Some Remarks on a Late Essay of Mr. Cassini, Wherein He Proposes to Find, by Observation, the Parallax and Magnitude of Sirius, By Edmund Halley, LL. D. R. S. S.

I. Some Remarks on a late Essay of Mr. Cassini, wherein he proposes to find, by Observation, the Parallax and Magnitude of Sirius. By Edmund Halley, LL.D. R. S. S. In the Memoires of the Royal Academie of Paris, for the Year 1717, but now very lately published, there is one very remarkable Essay, by Mr. Cassini, concerning the Annual Parallax of the Fix'd Stars, and particularly of Sirius; and in conclusion, he determines the Diameter of Sirius to be as much bigger than that of the Sun, as the Sun's is greater than that of the Earth, which he supposes to be 100 times: And the distance from the Sun to the Earth being certainly about 100 Diameters of the Sun, it will follow, that the Globe of Sirius must be a Sphere, whose Diameter must equal the distance between the Earth and Sun. To prove this, he tells us that he made use of an excellent Telescope of 34 French Feet, or 36 English, leaving an Aperture of but an Inch and half, to take off the spurious Rays of the Star, which then appeared round, and sufficiently well defined; and comparing his Body to that of Jupiter, which he says, was then 50 Seconds Diameter, he found that the Diameter of Jupiter was ten times greater than that of the Star, which by consequence was seen under an Angle of about 5 Seconds; which is his first Position. Then he tells us, that to make the Observations of the Parallax of this Star with all the exactness possible, he employed a Telescope of three Foot, in a Copper Tube, Tube, having fixed in the common Focus of the two Glasses, four threads crossing one another in the Center, under Angles of 45 Degrees. This Tube he firmly fix'd to the Plain of a Mural Arch, which had been for above 30 Years immovably cemented to the Wall of the Royal Observatory, to which he chose to fix it, because of the great Solidity thereof, and its being therefore the less liable to shake; and that after having stood 30 Years, there was no fear of its settling any further in the space of one Year; besides, that it was easy to perceive if any such alteration should happen to it. Having therefore fix'd his three Foot Tube as above, so that, about the beginning of April, 1714. New Style, (I suppose, because then Sirius was in Square to the Sun) the Star being exactly in the Meridian, past over the Center of the Tube, he observed that on the 20th of April the Star touched the Horizontal Thread with its under edge, being apparently all above it, in the inverting Tube, but really below. On the 15th of May, and 6th of June, it past again by the Center. On June the 27th it appeared a little under, and on July the 9th it was found to touch the under part of the Thread. On October the 5th it again past by the Center; but on December the 29th, it touched the upper part of the Thread. January the 18th, 1715. being the coldest Day of that Winter, it past exactly by the Center; and on the 27th of March, and the 1st of April, it almost touched the upper side of the Horizontal Thread, from which it seem'd a little separated. But on June the 7th, it past a little under the Center; and on June the 29th, the Sun being then in conjunction with Sirius, it past under the Thread, so as to touch it with its upper edge. Whence it appears, that in the space of the whole Year, there had been no other variation of the Meridian Altitude of Sirius, than the breadth of the Thread, which appear'd appear'd equal to the Diameter of the Star, which he takes to be five, or at most six Seconds. Supposing this to be so, he then shews that the whole Diameter of the annual Orb is to the distance of Sirius, as the Sine of $6''$ to the Sine of $39^\circ 33'$ the Latitude of the Star, whence the aforesaid immense magnitude of the Body thereof, is a necessary Consequence. But before this obtain a full assent, it may not perhaps be amiss to enquire whether the suppos'd visible Diameter of Sirius, were not an Optick Fallacy, occasioned by the great contraction of the Aperture of the Object Glass: For we all know that the Diameters of Aldebaran and Spica Virginis, are so small, that when they happen to immerge on the dark Limb of the Moon, they are so far from loosing their Light gradually, as they must do were they of any sensible magnitude, that they vanish at once with their utmost Lustre; and emerge likewise in a Moment, not small at first, but at once appear with their full Light, even tho' the Emerision happen very near the Cusp; where, if they were four Seconds in Diameter, they would be many Seconds of Time in getting entirely separated from the Limb. But the contrary appears to all those, that have observed the Occultations of these bright Stars. And tho' Sirius be bigger than either of them, yet he is by far less than two of them; and consequently his Diameter to theirs is less than the Square Root of 2 to 1, or than $\frac{1}{4}$ to 10; whence, in Mr. Cassini's excellent 36 Foot Glass, those Stars ought to be about four Seconds in Diameter; and they would undoubtedly appear so, if view'd after the same manner; whereas we are aliunde certain, that they are less than one single Second in Diameter. The great strength of their native Light, forming the resemblance of a Body, when it is nothing else but the spissitude of their Rays. As to the other part of the Argument, that the alteration of the declination of Sirius, on the score of the access of the Earth in December, and its recess in June, amounts to 6 Seconds; I can only remark, that, besides that a Radius of 3 Feet, as it seems that made use of was no more, is somewhat too small for so extremely nice an Observation, 6" being subtended by the $\frac{1}{100}$ part of an Inch, some of the Observations before recited do plainly shew, that the Refraction of the Medium did intermix with those Differences that might be occasioned by the Parallax. But the principal Objection against the Conclusion of this Argument, seems to be, that the Meridian altitude of Sirius at Paris being under 25 Degrees, the ordinary Refraction of the Star is $1'55''$ or 115 Seconds; and the Barometer rising and falling above two Inches in Thirty, shews that the density of the Air, on that score, may be a 15th part more at one time than another. Whence the Refractions being always proportional to the density of the Medium, as we have all seen it often demonstrated by Mr. Hanksbee, both in Vacuo, and in a doubly and trebly condensed Air, it is plain that in that Altitude the Refraction of a Star may differ about 7 or 8 Seconds, or the 15th part of $115''$, which is more than the whole Parallax supposed to have been observed. It were to be wish'd that Mr. Cassini would please to try this Matter by the Lucida Lyra, instead of Sirius, which, tho' somewhat less than him, is as near to the Solstitial Colure, and has much greater Latitude, being but 28 grad. from the Pole of the Ecliptick, whence its Parallax would be so much greater; and being at Paris within 10 grad. of the Zenith, the grand Objection of the difference of Refraction, would be almost wholly removed.