There was lately sent to one of the _Secretaries_ of the _Royal Society_ a Packet, containing some Copies of a Printed Paper, Entituled, The _Ephemerides_ of the _Comet_, made by the same Person, that sent it, called _Monsieur Auzout_, a _French_ Gentleman of no ordinary Merit and Learning, who desired, that a couple of them might be recommended to the said _Society_, and one to their _President_, and another to his Highness Prince _Rupert_, and the rest to some other Persons, nominated by him in a Letter that accompanied this present, and known abroad for their singular abilities and knowledge in Philosophical Matters. The end of the Communication of this Paper was, That, the motion of the _Comet_, that hath lately appeared, having been praedicted by the said _Monsieur {4} Auzout_, after he had seen it (as himself affirms) but 4 or 5 times: the _Virtuosi_ of _England_, among others, might compare also their Observations with his _Ephemerides_, either to confirm the _Hypothesis_, upon which the _Author_ had before hand calculated the way of this Star, or to undeceive him, if he be in a mistake. The said Author Dedicateth these his conceptions to the most Christian King, telling him, that he presents Him with a design, which never yet was undertaken by any _Astronomer_, all the World having been hitherto perswaded, that the motions of _Comets_ were so irregular, that they could not be reduced to any Laws, and men having contented themselves, to observe exactly the places, through which they did pass; but no man, that he knows, having been so bold as to venture to foretel the places, through which they should pass, and where they should cease to appear: Whereas he exhibites here the _Ephemerides_, determining day by day, in what place of the Heavens this _Comet_ shall be, at what hour it shall be in its _Meridian_, and at what hour it shall set; untill its too great remoteness, or the approach of the Sun, hide it from our eyes. Descending to particulars, he saith, that this Star, being disengaged from the beams of the Sun might have been observed, if his conjectures be good, ever since it hath been of 17 or 18 degrees _Southern Latitude_, and that about the middle of _November_ last, and sooner, unless it have been too small: That however it hath been seen in _Holland_ ever since the _2d._ of _December_ last, at which time, according to his reckoning, the Diurnal motion of the _Comet_ should already amount to 17 or 18 minutes. He finds, that this Star moveth _just enough_ in the Plan of a _Great Circle_, which inclineth to the _Equinoctial_ about 30 degrees, and to the _Ecliptick_ about 49d. or 491/2 cutting the _Equator_ at about 45_d_1/2, and the _Ecliptick_ at the 28_d_ of _Aries_, or a little more. He saith _just enough_, because he thinks, there may perhaps be some _parallaxe_, which he wisheth could be determined.