In that Tract he observes, first in General, that this second Comet is contrary to the precedent, almost in all particulars: seeing that the former moved very swift, this, pretty slow; that against the Order of the signs from East to West, this, following them, from West to East: that, from South to North, this, from North to South, as far as it hath been hitherto, that we hear off, observed: that, on the side opposite to the Sun, this, on the same side: that, having been in its Perigee at the time of its Opposition, this, having been there, out of the time of its Conjunction: where he taketh also notice, that this Comet differs in brightness from the other, as well in its Body, which is far more vivid and distinct, as in its Train, whose splendor is much greater, since it may be seen even with great Telescopes, which were useless in the former, by reason of its dimness. After this he descends to particulars, and informs us, that he began to observe this Comet April the second, and continued for some days following, and that as soon as he had made three or four Observations, he resolved to try again an Ephemerides; but that, having no instruments exact enough, and the Comet being in a place, destitute of Stars, and subject to Refractions, he feared to venture too much upon Observations so neer one another, since in such matters a perfect exactness is necessary, and wished to see some precedent Observations to direct him: which having obtained, he thereby verified what he had begun, and resolved to carry on his intended Ephemerides, especially being urged by his Friends, and engaged by his former undertaking, that so it might not be thought a meer hazard, that made him hit in the former; as also, that he might try, whether his Method would succeed as well in slower, as in swifter Comets, and in those, that are neer the Sun; as in such as are opposite thereunto, to the end, that men might be advertised of the determination of its use, if it could not serve but in certain particular Cases.
He relateth therefore, that he had finished this New Ephemerides April the sixth, and put it presently to the Press; in doing of which, he hopes, he hath not disobliged the Publick: seeing that, though we should loose the sight of this Star within a few days, by reason of its approach to the Sun, yet having found,
that it is always to rise before the Sun, and that we may again see it better, when it shall rise betimes, towards the end of May, and in the beginning of June, if the cleerness of the Day-break hinder us not; he thought it worth the while to try, whether the truth of this Ephemerides could be proved.
He affirms then, that the Line described by this Star resembles hitherto a Great Circle, as it is found in all other Comets in the midst of their Course. He finds the said Circle inclined to the Ecliptick about 26. d. 30′. and the Nodes, where it cuts it, towards the beginning of Gemini and Sagittary; that it declines from the Equator about 26. d and cuts it towards the 11. d. and consequently, that its greatest Latitude hath been towards Pisces, where it must have been March 24. and its greatest Declination, towards the 25 d. of the Equator, where it was to have been April 11.
He puts it in its Perigee March 27. about three of the Clock in the Afternoon, when it was about the 15 degrees of Pisces, a little more Westerly then Marshab, or the Wing of Pegasus, and that it was to be in Conjunction with the Sun, April 9. Where yet he noteth, that according to another Calculation, the Perigee was March 27. more towards Night, so that the Comet advances a little more towards the East, and retards towards the West; which not being very sensible in the first days, differs more about the end, and in the beginning; which he leaves to Observation.
He calculateth, that the greatest Motion it could make in one day, hath been 4. d. and 8′. or 9′; in one hour, about 10′. and 25″. so that its Diurnal Motion is to its last distance from the Earth a little more than as 1. to 14. and its Hourly Motion, as 1. to 330.
He wonders, that it hath not been seen sooner; the first Observations that he hath seen, but made by others, being of March 17. Whereas he finds, that it might have been seen since January, at least in the Months of February and March, when it rose at 2 of the Clock and before: because it is very likely, that, considering its bigness and brightness, when it was towards its Perigee, it was visible, since that towards the end of February it was not three times as much remote from the Earth, than when it was in its Perigee, and that towards the end of January it was not five times as much.
In the interim, saith he, the other Comet could be seen with the naked eye until January 31. when it was more than ten times further remote, than in its Perigee, although it was not by far so bright, nor its streamer shining as this hath appeared.