sir CHRISTOPHER WREN, knt. 251

tion as it had North at the ist Quadrature in m, its Latitude remaining un-chang’d.

But if the Star have 20, 40, or 60 Degrees North Latitude, the Parallaxesmay be express’d by the three small Ellipses plac’d one above another, in theLine <v P ; and Lines drawn from the Pole of the Ecliptick P, to the Place ofthe Sun design’d; and to be found in them, will shew which Way the Pa-rallax carries the Star, in Consequence, or in Antecedence; and in what Pro-portion its Distance from the said Pole is augmented or diministfd by it: But,for the Parallax of right Ascension and Distance from the Pole of the Globe jthat narrow Ellipsis plac’d next the Ecliptick, represents the parallactick Curveof a Star that has 20 Degrees North Latitude. Let Arches of Hour-circles bestruck from the Pole of the World A, to the nearest and remotest Points ofthis Ellipsis 3 they shew that the Star shall have its greatest Declination, orleast Distance from the Pole, a little after its first Quartile with the Sun, hebeing in 25; and its greatest Distance from the Pole, or least Declination, alittle after the second Quadrature, he being in v?.

The ingenious Reader will consider, that tho’ I count the Sun’s Longitudealong these Curves, yet the Places design’d by them, shew only those Pointsin them, whereon the Star appears by Reason of the Parallax of the Orb; andthe Distances of these Points from either of the said Poles in the Arch of agreat Circle, represent the Distance as the Parallax makes it appear, aug-mented or diminish’d, with respect to either of them.

As the Latitude of the Star’s Increase, the Parallaxes of Longitude, Lati-tude, right Ascension, and Declination, do all increase, as may be easily ap-prehended, by the sole Inspection and Consideration of this Figure; but withtoo many Varieties to be recounted, except by such as have a great deal ofLeisure, and are desirous to let the World fee their excellent Abilities, in re-tailing Things at length; I leave them to the sagacious Reader to collect fromthe Figure, and proceed to strew how the Appearances of the Pole-star shallbe alter’d by the Parallax of the Orb, if sensible at it.

The present Longitude of the Pole-star is n, 24 Deg. i, it’s Latitude 66Deg. North. Let P A in Fig. C, represent an Arch of the solstitial Colure,equal to 23 Deg. - 5 r, the Distance of the Pole of the World and Ecliptick, P e Fig. C.the Line of the Pole-star’s Longitude, and its Distance from the Pole of theEcliptick: About e let the parallactick Ellipsis 0 n q m be deferib’d in suchsort, that its longer Diameter may lie parallel to the Ecliptick, and may be inProportion to the lhortest, as the Rad. is to the Line of its Latitude. ’TisEvident, by bare Inspection of the Fig. that its greatest Distance from thePole of the Ecliptick shall then happen when the Star shall appear on n : Andthe Sun is in the fame Longitude with it in the beginning of our June ; it’sEast in December , when their Longitudes are opposite, or (to include both in°ur Expression) they shall both happen when the Sun, Earth, and Star, area ll in the fame Plane perpendicular to the Plane of the Ecliptick.

But the nearest Approach of the Pole-star to the Pole of the Globe, and itsgreatest Remove from it, will be distant from these Points about q and 0, as ap-pears by the Figure, perhaps not much different from the Times on which Mr.

Zqffiui places them; but to determine exactly the Place of these Points on theEurve, the Resolution of this Problem will be required ; A Point being given,a nd an Ellipsis deferib'd in the Superficies of the Sphere, to Jlrike two Arches ofgreat Circles through the said Point to the Ellipsis, Jo as one of them pall be theJhortejl, the other the longejl that can be betwixt them. There is then an Over-%ht committed in my Letter to Dr. Wallis, where I place the greatest Remove

the Pole-star from the Pole in June, the nearest Approach in December, Mr.

Galley acknowledges aloud, that Dr. Wallis, Dr. Gregory, and himself, saw

it