3. BY the number of satellites, which move round Jupiter and Saturn, the power of each of these planets is measured in a great diversity of distance; for the distance of the outermost satellite in each of these planets exceeds several times the distance of the innermost. In Jupiter the astronomers have usually placed the innermost satellite at a distance from the center of that planet equal to about 5⅔ of the semidiameters of Jupiter’s body, and this satellite performs its revolution in about 1 day 18½ hours. The next satellite, which revolves round Jupiter in about 3 days 13⅕ hours, they place at the distance from Jupiter of about 9 of that planet’s semidiameters. To the third satellite, which performs its period nearly in 7 days 3¾ hours, they assign the distance of about 14⅖ semidiameters. But the outermost satellite they remove to 25⅓ semidiameters, and this satellite makes its period in about 16 days 16½ hours[177]. In Saturn there is still a greater diversity in the distance of the several satellites. By the observations of the late ~CASSINI~, a celebrated astronomer in France, who first discovered all these satellites, except one known before, the innermost is distant about 4½ of Saturn’s semidiameters from his center, and revolves round in about 1 day 21⅓ hours. The next satellite is distant about 5¾ semidiameters, and makes its period in about 2 days 17⅔ hours. The third is removed to the distance of about 8 semidiameters, and performs its revolution in near 4 days 12½ hours. The fourth satellite discovered first by the great HUYGENS, is near 18⅔ semidiameters, and moves round Saturn in about 15 days 22⅔ hours. The outermost is distant 56 semidiameters, and makes its revolution in about 79 days 7⅘ hours[178]. Besides these satellites, there belongs to the planet Saturn another body of a very singular kind. This is a shining, broad, and flat ring, which encompasses the planet round. The diameter of the outermost verge of this ring is more than double the diameter of Saturn. ~HUYGENS~, who first described this ring, makes the whole diameter thereof to bear to the diameter of Saturn the proportion of 9 to 4. The late reverend Mr. POUND makes the proportion something greater, viz. that of 7 to 3. The distances of the satellites of this planet Saturn are compared by ~CASSINI~ to the diameter of the ring. His numbers I have reduced to those above, according to Mr. POUND’s proportion between the diameters of Saturn and of his ring. As this ring appears to adhere no where to Saturn, so the distance of Saturn from the inner edge of the ring seems rather greater than the breadth of the ring. The distances, which have here been given, of the several satellites, both for Jupiter and Saturn, may be more depended on in relation to the proportion, which those belonging to the same primary planet bear one to another, than in respect to the very numbers, that have been here set down, by reason of the difficulty there is in measuring to the greatest exactness the diameters of the primary planets; as will be explained hereafter, when we come to treat of telescopes[179]. By the observations of the forementioned Mr. POUND, in Jupiter the distance of the innermost satellite should rather be about 6 semidiameters, of the second 9-½, of the third 15, and of the outermost 26⅔[180]; and in Saturn the distance of the innermost satellite 4 semidiameters, of the next 6¼, of the third 8¾, of the fourth 20⅓, and of the fifth 59[181]. However the proportion between the distances of the satellites in the same primary is the only thing necessary to the point we are here upon.