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D X K'
which put = K'; and the horary motion of the moon in the ecliptic
The horary motion of the moon in latitude, calling the difference answering to 1o increase of the argument of latitude E, is 60'
The most difficult part in the above computations, and in which a person is most liable to make mistakes, is the computation of the moon's place; but if this be done at land for every 12 hours at least, and the distance of a proper star, or of 2 stars, one to the east, and the other to the west, from the moon's enlightened limb, be computed for every 6 hours at least, according to Mons. De la Caille's proposal, the rest of the computation, which will remain to be done at sea, will be very plain and concise.
Here follows the series of his determinations of the longitude during his voyage, delivered in an extract of his sea journal. The first column contains the day of the month; the 2d, the latitude; the 3d, the longitude, which he deduced from his observations of the moon, reduced to the nearest noon; the 4th shows the longitude by account, kept in the usual manner; the 5th gives the difference between the 3d and 4th columns, and expresses how much the longitude deduced from the observation of the moon is west of the longitude by account; the last column shows whether the distance of the sun from the moon, or distance of what star from the moon, was observed.
1761. Jan. 20
At noon took our departure from the Lizard, which bore full north, distance 21 miles, allowing its longitude from London to be 5° 14' west, and latitude 49° 57′ north.
27° 33'w. 2° 49'w.
42 N. 23
6 s. 29 44 March 9 24 9 s. 30 7 10 25 51 s. 29 32 13 29 49
The sun or stars whose distance from the moon's enlightened limb was taken.
Sun's E. limb from moon's w.
April 6 7 A. M. came to an anchor in the harbour before
James's fort at St. Helena; making the latitude per account 15° 55' s. longitude by common reckoning 1° 28′ E. longitude corrected by observation of the moon 4° 16' w. 4 N
By the comparison of the longitude determined by the moon, with the longitude by the common reckoning, they seemed to have been set by a current to the eastward about 20 miles per day, between February 10th and 15th, while, they were passing from 17° to 5o north latitude, at the distance of about 11° westward of the coast of Guinea; and he was told that ships passing near the coast of Guinea always meet currents, which set them in on the land, which are so much the stronger the nearer they approach the coast; as on the contrary if they approach the opposite coast of the Brasils, they will be set by a current to the westward, which appeared to have been their case; for between February 19th and 28th, during which time they passed by the most eastern part of the coast of Brasils, leaving Cape St. Augustin only 6° to the west, they appeared to have been set by a current, at the rate of 20 miles per day to the westward, and from this time to their arrival at St. Helena, they seemed to have been continually set to the westward, though slower than before; which must have been owing to their approaching so much nearer, and continuing so much longer near the eastern coast of South America, than the western coast of Africa.
Though Mr. M. had no observation of the moon within less than 8 days of his arrival at St. Helena, he makes the longitude of the island, by his account, to be only 14° east of its true situation, which is 5° west of London; whereas the account kept in the common manner made the island 14° east of London, or 74° east of its true situation, and most of the accounts on board the ship made it 10° east of the true longitude. Having got 12 observations in the compass of 11 days, between March 9th and 20th, he had the curiosity to compare them together. Setting aside any errors in the common method of keeping a ship's reckoning, and supposing her not to be affected by currents during this time, the same difference ought to have been found between all the longitudes by account, and the longitudes deduced from the moon, or the same error of the common account ought to have resulted from all the observations. The mean error of account from all the 12 observations is 5° 20', by which they were really more to the west than the account made them. And comparing each particular error of account with this quantity, the difference between them, in any of the 12 observations, scarcely exceeds a degree; whence we may suppose, that the longitude was deduced truly from every one of these 12 observations, within the compass of less than 110.
Mr. M. has set down in the annexed table the error of the common account, and the difference between 5° 20', the mean quantity of it, and each particular error of account, which, except in the first and last observations, does not exceed. The last observation, which differs most from the medium, was taken in some haste, on account of the position of the sails of the ship, which did not allow an uninterrupted view of the star; yet as he was tolerably satisfied with
After finding so great an agreement in the result of all the different observations, whether made on the same or different stars, or on the same or different nights, he cannot account for the great difference found by the Abbé De la Caille, in the result of several observations taken by himself, and a friend of his, at land, which ought to agree still nearer with one another than those made at Mr. M. cannot conceive that such able observers could be liable to an error of 5′ in measuring the distance of a star from the moon's limb, if their instruments were not faulty. The most likely and the most common cause of error lies in the speculums and dark glasses; for if these are not ground truly parallel, which he is afraid they very often are not, by the common methods, they may easily produce a refraction of some minutes.
As a proof how near different observations made in the compass of an hour or two will agree in giving the same longitude, February 11th, by 10 different observations of the distance of the moon from the sun, he made the longitude, reduced to noon as usual, 28° 57′, 29° 50′, 29° 16′, 29° 22′, 29° 53′, 28° 59′ 29° 30′, 29° 48′, 29° 30′, 29° 30′; none of which differ above half a degree from 29° 22′, which is the medium of them all. March 18th, by 4 different observations of the distance of Pollux from the moon, he found the longitude 23° 52′ twice, and 24° 8′ twice. He never found that a single observation would give the longitude above a degree different from the medium resulting from 3 or 4 observations, and seldom above half a degree; which argues, that the error of any single observation never exceeded 2 minutes, and seldom 1 minute.
From the whole, Mr. M. congratulates the curious astronomer and ingenious mariner, that the method of finding the longitude, proposed by Sir Isaac Newton, is by the improvement of the theory, of which he laid the foundation, and, by the great perfection to which our artists have carried the construction of instruments, rendered practicable in our times, at sea as well as at land, to a de
gree of exactness sufficient to make it of great and valuable utility to the extensive navigation and commerce of our native country.
XCIV. Reasons for a Lunar Atmosphere. By Mr. Samuel Dunn. p. 578. It has been a question which has been long debated among astronomers, whether the moon has an atmosphere or not? and the question it seems is not yet undecided. The best astronomers told him they never could discover any atmosphere about the moon. But this being unsatisfactory, Mr. D. began to consider by what methods, not already used, this problem was likely to be solved; and, among several others, thought of one, which he thought had not been used before, viz. by a nice examination of the two ends of Saturn's ring, at the time when the planet is on the dark edge of the moon. For the ring of Saturn being of a considerable length, and gradually emerging or immerging almost at right angles, either from or to the dark disk of the moon, the two extremities of this ring, and the body of Saturn, being duly observed, if both the preceding and subsequent extremities of the ring, and the body of Saturn also, should happen to appear not perfectly defined, exceedingly near to the moon's dark limb, but perfectly defined a little farther from it; by such an appearance, he concluded it might be strongly presumed, that there is a lunar atmosphere; and for want of such appearance, that there is none.
Such an observation he made 16th instant, (June 1762) or rather 17th, past 2 in the morning; the particulars of which follow.
The 16th at noon he set a pendulum clock, by which this observation was made, to solar time, by the sun's transit over the meridian. He waited to make this observation, but could not see the moon till 14h 22m, when she emerged from dark still clouds into a most clear and serene sky, nothing could be finer for observation; and thus she continued during the observation, and long after it. The telescope being rightly adjusted, at 14h 21m 3s, he saw a faint point of light, where the emersion afterwards appeared; but this faint point of light appearing and disappearing by alternate fits, he could not know if it was part of Saturn or of one of his satellites, till it was 14h 21m 13s, when this point of light was grown a little brighter and larger, and therefore he judged it was the tip of the ring just emerging. Yet it appeared so dull and hazy, that he had suspected his telescope, if he had not known it to have been rightly adjusted.
At 14h 22m 4s, the preceding part of the ring was emerged, and it appeared more bright; and now the body seemed emerging or emerged, but so very hazy and ill defined, both the body and the ring confused together, closely on the moon's dark limb, that he should not have taken it for Saturn, but for a comet emerging from behind the moon, had he not known otherwise from the tables, or seen Saturn the preceding mornings.
At 14h 22m 30s, the preceding end of the ring more plain and bright, the subsequent end of the ring more dull, and the body at this time appeared a little more distinct than before.
At 14h 22m 34s, the subsequent end of the ring appeared most dull, and the preceding end clear; after which, in some short space of time, the whole ring and body of Saturn appeared sharply and well defined.
Therefore, he concluded, that this diversity of appearance must have arisen from the effects of an atmosphere of the moon.
XCV. An Account of the Comet seen at Paris in June 1762. By Mons. De la Lande. p. 581.
Passage through the perihelion May 28, at 15h 27m, middle time. Perihelion distance 1.0124, supposing the distance of the sun from the earth to be 1.
They were not able to observe this comet later than the 5th of July. It was even at too great a distance on that day; and was but ill observed from the 30th of June. This comet resembles none of the 49 comets, whose elements are already known.
XCVI. Minutes of the Observation of the Transit of Venus over the Sun, June 6, 1761, taken at Calcutta in Bengal, Latitude 22° 30′, Longitude East from London nearly 92°. By Mr. Wm. Magee, p. 582.
The appulse uncertain, but very apparent at
The centre of Venus on the sun's limb
The interior contact at the ingress
Interior contact at the egress.
Centre of Venus on the sun's limb at the egress
8h 11m 35$
2 15 55
The above observations were minuted from a stop watch of Mr. Ellicott's, having no pendulum clock or time piece. The weather being cloudy for several days before, that of observation, there was no opportunity of ascertaining the error of the watch; but on the day of observation he found, on comparing the watch with a meridian line in the town hall, that when the centre of the sun's image was on the meridian line, the time by the watch was 4m 10 past 12. Comparing the watch the 7th, 8th, and 9th June with the meridian line, he found it had gained nearly 2 minutes each day, the time by the watch June 9 being 10m 5, when the sun was on the meridian. It took about 5o to wind the