, because in that part of its body which is turned from Jupiter it has a spot, which always appears as if it were in Jupiter's own body, whenever the satellite passes between Jupiter and our eye. PROPOSITION XVIII. THEOREM XVI. That the axes of the planets are less than the diameters drawn perpen dicular to the axes. The equal gravitation of the parts on all sides would give a spherical figure to the planets, if it was not for their diurnal revolution in a circle. By that circular motion it comes to pass that the parts receding from the axis endeavour to ascend about the equator ; and therefore if the matter is in a fluid state, by its ascent towards the equator it will enlarge the di ameters there, and by its descent' to wards the poles it will shorten the axis. So the diameter of Jupiter (by the concurring observations of astronomers) is found shorter betwixt pole and pole than from east to west. And, by the same argument, if our earth was not higher about the equator than at the poles, the seas would subside about the poles, and, rising toward* Ikf equator, would lay all things there under water. PROPOSITION XIX. PROBLEM III To find the proportion of the axis of a planet to the dia meter j j*,rpendici/lar thereto. Our countryman, Mr. Norwood, measuring a distance of 005751 feet of London measure between London and YorA:, in 1635, and obs,-rvino- the difference of latitudes to be 2° 28', determined the measure of one degree to be 3671 96 feet of London measure, that is 57300 Paris toises. M Picart, measuring an arc of one degree, and 22' 55" of the meridian be tween Amiens and Malvoisine, found an arc of one degree to be 57060 Paris toises. M. Cassini, the father, measured the distance upon the me ridian from the town of Collionre in Roussillon to the Observatory of Pari»; and his son added the distance from the Observatory to the Cita del of Dunkirk. The whole distance was 486156^ toises and the differ ence of the latitudes of Collionre and Dunkirk was 8 degrees, and 31