An Account of the Appearance of Mercury, Passing Over the Sun's Disk, on the 29th of October, 1723 Determining the Mean Motion, and Fixing the Nodes of That Planet's Orb. By Edmund Halley, LL. D. Astron. Reg. and R. S. S.

III. An Account of the Appearance of Mercury, passing over the Sun's Disk, on the 29th of October, 1723 determining the mean Motion, and fixing the Nodes of that Planet's Orb. By Edmund Halley, LL. D. Astron. Reg. and R. S. S. THE Transit of the Planet Mercury, over the Disk of the Sun, being one of the most curious and uncommon Appearances that the Heavens afford, our Astronomers, both at home and abroad, made due Preparation to observe, with the utmost Exactness, that which happened on the 29th of October, 1723, which I had predicted in the Year 1691 (Phil. Trans. No 193.) would be, in Part, visible in England. And the Sky proving, more than ordinary, favourable at that Time, we were enabled to observe the Ingress on the Sun's Limb, with the greatest Accuracy. Accordingly, the same Day, Octob. 29. styl. vet. at Greenwich in the Royal Observatory, I first perceiv'd, with my 24 Foot Tube, the Planet making a small Notch in the Sun's Limb at $2^h\ 41'\ 23''$ T. app. And at $2^h\ 42'\ 26''$ he was wholly enter'd, making an interior Contact, the Light of the Sun's Limb just beginning to appear behind his dark Body; which, notwithstanding the Slowness of the Motion, was, in a Manner, instantaneous. Then, applying the Micrometer to the said 24 Foot Tube, I open'd it so as to take in $16'\ 15''$ equal to the Sun's Semidiameter at that time; and causing the northern Edge of the Sun, to move exactly along one of the Pointers, I waited till the Center of Mer- Mercury came to move along the other, as I found it to do at $3^h\ 1' \ 16''$ T. app. But Refraction contracting this Difference of Declination about 5 Seconds (the Sun being then but about $11^\circ$ high) I concluded that the Centers of the Sun and Mercury, were truly in the same Parallel of Declination at $3^h\ 3' \ T.$ app. proxime. At Wansted in Essex my worthy Colleague, the Rev. Mr. James Bradly, Savilian Professor of Astronomy, observ'd with the Hugenian Telescope, of above 120 Foot long, the total Immersion, or interior Contact of the Limbs, at $2^h\ 26' \ 45''$ T. æq. that is $2^h\ 42' \ 38''$ T. app. twelve Seconds later than I found it at Greenwich; most of this Difference being due to the Difference of our Meridians. And applying the Micrometer to that vast Radius, he measured the Diameter of the Planet $10''\ 45''$. At $2^h\ 48' \ 57''$ he found the Difference of Declination between the southern Limbs of the Sun and Planet by the Micrometer, in a fifteen Foot Tube, to be $15' \ 19''$. Wherefore, allowing the observ'd Semidiameter of the Planet, and the Refraction, the said Difference was nearest $15' \ 30''$, and consequently, Mercury more southerly than the Sun's Center in respect of Declination $0' \ 45''$. Mr. George Graham, in Fleet-street, London, observ'd the first Impression on the Sun's Limb at $2^h\ 41' \ 9''$ T. app. and at $2^h\ 42' \ 19''$ Mercury was entirely within the Disk. At $3^h\ 6' \ 41''$ he measur'd with a Micrometer, in a twelve Foot Tube, the Distance of his Center from the nearest Limb of the Sun $2' \ 13''$. And again, at $3^h\ 25' \ 24''$ their Distance was found $3' \ 57''$. At $3^h\ 34' \ 43''$ he measur'd the Difference of Declination, from the northern Limb of the Sun $14' \ 57''$, which, corrected by Refraction, becomes $15' \ 4''$, that is, $1' \ 11''$ more northerly than the Sun's Center. In the Observatory at Paris, Signor Maraldi observed the first Appearance of Mercury on the Sun's Limb at $2^h\ 50'13''$ T. app. and the interior Contact at $2^h\ 51'48''$. And Mr. de Lisle, observing apart, concluded the same at $2^h\ 51'37''$, but suspects it might have been some few Seconds later. This Gentleman has communicated his Observation at large, from whence we shall only borrow the following observed Latitudes. | h | 1'' | 1'' | |---|-----|-----| | At 2 56 20 | Latitudo Borea Mercurii | 3 36 | | 3 00 40 | | 3 42 | | 3 10 20 | | 3 46 | | 3 16 12 | | 3 55 | At Bologna, in Italy, Signor Manfredi observed Mercury indenting the Sun's Limb at $3^h\ 26'22''$; and that he was gotten entirely within, at $3^h\ 27'45''$. And these are the Observations most to be depended on, that we have receiv'd from abroad. In order to deduce from this Phenomenon, so accurately observ'd, what may contribute to the Perfectioning of the Theory of Mercury's Motion, which (as appears by the near Agreement of our Numbers with this and many other Observations of him) seems to need but very little Correction; I carefully computed, from our Tables, the Motion of the Planet in five Hours, and found his apparent Motion on the Sun, to be in Longitude $29'21''$ Retrograde, and that his Latitude encreas'd northerly $4'17\frac{1}{2}''$ in the same time; whence the Horary Motion in Longitude $5'52''$, and in Latitude $0'51\frac{1}{2}''$, and thence the Angle of the visible Way with the Ecliptick $8^\circ\ 19'$, and the Horary Motion in that Way $5'56''$. Again, the Angle of the Ecliptick with with the Meridian, being in this Place $73^\circ 24'$, the visible Way of Mercury, made an Angle of $65^\circ 5'$ with the Meridian passing through the Center of the Sun, whence the Horary Change of Declination becomes exactly $2' 30''$. These Data I choose rather to take from the Theory, than from immediate Observation; because there is always an unavoidable, tho' small Uncertainty, in what we observe, yet greater than there can be in the Computation for so small a Space of Time, especially now the Theory is, as I said before, so very near the Truth. This premised, let us now enquire the true Time of the central Ingrefs, and the Latitude of the Planet at that Time. And first, by my own Account, Mercury was gotten into the Parallel of the Sun's Center, $21\frac{1}{2}$ Minutes after the central Ingrefs, in which Time he ascended to the Northward of $54''$, and so much, therefore, was he more Southerly than the Sun's Center at his Ingrefs. Mr. Bradly, $7\frac{1}{2}$ Minutes after the said Ingrefs, in which the Planet ascended $9' 19''$, found his Declination $45''$ South, and therefore at the Ingrefs, his Declination was $1' 4''$ South. And by by Mr. Graham's Observation, Mercury was more northerly than the Sun's Center $1' 11''$, $53' 20''$ after the central Ingrefs; but in that Time, Mercury ascended $2' 13''$, wherefore, according to him, at the Ingrefs the Planet had $1' 2''$ South Declination. We shall not therefore err above a Semidiameter of Mercury, if we assume his Declination, at that Time, to have been precisely one Minute. Now the Sun's Semidiameter being then $16' 15''$, one Minute is the Sine of $30' 32''$ in the Arch of the Sun's Limb; and consequently, the Point of this Ingrefs was $13' 4'$ more northerly than the Ecliptick; whence the Latitude of Mercury was then $3' 40''$ North, and Dif- Difference of Longitude $15^\circ 50''$, by how much he, at that Time, follow'd the Sun's Center. If therefore, to the Arch of $13^\circ 4'$, we add the Double of $8^\circ 19'$, or of the Angle which the visible Way made with the Ecliptick, we shall have $29^\circ 42'$ for the Point on the Sun's western Limb, at which the Planet made his Exit, likewise to the North of the Ecliptick. Hence the Chord, describ'd in the whole Transit, was of $137^\circ 14'$, and the Chord itself $30' 16''$; and the nearest Distance to the Sun's Center $5' 56''$. Now the Horary Motion in this Chord, being $5' 56''$, the whole Duration of this Mercurial Eclipse becomes $5^h 6'$ in respect of the Center of the Planet; and therefore the nearest Approach of their Centers was at $5^h 14' 30''$ at Greenwich, and the Exit at $7^h 47'$; both visible in our American Plantations, had there been any curious Person there qualified to observe them. It follows likewise, by the observ'd Diameter of Mercury, $10'' 45''$ that he was very little less than two Minutes of Time in passing the Limb; and, by the given nearest Distance to the Sun's Center, it is concluded that he was in Conjunction, in Point of Longitude, at $5^h 23' 15''$ having then precisely $6' 00''$ North Latitude. Nor can it be doubted, but that all this would have been found exceeding near to Truth, had not the too early setting of the Sun deprived all Europe of the desirable Sight. There being a very remarkable Period of the Motion of Mercury in 46 Years, in which Time, he makes 191 Revolutions about the Sun; this Transit of ours is found to have been preceded by two others at that Interval: The first, in the Year 1631, when Gassendus at Paris, on the 28th Day of October, styl. vet. was the first that ever observ'd this Appearance of Mercury within the Sun's Disk, and found him to pass off at at $10^h\ 28'$ mane. The second was, Octob. $28^o\ 1677$, when myself had the good Fortune to observe both the Ingress and Egress of the Planet in the Island of St. Helena; the middle Time, when he was nearest to the Sun's Center, being there but $3'\ 50''$ past Noon, and the visible Duration of the Transit of the Center of the Planet $5^h\ 14'\ 20''$; which was some small matter contracted by Parallax, and most likely might have been $5^h\ 15'\ 00''$ without it. Now in $5^h\ 15'$, Mercury describ'd the Chord of $146^o\ 52'$ in the Sun's Limb, being $31'\ 9''$, and consequently the nearest Distance to the Center was $4'\ 38''$, or the Sine of $16^o\ 34'$ the Sun's Semidiameter being Radius; that is, $1'\ 18''$ less than we found it in $1723$. Hence also it follows, that the true Conjunction in Longitude was $7$ min. of Time later than the nearest Approach of the Centers, viz. at $0^h\ 10'\ 50''$ at St. Helena, or at $0^h\ 35'$ past Noon at Greenwich: and, that the North Latitude of the Planet, at that Time, was $4'\ 41''$. Supposing, therefore, the nearest Distance of the Centers in the Transit of $1631$, to have been $3'\ 20''$, that is, $1'\ 18''$ less than in $1677$, we shall find that Mercury then describ'd a Chord of $156^o\ 20'$, traversing the Disk of the Sun in $5^h\ 21'\ 30''$; so that supposing his Exit at $10^h\ 28'$ at Paris, that is $10^h\ 18'\ 40''$ at Greenwich, he enter'd on the Sun at $4^h\ 57'\ 10''$ in the Morning; and was nearest his Center at $7^h\ 38'\ T.\ app.$ but in the same Longitude with him at $7^h\ 43'$, or Octob. $27^o\ 19^h\ 43'\ T.\ app.$ having then $3'\ 22''$ North Latitude. And here, I think I may, without Vanity, advertise the Reader, that above thirty Years since, viz. in Philosoph. Transf. No. $193$, for the Month of March, &c. $1697$, I predicted, by Help of the two former, this last Transit, with a surprising Exactness, Vol. XXXIII. even beyond my Hopes, making the Time of the middle, or nearest Approach of the Centers of the Sun and Mercury, Anno 1723, Octob. 29th 5h 19' T. app. which we found by Observation at 5h 14'½, only 4'½ Minutes sooner; and, in Latitude, Mercury was but six Seconds more southerly than I then had computed it; the Error, in Longitude, being little more than two Diameters of this exceeding small Planet; and, in Latitude, but a single Semidiameter thereof. So, that for the Future, Astronomers may trust my Table of these Transits, in Transit. No 193, to a few Minutes of Time, and not wait with the Uncertainty of Hours, nay Days, as has lately been done. But, in order to obtain a yet further Degree of Exactness by Help of this Observation, it may be most expedient to compare with it the Ingress I observ'd at St. Helena; because, in that, as well as in this, the Latitudes of the Planet being very small, a little Error in them will not so much affect the Longitudes. Supposing therefore, that Anno 1677, Octob. 27° 21' 26" 15" at St. Helena, or 21h 50' 15" T. app. at Greenwich, the Center of Mercury entered on the Sun, and that, at that Time, he was 8½ Degrees on the Sun's Limb, to the North of the Ecliptick (according to what is above concluded) it follows, that he had then 2' 20" North Latitude, and 16' 5" greater Longitude than the Sun's Center; as in this present Transit, Octob. 29° 2h 41' 30" T. app. at Greenwich, he had 3' 40" North Latitude, and 15' 50" more Longitude. Now the apparent Geocentric Differences of Longitude, are to the real Heliocentric Differences, as the Planet's true Distance from the Sun, to his Distance from the Earth; that is, in both Cases, as 313 to 676; wherefore, in 1677, Mercury wanted 34' 45" of the Conjunction with the Sun; and, in 1723, but 34" 13', at the Times of his apparent Ingress on the Disk. And, equating the Times, I find, that the Sun, Anno 1677, Octob. 27d 21h 34' 20" T. æq. was, in m 15° 36' 55" and, consequently Mercury's Heliocentric Place 8 15° 2' 10" : and, Anno 1723, Octob. 29d 2h 25' 30" T. æq. the Sun was in m 16° 39' 43", and therefore Mercury, at that Time, in 8 16° 5' 30". Mercury therefore, in 46 Years with 11 Intercalations, and besides 1d 4h 51' 10", has made 191 Revolutions to the Equinoctial Points, and over and above 1° 3' 20". But, by the Scholion to Prop. XIV. Lib. III. Natur. Philosoph. Principia Math. the Motion of the Aphelion of Mercury, from the Equinox in that Time, is 40' 18"; so that there remains 23' 2" of True Anomaly to be reduced to the Mean: Now the Mean Anomaly of Mercury, in both Cases, being 5 fig. 12°, 23' 2" of True Anomaly gives 15' 24" Mean Anomaly; which added to 40' 18" becomes 55' 42", for the Mean Motion above so many Revolutions: and this is to be encreased by 8" to reduce it to the Plane of Mercury's Orb, in all 55' 50". Hence, doubling the Interval, in 92 Julian Years 1d 9h 42' 20", the Mean Motion of Mercury from the Equinox is 8° 1° 51' 40", from which, taking 5° 44' 50" the Motion in 1d 9h 42' 20", we have his Motion in 92 Julian Years 11° 26° 6' 50", and in 100 Years, 2° 14° 2' 13", which is but 2° more than I had some Years since printed it, in my Astronomical Tables shortly to be published, and differs but one Hour's Motion therefrom in 3000 Years. The forementioned Proportion of the Distances, viz. 313 to 676, is also between the Latitudes seen from the Earth and the Inclinations, or Heliocentric Latitudes of the Planet: so that 2' 20", at the Ingress of 1677, gives 5' 2" ; and 3' 40" in 1723, becomes 7' 55" for the Latitudes at the Sun. And the Inclination of the Orb of Mercury to the Plane of the Ecliptick (determined by accurate Observations near his northern Limit) being $6^\circ 59' 20''$, we compute the Distance of the Planet from his Node, in the former $0^\circ 41' 7''$, and, in the latter, $1^\circ 4' 37''$; which, being deducted from his Heliocentric Places respectively, leave the Place of the ascending Node, in $1677$, $\approx 14^\circ 21' 3''$; and, in $1723$, $\approx 15^\circ 0' 53''$: So, that in 46 Years the Node is found $39' 50''$ forwarder in the Ecliptick; which is but $1' 30''$ more than the Præcession of the Equinox in the same Time. We may therefore safely assume the Plane of the Orb of Mercury to be immoveable in the Sphere of fix'd Stars, and its ascending Node to be $c^\circ 15^\circ 41'$ from the first Star of Aries. Nor can so very slow a Motion (supposing such to be) be fully defined, but by the utmost Care and Diligence of future Astronomers, after the Observation of many Ages. As to the rest of the Theory of this Planet's Motion, I make his mean Distance from the Sun, $38710$ such Parts as the mean Distance of the Sun and Earth is $100000$; and his greatest Equation $23^\circ 42' 37''$. The Epoch of his middle Motion, ineunte Anno $1723$, fyl. vet. from the Equinoctial Point, I make $\approx 19^\circ 9' 31''$; and that of his Aphelion to the same Time $\approx 13^\circ 3' 34''$: the Aphelion moving secundum Seriem Signorum, seven Minutes in eight Years. And these Numbers I presume, may represent the Motion of Mercury, with an Exactness equal to that of any of the other Planets; perhaps as near as the Sun's Place by any Tables, or those of the fixed Stars by any Catalogue yet extant. It were to be wished, that some good Observation, like this, had been made of the like Transit of Mercury at his other Node in April, where he was seen indeed deed April 23° 1661, but so imperfectly, that neither Ingress nor Egress was any where observ'd; and, though it be certain, that he traversed the Sun on April 26°, 1674; and again April 24, 1707, yet we were so unfortunate, that the Conjunction in both happened so near Midnight, that he escaped unseen by all the Astronomers of Europe, excepting singly Mr. Roemer at Copenhagen, whose Observation I have lately received by the Favour of Mr. De l'Isle the Astronomer, communicated in the Words of the Manuscript Journal of Observations of the said Mr. Roemer. "Hodie sexto Maii (Anno 1707) hora matutina "4h 19', spectabatur Mercurius in extremo margine "Solis jamjam exiturus; altus supra imum solis "marginem § diametri solaris, & ad sinistram in "Tubo (sc. invertente) Accuratus hæc determi- "nare non licuit ob moram nimis brevem." It was great Pity, that he did not, at least, estimate, how many Diameters of his Body he was distant from the Limb of the Sun, or what Part of a Diameter, if so near: But having examined this Observation, I find that the Sun, at that Time, was but just risen, or rather rising, and soon after entered into a Cloud, so that the Limb of the Sun could not be distinctly seen, it always undulating and sparkling much, when so near the Horizon; in which Circumstance, a just Observation could hardly be made. Let us now see how our Numbers, corrected as above, will represent this Observation. Anno 1707, April 24° 16h 19' at Copenhagen is 15h 28' at Greenwich, but 15h 24 20" T. æq. To this Time, I find the Sun's true Place 8° 14° 50' 1", and his Distance from the Earth 101005. The correct Epocha of Mercury's mean Motion, for the Year 1707, is 3° 13° 18' 45", to which adding, for the rest of the Time, 3° 19° 9' 28", we shall have his middle Motion at the Time of the Observation m 2° 28' 13"; and, taking his Apheilion in 2° 12' 49" 49" therefrom, we have his mean Anomaly 10° 19' 38" 24", and thereby the Equation to be added 12° 39' 41", and thence the Place of Mercury in his Orb m 15° 7' 54". But the correct Place of the descending Node is m 14° 46' 25", and therefore Mercury, being 21' 29" past the Node, had 2' 36" South Latitude at the Sun; and his Place, reduced to the Ecliptick, was m 15° 7' 45", that is, 17' 44" past the Conjunction of the Sun, which diminished in the Proportion of 5567 to 4533, or of the Distance of the Planet from the Earth to his Distance from the Sun, becomes 14' 27"; and by so much was he past the Conjunction as viewed from the Earth. Again, by the same Proportion, his Geocentric Latitude, at that Time, was 2' 7" South; and therefore, his apparent Distance from the Sun's Center, was 14' 37"; that is, but 1' 18" from his western Limb; so that he might well be said to be, jamjam exiturus. But, that Mercury should at that Time be so far northerly, as Mr. Roemer's Words import, was absolutely impossible; and, I am apt to believe, that so acute an Astronomer as Mr. Roemer was, could not himself be the Observer, but some Person less acquainted with these Matters; which the Words spectabatur Mercurius, instead of Mercurium vidi, seem to import. If he had then had North Latitude, he must needs have been seen in the Sun in April 1720, which we are assured he was not. Lastly, it may not be amiss to advertise, that on the last Day of October 1736, Mercury will again traverse the northern Part of the Sun's Disk, both Ingress and Egress being visible to all Europe. FINIS.