Perhaps when Saturn comes into the Northern Signs, and is at a good height from the Horizon (for at the writing of this he is at his loweſt) you may happen to make ſome new Diſcoveries, good Brother, if you would but make uſe of your two Teleſcopes of 170 and 210 Foot long; the longeſt, and the beſt I believe now in the World. For tho’ we have not yet had an opportunity of obſerving the Heavens with them (as well by reaſon of their Unwieldineſs, as for the Interruption of our Studies by your Abſence) yet I am ſatisfied of their Goodneſs by our trial of them one Night, in reading a Letter at a vaſt diſtance by the Help of a Light. I cannot but think of thoſe times with Pleaſure, and of our diverting Labour in poliſhing and preparing ſuch Glaſſes, in inventing new Methods and Engines, and always puſhing forward to ſtill greater and greater Things. But to return to the Figures, of which there remains ſomething further to be ſaid. [The proportion of the Diameter of Jupiter, and of the Orbs of his Satellites, to the Orbit of the Moon round the Earth.] I have there made the Diameter of Jupiter about two third parts of our diſtance from the Moon: for the Diameter of Jupiter is above twenty times bigger than that of the Earth; which is about a thirtieth part of the Moon’s diſtance. The Orbit of the outermoſt of Jupiter’s Satellites is to that of the Moon round the Earth, as 8 and ½ is to 1. And each of theſe Moons, by the Shadow they make upon Jupiter, cannot be leſs than our Earth. Their [The Periods of Jupiter’s Moons.] Periods, that I may not omit them, are according to Caſſini’s Account theſe. That of the inmoſt is one day, 18 hours, 28 minutes, and 36 ſeconds. The Second ſpends 3 days, 13 hours, 13 min., 52 ſeconds in going round him. The Third 7 days, 3 hours, 59 min., 40 ſec. The Fourth 16 days, 18 hours, 5 min., 6 ſec. The Diſtance of the innermoſt from Jupiter himſelf is 2⅚ of his Diameters. That of the Second is 4 and a half: Of the Third 7 and one ſixth part: Of the Fourth 12 and two thirds, of the ſame [And Saturn’s.] Diameters. The Innermoſt of Saturn’s Satellites moves round him in 1 day, 21 hours, 18 min., 31 ſec. The Second in 2 days, 17 hours, 41 min., 27 ſec. The Third in 4 days, 13 hours, 47 min., 16 ſec. The Fourth in 15 days, 22 hours, 41 min., 11 ſec. The Fifth in 79 days, 7 hours, 53 min., 57 ſec. Their Diſtances from the Center of Saturn are, that of the firſt almoſt one, that is 39 fortieth parts of the Diameter of his Ring; that of the ſecond one and a quarter of thoſe Diameters; of the third one and three quarters of them; of the fourth four, or according to my Calculation, but 3 and a half; of the 5th 12, which were found with vaſt Pains and Labour.