XXXIX. On the Transit of Venus, and other Astronomical Observations made at Cavan, near Strabane, in the County of Donegal, Ireland, by Appointment of the Royal Society. By Mr. Charles Mason. p. 454. The first of these is a series of observed equal altitudes of the sun and stars, from April 3 till October 23, 1769, to regulate the clock. 2d. A like series of apparent zenith distances of the sun, moon, and stars. 3d. A like series of meridional zenith distances, for the latitude of the place, the medium of which is 54° 51′40′′.8. 4th. Another series of the difference of right ascension between the moon's limb and stars. 5th. Eclipses of Jupiter's satellites, also occultations of fixed stars by the moon, and other phenomena, for the longitude. 6th. The sun, moon, and stars passing the meridian, by a transit instrument. 7th. Also the observations of the transit of Venus, June 3, 1769, and of the sun's eclipse the next day. The times of the transit by the clock were as below: 17m 53s the external contact of Venus and the sun. 30 internal ditto, judging by their peripheries. At 11h 11 35 4 35 8 ditto, when the thread of light broke out. 37.8 the sun passed the meridian. Though the air at external contact was not quite so clear as sometimes seen, yet the sun's limb appeared well defined, and the spots in the disk very strong, their edges keen and distinct. At the internal contact, the air was much changed, and the limb of Venus seemed to cohere to the sun's limb, by a protuberance that appeared like a dark shade: which seemed to prevent seeing the thread of light for about 40' longer than expected. When the planet was upon the sun's disk, there appeared a faint light shade (having a gentle fluctuating motion) round its periphery, and widest on that part farthest on the sun's disk: it appeared as per fig., the black circle representing the periphery of Venus, and the dotted one that of the shade, which was very regular and well defined; v the upper, and m the lower part of the planet: and the whole shade was apparently of equal brightness. At 22h 15m Os Cloudy with rain. 22 50 23 28 m o The clouds began to break; and from this time to 23h 54m Mr. M. endeavoured with a micrometer (of Mr. Dollond's construction) to get measurements for determining the digits eclipsed; but was so interrupted by flying clouds, that nothing could be done with certainty; then cloudy with rain till the end of the eclipse was past. XL. The Transit of Venus and other Astronomical Observations, made in the West Indies. By M. Pingré, of the Royal Acad. of Sciences at Paris. p. 497. At Cape Francis in the island of St. Domingo. June 3, first perceived Venus entering on the sun's disk, apparent time, as below: At 2h 26m 14 2 26 16 2 26 20 With Dollond's 24 feet telescope. M. de Fleurieu. With a common telescope of 2 feet, only 2 lenses. M. des 2 26 12 With a 5-feet achromatic. M. Pingré. After having given their eyes some respite, they returned to the telescopes; and M. de Fleurieu perceived a luminous little circle all round Venus, not yet entered more than about one third of her diameter. This luminous thread made, to all appearance, a perfect circle with the part of the circumference of Venus already advanced on the solar disk. Mr. P. likewise observed the same phenomenon, but a good while after M. de Fleurieu. Venus appeared totally entered at 2h 44m 45s By M. de Fleurieu. During both these observations, every thing was quiet and still, not a word uttered, to intimate that any one had observed the contact. Stormy weather almost every night hindered them from observing the eclipses of the satellites. However, the 10th of June proving a clear night, afforded an opportunity of determining the latitude of the observatory; which by meridian altitudes of several stars, both to the north and south, Mr. P. determined to be 19° 47′ 3′′. The New church of the Cape, situated nearly in the middle of the town, may be about 20" or 25" more southward than their observatory, whence its latitude 19° 46′ 40′′ N. As to the longitude, they had no other way but to take with a quadrant some altitudes of the moon's lower limb: On computing these altitudes by M. Clairaut's tables, corrected nearly by observations made at Paris the 30th of May and the 1st of June 1751, Mr. P. finds the longitude of Cape François, west of the meridian of Paris, by his own altitudes, 4h 58m 8', and by those of M. de Fleurieu 4h 58m 20. The time above noted for the total entry of Venus, is that when they perceived a very slender thread of light between the limbs of the sun and Venus. They judged that the limbs were in contact, but a few seconds before that instant. At the exit of Venus in 1761, the limbs, being not yet in contact, and even sensibly distant asunder, Mr. P. saw as it were a dark spot detach itself from Venus, and gain the limb of the sun; at which instant he estimated the internal contact. Many have this year seen the same phenomenon at the total entry of Venus. Mr. P. was in expectation of it; but neither he nor his associates perceived any such thing. In 1761 the sun's limbs were most exquisitely well defined; in 1769 they undulated, especially at the beginning of the entry; at the total entry the undulation was considerably less; and notwithstanding this undulation he believes their observation a good one. On comparing the duration of the transit observed at the Prince of Wales's Fort, with that of Father Hell, at Wardhus, he finds on a first calculus, which he believes at least nearly exact, that the sun's parallax is 9".11. Aug. 16, at St. Croix in Teneriffe, the first satellite emerged at 9h 16m 5*, apparent time. XLI. Observations of Immersions and Emersions of Jupiter's first Satellite, made at Funchal, in Madeira, with a Reflecting Telescope of 18 Inches Focus, made by Mr. Short. By the late Thomas Heberden, M.D., F.R. S. p. 502. The time was found by taking equal altitudes, with a quadrant of 12 inches radius, made by Mr. Bird, and with the help of a good pendulum clock made in London. And the latitude of the place of observation in Funchal, by a mean of several observations made with the same quadrant 32° 33′ 35′′. By comparing these observations with similar ones made at Greenwich, the mean among the the whole gives 1h 6m 55.6 for the longitude of the place. XLII. Account of the Transit of Mercury, observed at Norriton, in Pennsylvania, Nov. 9, 1769, agreeable to an Appointment of the American Philoso phical Society, held at Philadelphia, for promoting useful Knowledge. By Wm. Smith, D.D., John Lukens, Esq., David Rittenhouse, M. A., and Mr. Owen Biddle. Communicated by Ben. Franklin, LL.D., F.R.S. p. 504. These gentlemen had the same telescopes now as before, in the transit of Venus, viz. the college reflector, with Dollond's micrometer; used by Dr. Smith, with a magnifying power of 200, to observe the contacts. 2. A refractor of 42 feet, magnifying 140 times, used by Mr. Lukens. 3. Mr. Rittenhouse's refractor, with about the same power, used by himself. Mr. Biddle had no telescope; but was very serviceable in the other parts of the observation. The first external contact was observed to the same instant by all the three observers, who had no communication with each other, the two refractors being out of doors, and the reflector within the observatory; and the contacts noted, as at the transit of Venus, by signals given to persons set at the windows of the observatory, to count the clock. The contacts were as follow: 1769, Nov. 9, apparent time, At 2h 35m 17s first external contact, by all the three observers. 2 2 36 35 first internal contact, by Dr. Smith and Mr. Rittenhouse. 36 33 first internal contact, by Mr. Lukens. The sun's diameter, per micrometer ... ... 35' 20".24. 0 8.22 Mercury's diameter taken backwards and forwards several times, and the sum halved, gave only By the contacts of Mercury at Philadelphia and Norriton, they get the latter 55% of time west of the state-house observatory; the same they made by the eclipses of Jupiter's satellites. XLIII. Investigations of Twenty Cases of Compound Interest. By J. Robertson, Lib. R. S. p. 508. The late Wm. Jones, Esq. F.R.S., among the variety of mathematical matters to which he gave attention, considered the business of compound interest fully, and did, many years ago, cause to be engraved on a copper-plate, more cases in interest than had been exhibited before that time: several copies of impressions from that plate were distributed among his friends; to whom it appeared that he had treated this subject in a more extensive manner than had been done by other mathematicians. The theorems, or rules, for the cases of compound interest, without their investigations, were inserted by Mr. Jones, in the quarto edition of logarithms, published by Gardiner; and the rules were also communicated to Mr. Dodson, who published them, by Mr. Jones's leave, with examples to illustrate the use of his antilogarithmic tables: but the investigations of these theorems not having yet been made public, it is apprehended that gentlemen curious in these speculations would be pleased to see them. In this subject 5 particulars are taken into consideration. 1st. The annuity, rent, or pension; 2d. The times that annuity, rent, or pension is to continue; 3d. The rate of interest used in the computation; 4th. The amount of those rents, and their interest, when they are forborn to be received any times after they are due: 5th. The present worth of those rents, some times before they are due; or of a sum to be received before it is due, discount being allowed. And the investigations naturally fall under two heads. 1st. The consideration of amounts. 2dly. The consideration of discounts. Under the first head and equation is to be obtained between the annuity, time, rate and amount, from the known proportion that subsists between sums of money put to interest, during the same length of time, and the amounts of the principal and interest together. Under the 2d head another equation is to be formed between the annuity, rate, time and present worth, from the known proportion that subsists between the sums discounted, and their present worths, when done for the same time. As these equations involve quantities common to both of them, therefore other equations may be thence deduced, containing all the 5 terms before specified. hence, any 3 of the 5 terms being given, the other 2 are to be found; which admits of 20 cases. And Some of these cases will produce affected equations, where the index of the highest power of the unknown quantity will be the number of times the rent is to continue, or to be paid: therefore the solution of those cases will be given by a method of approximation, as no better way has yet been discovered for the solution of affected equations, in numbers, above the 3d or 4th degree. The algebraical investigations are then given; but it is unnecessary that they should be here retained. XLIV. A Copy of a Letter from John Ellis, Esq., F.R.S. to Dr. Linnæus, F.R.S., &c. with the Figure and Characters of that elegant American Evergreen Tree, called by the Gardeners the Loblolly-Bay, taken from Blossoms blown near London, and showing that it is not an Hibiscus, as Mr. Miller calls it; nor an Hypericum, as Dr. Linnæus supposes it; but a new Genus, to which Mr. Ellis gives the Name of Gordonia. p. 518. We have lately got into a method of cultivating the loblolly-bay, or alcea floridana, &c. of Catesby's History of Carolina, vol. i. tab. 44, p. 44. This tree has lately produced some well-blown flowers, in the botanic garden of Mr. Bewick, at Clapham near London, who sent them to me to examine their characters while fresh I had by me some dried specimens, which had been sent from our friend Dr. Alex. Garden, of Charlestown. On comparing these with the |