_Thirdly_, 'tis noted, That this _Comet_ did very much digress from the _Hypothesis_, delivered by _M. Auzout_, in regard that, whereas according to that _Hypothesis_, this Star should not arrive to the _Ecliptick_ till after the space of 3 months, it arrived there the 28 of _April_. And then, that its first Conjunction with the Sun hapned between the 19 and 20 of _April_, and the second, the last of _April_, not (as _M. Auzout_, would have it) the 15 of _May_. So that he concludes, that this Comet never came down to the _Pleiads_ and the _Eye of Taurus_, as the Hypothesis of _M. Auzout_ requires, but that from _April_ 20. it did immediately take its course towards the Ecliptick, deflecting every day more and more from the _Section_ of a _Great Circle_, to the _Lucida_ of _Aries_, arriving at the _Ecliptick_ the last of _April_, about the 8th or 10th deg. of _Taurus_; not in _July_ about the 8th of _Gemini_, and the _Eye of Taurus_. _Fourthly_, He intimates, that if this Comet had appeared some weeks sooner, it would have confronted the former Comet, being yet in its vigour and of a conspicuous bigness, in the same place, where that was, viz. the _Head of Aries_. _Fifthly_, He observes, that this Star in progress of time became _Retrograde_, whence it came to pass, that in the Months of _June_ and _July_ it did not appear again before the Rising of the Sun, though the Sun left it far behind: whereas, if it had proceeded toward the _Eye of Taurus_, it would have appeared again in the morning. _Sixthly_, He maintains, that this Comet was not the same with the former; which he thinks may be demonstrated, onely by a due Delineation of both their Course upon the _Globe_; where he saith it to be evident, that the former could never come to the _Head_ of _Pegasus_, as moving already in _February_ in a streight Course about the _Head_ of _Aries_; Besides, that the _former_ went in the very beginning in a _Retrograde_ motion; but _this_ perpetually in a direct one: _that_, about the end, very slow, its Head lessning and growing dark; _this_ swift enough, with its head conspicuous and bright. To which he adds, that the whole Course of the former was made under a quite different _Angle_ of the _Orbite_ and _Ecliptick_, and a different Motion of the _Nodes_ from the latter: As also that their _Faces_ differed very much from one another; the _first_ exhibiting all along a matter, which as to its density and rarity, altered from day to day exceedingly, whereas the _second_ retained (to the Authors admiration, who affirms, never to have observed the like) all the time he saw it, one and the same round, dense and bright Speck or Kernel.