I did found my _Hypothesis_ upon three Observations only, _viz._ those of the 22, 26, and 31. of _December_. Nor have I done, as some have fancied of me, who having been able to observe the Comet, the 27, 28, 29, 30, and 31. of _December_, and to see the diminution of its motion, have judged, that I had only determined that diminution for the time to come, conform to the augmentation thereof in time passed until the 29. of _December_. For _January_ 1. (on which day I composed my _Ephemerides_) I knew not (nor any person here) that the motion of the Comet did diminish; but on the contrary, most men believed, it was not the same Comet. But Signior _Cassini_ knows very well, that that was not necessary, seeing that two portions of a _Tangent_ being given, and the _Angles_ answering thereunto, 'tis easie to find the position and magnitude of its Circle. The reason, which I think the true one, of the diminution of its Motion in Longitude, and of its Retrogradation, by me conjectured in my _Ephemerides_, I began to be assured of, _Febr._ 10. For until the sixth, the Comet had alwaies advanced, as Signior _Cassini_ also hath very well noted: but after that day, I found that it returned in augmenting alwaies its Latitude. And I have constantly observed it, until _March_ 8. between many Stars, which must be the same with these mentioned by _Cassini_, whereof the number was so great, that I think, I saw of them _March_ 6. with one _Aperture_ of my Glass, more than 40. or 50. and especially, above the head of _Aries_; but I did not particularly note the scituation of more than 12. or 15; amongst which I have observed the position of the Comet since _January_ 28. every day, when the weather did permit, _viz._ _January_ 29. _February_ 3, 6, 10, 17, 19, 24, 26, 27. and _March_ 6, {20} 7, 8. I left it on _March_ 8. at the 18. of the Horn of _Aries_, almost in the same latitude: and I am apt to believe, it will be Eclipsed, which I wish I may be able to observe this evening, if it be not already passed.