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co conceive, that a Star really placed in the very Pole of the Ecliptick, would, to an Eye carried along with the Earth, seem to change its Place continually, and (neglecting the finall Difference on the Account of the Earth’s diurnal Revolution on its Axis) would seem to describe a Circle round that Pole, every Way distant therefrom 3So that its Longitude would be varied through all the Points of the Ecliptick every Year; but its Latitude would always remain the fame. Its right Ascension would allb change, and its Declination, according to the different Situation of the Sun in refpedt to the equinoctial Points ; and its apparent Distance from the North Pole of the Equator would be 7' less at the Autumnal, than at the vernal Equinox.
The greatest Alteration of the Place of a Star in the Pole of the Ecliptick (or which in Effedt amounts to the same, the Proportion between the Velocity of Light and the Earth’s Motion in itsOrbit) being known; it will not be difficult to find what would be the Difference upon this Account, between the true and apparent Place of any other Star at any time ; and on the contrary, the Difference between the true and apparent Place being given ; the Proportion between the Velocity of Light and the Earth’s Motion in its Orbit may be found.
As I only observed the apparent Difference of Declination of the Stars, I shall not now take any farther Notice in what manner such a Cause as I have here suppofed would occasion an Alteration in their apparent Places in other Refpedts; but, supposing the Earth to move equally in a Circle, it may be gathered from what hath been already said, that a Star which
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is neither in the Pole nor Plain of the Ecliptick, will seem to describe about its true Place a Figure, insensibly different from an Ellipse, whose Tranfverse Axis is at Right-angle to the Circle of Longitude pasting through the Stars true Place, and equal to the Diameter of the little Circle described by a Star (as was before supposed) in the Pole of the Ecliptick ; and whose Conjugate Axis is to its Tranfverse Axis, as the Sine of the Stars Latitude to the Radius. And allowing that a Star by its apparent Motion does ex-a&ly defcribe such an Ellipse, it will be found, that if A be the Angle of Position (or the Angle at the Star made by two great Circles drawn from it, thro’ the Poles of the Ecliptick and Equator) and B be another Angle, whose Tangent is to the Tangent of A as Radius to the Sine of the Latitude of the Star ; then B will be equal to the Difference of Longitude between the Sun and the Star, when the true and apparent Declination of the Star are the same. And if the Sun’s Longitude in the Ecliptick be reckoned from that Point, wherein it is when this happens; then the Difference between the true and apparent Declination of the Star (on Account of the Cause I am now considering) will be always, as the Sine of the Sun’s Longitude from thence. It will likewise be found, that the greatest Difference of Declination that can be between the true and apparent Place of the Star, will be ,to the Semi-Tranfverse Axis of the Ellipse (or to the Semi-diameter of the little Circle described by a Star in the Pole of the Ecliptick) as the Sine of A to the Sine of B.
If the Star hath North Latitude, the Time, when its true and apparent Declination are the same, is before