ould 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 {303} _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