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46" 13"". And by a good calculation (which, that I may not tire the reader, it is better to omit) I find that a circle described on a as a centre, with the radius LM, will meet the right line FH in the point M, at II hours 20 minutes 40 seconds; but that being described round b as a centre, it will meet HG in the point N at IX hours 29 minutes 22 seconds, according to the time reckoned at London: and therefore, Venus will be seen entirely within the Sun at the banks of the Ganges for 7 hours 8 minutes 42 seconds : we have then rightly supposed that the duration will be 7 hours 8 minutes, since the part of a minute here is of no consequence.
But adapting the calculation to Port-Nelson, I find, that the Sun being about to set, Venus will enter his disc; and immediately after his rising she will leave the same. That place is carried in the intermediate time through the hemisphere opposite to the Sun, from c to d, with a motion conspiring with the motion of Venus; and therefore, the stay of Venus on the Sun will be about 4 minutes longer, on account of the parallax ; so that it will be at least 7 hours 24 minutes, or 111 degrees of the equator.
And since the latitude of the place is 56 degrees, as the square of the radius is to the rectangle contained under the sines 554 and 34 degrees, so is AB, which is 1' 2'', to cd, which is 28" 33"". And if the calculation be justly made, it will appear that a circle described on c as a centre, with the radius LM, will meet the right line FH in 0 at II hours 12 minutes 45 seconds; and that such a circle described on d as a centre, will meet HG in P, at IX hours 36 minutes 37 seconds; and therefore the duration at Port-Nelson will be 7 hours 23 minutes 52 seconds, which is greater than at the mouth of the Ganges by 15 minutes 10 seconds of time. But if Venus should pass over the Sun without having any latitude, the difference would be 18 minutes 40 seconds; and
if she should pass 4' north of the Sun's centre, the difference would amount to 21 minutes 40 seconds, and will be still greater, if the planet's north latitude be more increased.
From the foregoing hypothesis it follows, that at London, when the Sun rises, Venus will have entered his disc; and that, at IX hours 37 minutes in the morning, she will touch the limb of the Sun internally at going off; and lastly, that she will not entirely leave the Sun till IX hours 56 minutes.
It likewise follows from the same hypothesis, that the centre of Venus should just touch the Sun's northern limb in the year 1769, on the third of June, at XI o'clock at night. So that, on account of the parallax, it will appear in the northern parts of Norway, entirely within the Sun, which then does not set to those parts; while, on the coasts of Peru and Chili, it will seem to travel over a small portion of the disc of the setting Sun; and over that of the rising Sun at the Molucca Islands, and in their neighbourhood. But it the nodes of Venus be found to have a retrograde motion (as there is some reason to believe from some later observations they have), then Venus will be seen every where within the Sun's disc; and will afford a much better method for finding the Sun's parallax, by almost the greatest difference in the duration of these eclipses that can pos. sibly happen.
But how this parallax may be deduced from observations made somewhere in the East Indies, in the year 1761, both of the ingress and egress of Venus, and compared with those made in its going off with us, namely, by applying the angles of a triangle given in specie to the circumference of three equal circles, shall be explained on some other occasion,
Showing that the whole method proposed by the Doc
tor cannot be put in practice, and why.
27. In the above Dissertation, the Doctor has explained his method with great modesty, and even with some doubtfulness with regard to its full success. For he tells us, that by means of this transit the Sun's parallax may only be determined within its five hundredth part, provided it be not less than 12"; that there may be a good observation made at Port-Nelson, as well as about the banks of the Ganges ; and that Venus does not pass more than 4 minutes of a degree below the centre of the Sun's disc.—He has taken all proper pains not to raise our expectations too high, and yet, from his well-known abilities, and character as a great astronomer, it seems mankind in general have laid greater stress upon his method, than he ever desired them to do. Only, as he was convinced it was the best method by which this important problem can ever be solved, he recommended it warmly for that reason. He had not then made a sufficient number of observations, by which he could determine, with certainty, whether the nodes of Venus's orbit have any motion; or if they have, whether it be backward or forward with respect to the stars. And consequently, having not then made his own tables, he was obliged to calculate from the best that he could find. But those tables allow of no motion to Venus's nodes, and also reckon her conjunction with the Sun to be about half an hour too late.
28. But more modern observations prove, that the nodes of Venus's orbit have a motion backward, or contrary to the order of the signs, with respect to the fixed stars. And this motion is al. lowed for in the Doctor's tables, a great part of which were made from his own observations. And
it appears by these tables, that Venus will be so much farther past her descending node at the time of this transit, than she was past her ascending node at her transit, in November 1639; that instead of passing only four minutes of a degree below the Sun's centre in this, she will pass almost 10 minutes of a degree below it: on which account, the line of her transit will be so much shortened, as will make her passage over the Sun's disc about an hour and 20 minutes less than if she passed only 4 minutes below the Sun's centre at the middle of her transit. And therefore, her parallax from the Sun will be so much diminished, both at the beginning and end of her transit, and at all places from which the whole of it will be seen, that the difference of its durations, as seen from them, and as supposed to be seen from the Earth's centre, will not amount to 11 minutes of time.
29. But this is not all; for although the transit will begin before the Sun sets to Port-Nelson, it will be quite over before he rises to that place next morning, on account of its ending so much sooner than as given by the tables to which the Doctor was obliged to trust. So that we are quite deprived of the advantage that otherwise would have arisen from observations made at Port-Nelson.
30. In order to trace this affair through all its intricacies, and to render it as intelligible to the reader as I can, there will be an unavoidable necessity of dwelling much longer upon it than I could otherwise wish. And as it is impossible to lay down truly the parallels of latitude, and the situations of places at particular times, in such a small disc of the Earth as must be projected in such a sort of diagram as the Doctor has given, so as to measure thereby the exact times of the beginning and ending of the transit at any given place, unless the Sun's disc be made at least 30 inches diameter in the projection, and to which the Doctor did not quite trust without making some calculations; I shall take a different
method, in which the Earth's disc may be made as large as the operator pleases: but if he makes it only 6 inches in diameter, he may measure the quantity of Venus's parallax from the Sun upon it, both in longitude and latitude, to the fourth part of a second, for any given time and place; and then, by an easy calculation in the common rule of three, he may find the effect of the parallaxes on the duration of the transit. In this I shall first suppose with the Doctor, that the Sun's horizontal parallax is 12"; and consequently, that Venus's horizontal parallax from the Sun is 31". And after projecting the transit, so as to find the total effect of the parallax upon its duration, I shall next show how nearly the Sun's real parallax may be found from the observed intervals between the times of Venus's egress from the Sun, at particular places of the earth; which is the method now taken both by the English and French astronomers, and is a surer way whereby to come at the real quantity of the Sun's parallax, than by observ. ing how much the whole contraction of duration of the transit is, either at Bencoolen, Batavia, or Pondicherry.
Showing how to project the transit of Venus on the Sun's
disc, as seen from different places of the Earth; so as to find what its visible duration must be at any given place, according to any assumed parallax of the Sun; and from the observed intervals between the times of Venus's egress from the Sun at particular places, to find the Sun's true horizontal parallax.
31. The elements for this projection are as follows: I. The true time of conjunction of the Sun and
Venus; which, as seen from the Earth's centre, and reckoned according to the equal time at