Considering (Most Serene Prince) that the publishing this present Treatise, of so different an Argument from that which many expect, and which according to the intentions I proposed in my [A] Astronomicall Advisor, I should before this time have put forth, might peradventure make some thinke, either that I had wholly relinquished my farther imployment about the new Celestial Observations, or that, at least, I handled them very remissely; I have judged fit to render an account, aswell of my deferring that, as of my writing, and publishing this treatise.

As to the first, the last discoveries of _Saturn_ to be tricorporeall, and of the mutations of Figure in _Venus_, like to those that are seen in the Moon, together with the Consequents depending thereupon, have not so much occasioned the demur, as the investigation of the times of the Conversions of each of the Four Medicean Planets about _Jupiter_, which I lighted upon in _April_ the year past, 1611, at my being in _Rome_; where, in the end, I assertained my selfe, that the first and neerest to _Jupiter_, moved about 8 _gr._ & 29 _m._ of its Sphere in an houre, makeing its whole revolution in one naturall day, and 18 hours, and almost an halfe. The second moves in its Orbe 14 _gr._ 13 _min._ or very neer, in an hour, and its compleat conversion is consummate in 3 dayes, 13 hours, and one third, or thereabouts. The third passeth in an hour, 2 _gr._ 6 _min._ little more or less of its Circle, and measures it all in 7 dayes, 4 hours, or very neer. The fourth, and more remote than the rest, goes in one houre, 0 _gr_ 54 _min._ and almost an halfe of its Sphere, and finisheth it all in 16 dayes, and very neer 18 hours.