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If therefore it should happen that this transit should be properly observed by skilful persons at both these places, it is clear, that its duration will be 17 minutes longer, as seen from PortNelson, than as seen from the East-Indies. Nor is it of much consequence (if the English shall at that time give any attention to this affair) whether the observation be made at Fort-George, commonly called Madras, or at Bencoolen on the western shore of the island of Sumatra, near the equator. But if the French should be disposed to take any pains herein, an observer may station himself conveniently enough at Pondicherry on the west shore of the bay of Bengal, where the altitude of the pole is about 12 degrees. As to the Dutch, their celebrated mart at Batavia will afford them a place of observation fit enough for this purpose, provided they also have but a disposition to assist in advancing, in this particular, the knowledge of the heavens. And indeed I could wish that many observations of the same phenomenon might be taken by different persons at several places, both that we might arrive at a greater degree of certainty by their agreement, and also lest any single observer should be deprived, by the intervention of clouds, of a sight, which I know not whether any man living in this or the next age will ever see again; and on which depends the certain and adequate solution of a problem the most noble, and at any other time not to be attained to. I recommend it, therefore, again and again, to those curious astronomers, who (when I am dead) will have an opportunity of observing these things, that they would remem

the Sun at 7; and the same place must be at g, and Venus at r, when she begins to leave the Sun at U, as seen from g. So that Venus must move from N to n in her orbit, while she is seen to pass over the Sun from Port-Nelson; from E to e in passing over the Sun, as seen from the Earth's centre; and only from R tor while she passes over the Sun, as seen from the banks of the Ganges.

ber this my admonition, and diligently apply themselves with all their might to the making of this observation; and I earnestly wish them all imaginable success; in the first place, that they may not, by the unseasonable obscurity of a cloudy sky, be deprived of this most desirable sight; and then, that having ascertained with more exactness the magnitudes of the planetary orbits, it may redound to their immortal fame and glory.

We have now shewn, that by this method the Sun's parallax may be investigated to within its five-hundredth part, which doubtless will appear wonderful to some. But if an accurate observation be made in each of the places above marked out, we have already demonstrated that the durations of this eclipse made by Venus will differ from each other by 17 minutes of time; that is, upon a supposition that the Sun's parallax is 12". But if the difference shall be found by observation to be greater or less, the Sun's parallax will be greater or less, nearly in the same proportion. And since 17 minutes of time are answerable to 12 seconds of solar parallax, for every second of parallax there will arise a difference of more than 80 seconds of time; whence, if we have this difference true to two seconds, it will be certain what the Sun's parallax is to within a 40th part of one second; and therefore his distance will be determined to within its 500dth part at least, if the parallax be not found less than what we have supposed: for 40 times 12 make 500.

And now I think I have explained this matter fully, and even more than I needed to have done, to those who understand astronomy; and I would have them take notice, that on this occasion, I have had no regard to the latitude of Venus, both to avoid the inconvenience of a more intricate calculation, which would render the conclusion less evident; and also because the motion of the nodes

of Venus is not yet discovered, nor can be determined but by such conjunctions of the planet with the Sun as this is. For we conclude that Venus will pass 4 minutes below the Sun's centre, only in consequence of the supposition that the plane of Venus's orbit is immoveable in the sphere of the fixed stars, and that its nodes remain in the same places where they were found in the year 1639. But if Venus in the year 1761, should move over the Sun in a path more to the south, it will be manifest that her nodes have moved backward among the fixed stars; and if more to the north, that they have moved forward; and that at the rate of 5 minutes of a degree in 100 Julian years, for every minute that Venus's path shall be more or less distant than the above-said 4 minutes from the Sun's centre. And the difference between the duration of these eclipses will be somewhat less than 17 minutes of time, on account of Venus's south latitude; but greater, if by the motion of the nodes forward she should pass on the north of the Sun's centre.

But for the sake of those who, though they are delighted with sidereal observations, may not yet have made themselves acquainted with the doctrine of parallaxes, I choose to explain the thing a little more fully by a scheme, and also by a calculation somewhat more accurate.

Let us suppose that at London, in the year 1761, on the 6th of June, at 55 minutes after V in the morning, the Sun will be in Gemini 15° 37', and therefore that at its centre the ecliptic is inclined toward the north, in an angle of 6° 10′; and that the visible path of Venus on the Sun's disc at that time declines to the south, making an angle with the ecliptic of 8° 28': then the path of Venus will also be inclined to the south, with respect to the equator, intersecting the parallels of declination at

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an angle of 2° 18'*. Let us also suppose, that Venus, at the forementioned time, will be at her least distance from the Sun's centre, viz. only four minutes to the south; and that every hour she will describe a space of 4 minutes on the Sun, with a retrograde motion. The Sun's semidiameter will be 15′ 51′′ nearly, and that of Venus 37". And let us suppose, for trial's sake, that the difference of the horizontal parallaxes of Venus with the Sun (which we want) is 31", such as it comes out if the Sun's parallax be supposed 12". Then, on the centre C (Plate XV Fig. 2.) let the little circle AB, representing the Earth's disc, be described, and let his semidiameter CB be 31"; and let the ecliptic parallels of 22 and 56 degrees of north latitude (for the Ganges and Port-Nelson) be drawn within it, in the manner now used by Astronomers for constructing solar eclipses. Let BCg be the meridian in which the Sun is, and to this, let the right line FHG representing the path of Venus be inclined at an angle of 2° 18'; and let it be distant from the centre C 240 such parts, whereof CB is 31. From Clet fall the right line CH, perpendicular to FG; and suppose Venus to be at Hat 55 minutes after V in the morning. Let the right line FHG be divided into the horary space III IV, IV V, V VI, &c. each equal to CH; that is, to 4 minutes of a degree. Also, let the right line LM be equal to the diffe

This was an oversight in the Doctor, occasioned by his placing both the Earth's axis BCg (Fig. 2. of Plate XV.) and the axis of Venus's orbit CH on the same side of the axis of the ecliptic CK; the former making an angle of 6° 10′ therewith, and the latter an angle of 8° 28'; the difference of which angles is only 2° 18'. But the truth is, that the Earth's axis, and the axis of Venus's orbit, will then lie on different sides of the axis of the ecliptic, the former making an angle of 6o therewith, and the latter an angle of 81°. Therefore, the sum of these angles, which is 141° (and not their difference 2° 18), is the inclination of Venus's visible path to the equator and parallels of declination.

rence of the apparent semidiameters of the Sun and Venus, which is 15' 13"; and a circle being described with the radius LM, on a centre taken in any point within the little circle AB representing the Earth's disc, will meet the right line FG in a point denoting the time at London when Venus shall touch the Sun's limb internally, as seen from the place of the Earth's surface that answers to the point assumed in the Earth's disc. And if a circle be described on the centre C, with the radius LM, it will meet the right line FG, in the points Fand G; and the spaces FH and GH will be each equal to 14′ 4′′, which space Venus will appear to pass over in 3 hours 40 minutes of time at London; therefore F will fall in II hours 15 minutes, and G in IX hours 35 minutes in the morning. Whence it is manifest that if the magnitude of the Earth, on account of its immense distance, should vanish as it were into a point; or if, being deprived of a diurnal motion, it should always have the Sun vertical to the same point C; the whole duration of this eclipse would be 7 hours 20 minutes. But the Earth in that time being whirled through 110 degrees of longitude, with a motion contrary to the motion of Venus, and consequently the abovementioned duration being contracted, suppose 12 minutes, it will come out 7 hours 8 minutes, or 107 degrees nearly.

Now Venus will be at H, at her least distance from the Sun's centre, when in the meridian of the eastern mouth of the Ganges, where the altitude of the pole is about 22 degrees. The Sun therefore will be equally distant from the meridian of that place, at the moments of the ingress and egress of the planet, viz. 534 degrees; as the points a and b (representing that place in the Earth's disc AB) are, in the greater parallel, from the meridian BCg. But the diameter ef of that parallel will be to the distance ab, as the square of the radius to the rectangle under the sines of 55 and 68 degrees; that is, of 1' 2" to

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