Next, it is observed, that though this Star did afterwards slacken its pace, yet it retained the vividness of its Colour, both of the Head and Train; the Head especially, keeping at the time as well of the last observations, as of the
first, the brightness of its single kernel, though the environing more dilute matter were then almost all lost; it being, according to the Author, more and more attenuated, and grown narrow, the nearer the Star approached to the Sun.
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.
All which he concludes 1, With an Intimation of his sense concerning two other Comets, pretended to have been lately seen, One at Rome, about the
Girdle of Andromeda, in the Months of February and March, 1664. the other in Germany in Capricorne, about Saturne in the head of Sagittary, during the Months of September and October, 1665. 2ly, With an Advertisement of what he has done in that important Work for the Advancement of Astronomy, the due Restitution of the Fixt Stars, vid. That he has almost finish't it; himself alone, without trusting to any other mans labour, that was not directed by him.
The Second Part of this Book (the Mantissa to the Prodromus Cometicus) endeavours to justifie the Authors Observations touching the former Comet, excepted against by M. Auzout, in several particulars; as 1. That it had not pass'd to the First, but Second Star in Aries, and had mov'd in quite another Line, than He had described. 2. That its proper motion about the end of January and the beginning of February, 1665. had not been rightly assigned. 3. That the Bignesse of its Diameter had not been truly delivered; Nor 4. The Faces of its Head in due manner represented.
To all which the Author endeavors to answer: 1. By delivering all his Observations of that Comet, thereby to shew, what care and diligence he had used, particularly to make out, how great its Diurnal motion had been; in what proportion, and how far, it decreased, and where and in what degree it increased again: Which being, as he conceives, duly and exactly deduced, and demonstrated, he esteems it afterwards to be easie for every one, versed in these matters, certainly to collect and to judge, what way the Comet, after it became invisible to the naked Eye, and could be no longer observed with Sextants and Quadrants, had taken, and what Line it had described. 2, By subjecting all those Observations, with great diligence and labour, to a rigid Calculus, thereby to obtain, for every day, the Longitudes, Latitudes, Right Ascensions, Declinations, Proper motion, Angle of the Ecliptick and the Æquator, and the Nodes of that Comet; for the construction of an Ephemerides of its whole Motion. From all which he pretends to prove, that he has not erred in his Observation of February 18, nor been prepossest by any Hypothesis, nor deluded by any Fixt Star, as M. Auzout thinketh; but that near the First Star of Aries there then appear'd a Phænomenon, most like to that Comet, that was seen some dayes before, if compared with the Observations make thereof Febr. 12, 13, 14. Though he will not hitherto positively determine, whether that Phænomenon, which appear'd to him February 18. was