{ "id": "59a68da046b185738c7c8626417e52b517333742", "text": "LXIII. An Account of a printed Memoir, in Latin, presented to the Royal Society, intitled, De Veneris ac Solis congressu observatio, habita in astronomicâ speculâ Bononiensis Scientiarum Instituti, die 5 Junii 1761. Auëtore Eustachio Zanotto, ejusdem Instituti Astronomo, ac Regiæ utriusque Londinensis et Berolinensis Academiæ Socio. By Nathanael Bliss, Savilian Professor of Geometry, and F. R. S.\n\nRead July 1, 1762.\n\nTHE planet Venus hath been so seldom observed in those circumstances, which are of the greatest use in determining some of the most essential elements of its motion, that every such observation, made by an accurate astronomer, cannot but be very acceptable to the public.\n\nAt Bologna, on the night preceding the day of the transit, the weather was very unfavourable; but early in the morning, the clouds, which covered the whole hemisphere, began to break, and were driven off towards the horizon, by a gentle wind: so that the observations were retarded only during the space of about half an hour. Father Frisi, professor of mathematics at Pisa, and Signors Mathenci and Marini, assisted in making the observations; the two latter observing, in the upper room of the observatory, together with Mr. Professor Zanotti; and Father Frisi, accompanied by the two professors of mathematics Signors Casali and Canterzani, in a lower chamber.\n\nS. Zanotti,\nS. Zanotti, in order to determine the place of Venus on the Sun, made use of a quadrant of 2 feet radius, in the telescope of which were placed two wires, the one in an horizontal, the other in a vertical direction: by observing the appulses of the limbs of the Sun and Venus to these wires, successively, no error from refraction can take place. But it is of no small consequence to the accuracy of these observations, that the wires should be placed truly perpendicular to each other. For this purpose, the quadrant was placed in the plane of the meridian, and a star, during its transit, was observed more than once, accurately to run along the horizontal wire. Though the position of the vertical wire was often tried by terrestrial objects, yet other methods of examination were made use of. At the same altitude, both before and after noon, the passage of the Sun not only over the horizontal, but also over the vertical wire, was observed, that it might from thence appear, whether the times of passage, when the necessary errors in observing are allowed for, were equal in both cases. In each of the following observations, the altitude is not nicely determined; because an error of one degree would occasion little or no difference in the quantity of the parallax.\n\nThe observations, fourteen in number, as given by the author, follow:\n\nObservation 1st. Altitude $5^\\circ 14'$.\n\n| Time | Description |\n|------|-------------------------------------|\n| H | 54° 37' o's preceding limb at the horizontal wire. |\n| | 54° 45½' o's preceding limb at the vertical wire. |\n| | 56° 15' a's preceding limb at the vertical wire. |\nH\n\n16 56 20 ♀'s consequent limb at the vertical wire.\n57 20 ♀'s preceding limb at the horizontal wire.\n57 26 ♀'s consequent limb at the horizontal wire.\n57 54 ♂'s consequent limb at the horizontal wire.\n16 57 55 ♂'s consequent limb at the vertical wire.\n\nObservation 2d. Altitude 7° 0'.\n\nH\n\n17 5 56½ ♂'s preceding limb at the horizontal wire.\n5 59½ ♂'s preceding limb at the vertical wire.\n7 25½ ♀'s preceding limb at the vertical wire.\n7 30½ ♀'s consequent limb at the vertical wire.\n8 35½ ♀'s preceding limb at the horizontal wire.\n8 40½ ♀'s consequent limb at the horizontal wire.\n9 11½ ♂'s consequent limb at the horizontal wire.\n17 9 13 ♂'s consequent limb at the vertical wire.\n\nObservation 3d. Altitude 8° 10'.\n\nH\n\n17 12 50½ ♂'s preceding limb at the horizontal wire.\n12 53 ♂'s preceding limb at the vertical wire.\n14 16 ♀'s limb at the vertical wire.\n14 22 ♀'s consequent limb at the vertical wire.\n15 27 ♀'s preceding limb at the horizontal wire.\n15 32 ♀'s consequent limb at the horizontal wire.\n16 4 ♂'s consequent limb at the horizontal wire.\n17 16 7 ♂'s consequent limb at the vertical wire.\n\nObservation 4th. Altitude 9° 8'.\n\nH\n\n17 19 24 ♂'s preceding limb at the horizontal wire.\n19 29 ♂'s preceding limb at the vertical wire.\nH\n\n17 20 50 ♀'s preceding limb at the vertical wire.\n20 55½ ♀'s consequent limb at the vertical wire.\n21 57½ ♀'s preceding limb at the horizontal wire.\n22 3 ♀'s consequent limb at the horizontal wire.\n22 35 ♂'s consequent limb at the horizontal wire.\n17 22 45½ ♂'s consequent limb at the vertical wire.\n\nObservation 5th. Altitude 10° 50'.\n\nH\n\n17 29 41 ♂'s preceding limb at the horizontal wire.\n29 55½ ♂'s preceding limb at the vertical wire.\n31 14½ ♀'s preceding limb at the vertical wire.\n31 20 ♀'s consequent limb at the vertical wire.\n32 10 ♀'s preceding limb at the horizontal wire.\n32 16 ♀'s consequent limb at the horizontal wire.\n32 50½ ♂'s consequent limb at the horizontal wire.\n17 33 15½ ♂'s consequent limb at the vertical wire.\n\nObservation 6th. Altitude 14° 12'.\n\nH\n\n17 49 38½ ♂'s preceding limb at the horizontal wire.\n49 42½ ♂'s preceding limb at the vertical wire.\n50 55 ♀'s preceding limb at the vertical wire.\n51 1½ ♀'s consequent limb at the vertical wire.\n51 58½ ♀'s preceding limb at the horizontal wire.\n52 4½ ♀'s consequent limb at the horizontal wire.\n52 42½ ♂'s consequent limb at the horizontal wire.\n17 53 7½ ♂'s consequent limb at the vertical wire.\n\nObservation\nObservation 7th. Altitude $17^\\circ 0'$.\n\n| H | 6 3½ | o's preceding limb at the horizontal wire. |\n|---|------|------------------------------------------|\n| | 6 15 | o's preceding limb at the vertical wire. |\n| | 7 11 | q's preceding limb at the vertical wire. |\n| | 7 17 | q's consequent limb at the vertical wire. |\n| | 8 31 | q's preceding limb at the horizontal wire. |\n| | 8 36½| q's consequent limb at the horizontal wire. |\n| | 9 18 | o's consequent limb at the horizontal wire. |\n| | 9 31½| o's consequent limb at the vertical wire. |\n\nObservation 8th. Altitude $23^\\circ 40'$.\n\n| H | 18 44 | 36½ | o's preceding limb at the horizontal wire. |\n|---|-------|-----|------------------------------------------|\n| | 45 15½| o's preceding limb at the vertical wire. |\n| | 46 7½ | q's preceding limb at the vertical wire. |\n| | 46 14 | q's consequent limb at the vertical wire. |\n| | 46 39½| q's preceding limb at the horizontal wire. |\n| | 46 47 | q's consequent limb at the horizontal wire. |\n| | 47 36 | o's consequent limb at the horizontal wire. |\n| | 18 48 | 49 | o's consequent limb at the vertical wire. |\n\nObservation 9th. Altitude $31^\\circ 42'$.\n\n| H | 19 30 | 15 | o's preceding limb at the horizontal wire. |\n|---|-------|---|------------------------------------------|\n| | 30 22 | o's preceding limb at the vertical wire. |\n| | 30 59 | q's preceding limb at the vertical wire. |\n| | 31 5 | q's consequent limb at the vertical wire. |\n| | 32 6 | q's preceding limb at the horizontal wire. |\n| | 32 11 | q's consequent limb at the horizontal wire. |\n| | 33 11½| o's consequent limb at the horizontal wire. |\n| | 19 34 | o | o's consequent limb at the vertical wire. |\n\nF f f 2 Observation\nObservation 10th. Altitude $34^\\circ 15'$.\n\nH\n\n| Time | Description |\n|------|--------------------------------------------------|\n| 19 | 44 $\\frac{1}{2}$ O's preceding limb at the horizontal wire. |\n| | 44 $\\frac{1}{2}$ O's preceding limb at the vertical wire. |\n| | 44 $\\frac{58}{1}$ Q's preceding limb at the vertical wire. |\n| | 45 $\\frac{5}{2}$ Q's consequent limb at the vertical wire. |\n| | 45 $\\frac{59}{1}$ Q's preceding limb at the horizontal wire. |\n| | 46 $\\frac{4}{2}$ Q's consequent limb at the horizontal wire. |\n| | 47 $\\frac{7}{2}$ O's consequent limb at the horizontal wire. |\n| 19 | 48 $\\frac{4}{2}$ O's consequent limb at the vertical wire. |\n\nObservation 11th. Altitude $37^\\circ 21'$.\n\nH\n\n| Time | Description |\n|------|--------------------------------------------------|\n| 20 | 2 $\\frac{1}{2}$ O's preceding limb at the horizontal wire. |\n| | 2 $\\frac{14}{1}$ O's consequent limb at the vertical wire. |\n| | 2 $\\frac{38}{1}$ Q's preceding limb at the vertical wire. |\n| | 2 $\\frac{44}{1}$ Q's consequent limb at the vertical wire. |\n| | 3 $\\frac{46}{1}$ Q's preceding limb at the horizontal wire. |\n| | 3 $\\frac{52}{1}$ Q's consequent limb at the horizontal wire. |\n| | 4 $\\frac{59}{1}$ O's consequent limb at the horizontal wire. |\n| 20 | 5 $\\frac{49}{1}$ O's consequent limb at the vertical wire. |\n\nObservation 12th. Altitude $41^\\circ 7'$.\n\nH\n\n| Time | Description |\n|------|--------------------------------------------------|\n| 20 | 23 $\\frac{1}{2}$ O's preceding limb at the horizontal wire. |\n| | 23 $\\frac{1}{2}$ O's preceding limb at the vertical wire. |\n| | 23 $\\frac{18}{1}$ Q's preceding limb at the vertical wire. |\n| | 23 $\\frac{24}{1}$ Q's consequent limb at the vertical wire. |\n| | 24 $\\frac{41}{1}$ Q's preceding limb at the horizontal wire. |\n| | 24 $\\frac{48}{1}$ Q's consequent limb at the horizontal wire. |\n| | 26 $\\frac{0}{1}$ O's consequent limb at the horizontal wire. |\n| 20 | 26 $\\frac{36}{1}$ O's consequent limb at the vertical wire. |\n\nObservation\nObservation 13th. Altitude 44° 10'.\n\nH 20 40 16 ⊙'s preceding limb at the horizontal wire.\n 40 22 ⊙'s preceding limb at the vertical wire.\n 40 33 1⁄2 ♈'s preceding limb at the vertical wire.\n 40 39 ♈'s consequent limb at the vertical wire.\n 41 56 1⁄2 ♈'s preceding limb at the horizontal wire.\n 42 • 1 1⁄2 ♈'s consequent limb at the horizontal wire.\n 43 17 1⁄2 ⊙'s consequent limb at the horizontal wire.\n 20 43 53 1⁄2 ⊙'s consequent limb at the vertical wire.\n\nObservation 14th. Altitude 46° 28'.\n\nH 20 53 51 1⁄2 ⊙'s preceding limb at the horizontal wire.\n 53 58 1⁄2 ⊙'s consequent limb at the vertical wire.\n 54 3 1⁄2 ♈'s preceding limb at the vertical wire.\n 54 9 ♈'s consequent limb at the vertical wire.\n 55 30 ♈'s preceding limb at the horizontal wire.\n 55 36 ♈'s consequent limb at the horizontal wire.\n 56 54 ⊙'s consequent limb at the horizontal wire.\n 20 57 25 1⁄2 ⊙'s consequent limb at the vertical wire.\n\nWhen the planet drew near to the edge of the Sun's disk, the observers prepared to determine the time of the two contacts, Professor Zanotti, with the telescope of the quadrant of 2 1⁄2 feet focus, Professor Mathenci, with the telescope of 22 feet, and Signor Marini, with that of 10 feet.\nThe internal contact was observed\n\nAt $H$ 21 4 34 with the telescope of $2\\frac{1}{2}$ feet.\n$21 4 58$ - - - - - - 10 feet.\n$21 4 58$ - - - - - - 22 feet.\n\nThe external contact was observed\n\nAt $H$ 21 22 39 with the telescope of $2\\frac{1}{2}$ feet.\n$21 23 0$ - - - - - - 10 feet.\n$21 23 7$ - - - - - - 22 feet.\n\nDuring the intervals of the observations made with the quadrant, the planet was always observed to be perfectly round, without any ring or nebulosity.\n\nIt may, at first sight, seem wonderful, says Signor Zanotti, that observations made with different telescopes, one of 10, the other of 22 feet, should so nearly coincide, the times of the first contact agreeing to the same second, and those of the last differing only 7 seconds, by which the contact was seen to happen so much later through the longer telescope; and the blame might be laid either upon the longer telescope, or upon the observer. The goodness of the telescope will readily be allowed, when it is known, that it was made by Campani; and the skill and dexterity of the observer are too well known, to give room for any suspicion on his part. It may rather be attributed to the near equality of the magnifying power of the two instruments; the longer telescope having an eye-glass of 3 inches focal length, and the shorter an eye-glass of $1\\frac{1}{4}$; by means of which,\nwhich, the images of the Sun and Venus were nearly equal in both.\n\nThe author then proceeds to determine, by calculation, (the method of which he has at large explained) the difference of longitude between the centers of the Sun and Venus; and also the planets latitude, which, as seen from the Earth's center, are, at the time of each observation, as in the following table.\n\nN. B. The author has not mentioned the exact quantity of the Sun's parallax, which he made use of in these computations: but, from some trials, it should seem, that he supposed the parallax of the Sun to be $10\\frac{1}{2}$ or 11 seconds.\n| True time, after the noon | Difference of longitude between o and q | Latitude q South |\n|--------------------------|----------------------------------------|-----------------|\n| H ' \" | ' \" | ' \" |\n| 16 56 17½ | 5 46 East | 8 31 |\n| 17 7 28 | 5 7 East | 8 40½ |\n| 17 14 19 | 4 41½ East | 8 46 |\n| 17 20 52¾ | 4 15½ East | 8 56 |\n| 17 31 17¼ | 3 36½ East | 8 54 |\n| 17 5° 58¼ | 2 18 East | 9 0 |\n| 18 7 14 | 1 21½ East | 9 14 |\n| 18 46 10¾ | 1 19 West | 9 46 |\n| 19 31 12 | 4 19½ West | 10 4 |\n| 19 45 2 | 5 1½ West | 10 13 |\n| 20 2 41 | 6 20½ West | 10 28½ |\n| 20 23 21 | 7 46½ West | 10 41 |\n| 20 40 36¼ | 8 46 West | 10 49 |\n| 20 54 6¼ | 9 46 West | 11 0 |\n\nThese longitudes and latitudes do not exactly answer to the interval of time between each observation; but the observer has related them faithfully as they were taken; and if we consider, that they were determined by time, and that an error of half a second will have a considerable influence upon each observation, it will readily be allowed, that the observations are carefully made, and agree very well together, though\nthough taken with an instrument of so small a radius. The following are the elements deduced from those observations, which were made at the distance of at least an hour and an half:\n\nThe horary motion of ♃ in longitude - 0° 3' 55\" 4\nThe horary motion in latitude - 0° 0' 36\" 3\n\nThe true time of the conjunction of ☽ and ♃ - H 18' 26\" 0\n\nThe latitude of ♃ at the conjunction - 0° 9' 27\" 5\n\nFrom these numbers the author deduced the following elements, by trigonometrical calculation:\n\nThe angle of the path with the ecliptic - 8° 49' 23\"\nThe horary motion in the path - 0° 3' 58\" 2\nThe part of the path between the middle of the transit and the conjunction - 0° 1' 27\"\nThe distance of the path from ☽’s center southwards - 0° 9' 21\"\nThe length of the path within the ☽’s disk - 0° 25' 29\" 1\nThe difference of longitude of ☽ and ♃ at the ingress - 0° 14' 2\"\nThe difference of longitude at the egress - 0° 11' 9\" 1\nThe latitude of ♃ at the ingress south - 0° 7' 17\"\nThe latitude of ♃ at the egress south - 0° 11' 12\"\n\nThe time of the middle of the transit - H 18' 4\" 6\nThe ingress of the center of ♃ on the ☽’s disk - 14' 51\" 49\"\nThe egress of the center of ♃ - 21' 16\" 23\"\nIt appears also by his calculation, that the time of the internal contact was accelerated $30''$, and the last contact $18''$, by parallax. The internal contact, therefore, as seen from the center of the Earth, was at $21^h\\ 5'\\ 28''$, and the external contact was at $21^h\\ 23'\\ 25''$, and the egress of the planet's center at $21^h\\ 14'\\ 33''$.\n\nFrom the time of the planet's passage over the edge of the Sun's disk, as seen from the Earth's center, the author very accurately determines the planet's diameter to be $57''\\frac{3}{4}$.\n\nThe egress of the center of Venus, as deduced from the position of its path, and from the other elements, as related above, differs near two minutes from the observed time, when corrected by parallax, and reduced to the Earth's center. This difference is entirely to be attributed to an error in the motion of Venus in longitude, which, perhaps, could not be deduced with sufficient accuracy from these observations, and from a small error in some of the other elements; all which the author might have taken, with the utmost accuracy, from the tables either of Dr. Halley or M. Cassini. Perhaps also, some part of this difference might arise from our ignorance of the true quantity of the Sun's parallax.\n\nHitherto our author has given us those elements, which might immediately be determined from his observations: the following are deduced from the tables. From the motion of Venus in latitude, it may readily be collected, that the planet was in its node on June 5, at $14^h\\ 55'\\ 9''$. The place of the Sun at that time, according to the tables of the Abbé De la Caille, was in $\\pi\\ 14^\\circ\\ 59'\\ 5''\\frac{1}{2}$; and the planet's\nplanet's elongation from the Sun, at the same time, was $1^\\circ 0' 58''$. Therefore, the longitude of Venus, and also of the node, was in $\\Pi 13^\\circ 58' 7''\\frac{1}{2}$. The angle at the Sun, or the difference of the longitude of the planet and the Earth, as seen from the Sun, was $0^\\circ 24' 15''$. Therefore, the longitude of the descending node of Venus, as seen from the Sun, was in $\\Pi 14^\\circ 34' 50''$.\n\nThe latitude of Venus, as seen from the Earth, at the time of the conjunction, was $0^\\circ 9' 27''\\frac{5}{6}$; by solving a triangle of which, the computed distances of the Earth and Venus from the Sun constitute two sides, the angle at the Sun, or the planet's heliocentric latitude, viz. $0^\\circ 3' 46''$, will be determined. With this heliocentric latitude, and the calculated place of the Sun at the time of the conjunction, and the longitude of the node, as before laid down, from two sides of a spheric right-angled triangle, an angle may be computed, which will express the inclination of the planet's orbit with the ecliptic. The place of the Sun, at the time of the conjunction, was in $\\Pi 15^\\circ 36' 10''$. The difference of the heliocentric longitude of the earth, and the node, was $1^\\circ 1' 20''$. Therefore the angle of the inclination of the orbit of Venus with the ecliptic is $3^\\circ 30' 49''$.\n\nN. B. The several numbers contained in this paper, are taken from the correct numbers written in the margin of the printed memoir, with the author's own hand, and which seem to be the result of his latest calculations. And though his observations were made with great care, and faithfully calculated, yet the results will not be found so accurate, as could be\nbe wished; since the latitude of Venus, deduced from these observations, is, in all probability, $10''$ or $12''$ too little; a quantity, which must have a very sensible influence, both on the place of the node, and the inclination of the planet's orbit with the ecliptic; the latter of which ought to be deduced from observations made on the planet, when in its greatest latitudes.\n\nIn the lower chamber of the observatory, the observers made use of two telescopes, one of 6, the other of 8 feet, furnished with wires at half-right angles, in order to determine the place of Venus on the Sun, by causing the Sun's southern limb to run down one of the threads: the following observations were made:\n\n**Observation 1st.**\n\n| Time | Description |\n|------|-------------|\n| 18 11 40½ | Sun's center at the horary wire. |\n| 18 11 50 | Venus's center at the horary wire. |\n| 26 | The difference between the horary and oblique wires. |\n\n**Observation 2d.**\n\n| Time | Description |\n|------|-------------|\n| 19 24 1½ | Center of ♀ at horary wire. |\n| 19 24 17½ | Center of ♂ at horary wire. |\n| 23 | Difference between the horary and oblique wires. |\n\nObservation\nObservation 3d.\n\nH 20 16 53 Center of ♃ at horary wire.\n20 17 23 Center of ⊙ at horary wire.\n20 {Difference between the horary and oblique wires.\n\nObservation 4th.\n\nH 20 47 22½ Center of ♃ at horary wire.\n20 47 55½ Center of ⊙ at horary wire.\n17 {Difference between the horary and oblique wires.\n\nObservation 5th.\n\nH 20 59 17 Center of ♃ at horary wire.\n20 59 54½ Center of ⊙ at horary wire.\n15¾ {Difference between the horary and oblique wires.\n\nThe internal contact was observed, by three different telescopes,\n\nAt H 21 4 54 with a telescope of 6 feet.\n21 5 8 feet.\n21 4 56 11 feet.\nThe external contact was observed\n\nAt $21^{\\text{h}}\\ 22^{\\text{m}}\\ 53^{\\text{s}}$ with a telescope of 6 feet.\n$21^{\\text{h}}\\ 22^{\\text{m}}\\ 50^{\\text{s}}$ - - - - - - 8 feet.\n$21^{\\text{h}}\\ 22^{\\text{m}}\\ 59^{\\text{s}}$ - - - - - - 11 feet.\n\nProfessor Canterzani examined the observations by projection, and found them to agree very nearly with those made in the upper chamber by Signor Zanotti.\n\nEND of PART I.\n\nERRATUM.\nPage 198, Line 11, for from, read with.\n\nERRATUM in Vol. LI. 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Auctore Eustachio Zanotto, Ejusdem Instituti Astronomo, ac Regiae utriusque Londinensis et Berolinensis Academiae Socio. By Nathanael Bliss, Savilian Professor of Geometry, and F. R. S.", "authors": "Nathanael Bliss, Eustachio Zanotto", "year": 1761, "volume": "52", "journal": "Philosophical Transactions (1683-1775)", "page_count": 17, "jstor_url": "https://www.jstor.org/stable/105640" } }