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longitude, and 4 minutes for each degree: adding the time if the longitude be east, but subtracting it if the longitude be west.

48. The distance of either of these places from HCI (the axis of Venus's orbit) at any hour or part of an hour, being measured upon the scale AB in Fig. 3. will be equal to the parallax of Venus from the Sun in the direction of her path; and this parallax, being always contrary to the position of the place, is eastward as long as the place keeps on the left hand of the axis of the orbit of Venus, as seen from the sun; and westward when the place gets to the right hand of that axis. So that, to all the places which are posited in the hemisphere HVI of the disc, at any given time, Venus has an eastern parallax; but when the Earth's diurnal motion carries the same places into the hemisphere HOI, the parallax of Venus is westward.

49. When Venus has a parallax toward the east, as seen from any given place on the Earth's surface, either at the time of her total ingress, or beginning of egress, as seen from the Earth's centre; add the time answering to this parallax to the time of ingress or egress at the Earth's centre, and the sum will be the time, as seen from the given place on the Earth's surface but when the parallax is westward, subtract the time answering to this parallax from the time of total ingress or beginning of egress, as seen from the Earth's centre, and the remainder will be the time, as seen from the given place on the surface, so far as it is affected by this parallax.-The reason of this is plain to every one who considers,

In a former edition of this, I made a mistake, in taking the parallax in longitude instead of the parallax in the direction of the orbit of Venus; and the parallax in latitude instead of the parallax in lines perpendicular to her orbit. But in this edition, these errors are corrected; which make some small differences in the quantities of the parallaxes, and in the times depending on them; as will appear by comparing them in this with those in the former edition.

that an castern parallax keeps the planet back, and a western parallax carries it forward, with respect to its true place or position, at any instant of time, as seen from the Earth's centre.

50. The nearest distance of any given place from VCO, the plane of Venus's orbit at any hour or part of an hour, being measured on the scale AB in Fig. 3. will be equal to Venus's parallax in lines perpendicular to her path; which is northward from the true line of her path on the Sun, as seen from the Earth's centre, if the given place be on the south side of the plane of her orbit VCO on the Earth's disc; and the contrary, if the given place be on the north side of that plane; that is, the parallax is always contrary to the situation of the place on the Earth's disc, with respect to the plane of Venus's orbit on it.

51. As the line of Venus's transit is on the southern hemisphere of the Sun's disc, it is plain that a northern parallax will cause her to describe a longer line on the Sun, than she would if she had no such parallax ; and a southern parallax will cause her to describe a shorter line on the Sun, than if she had no such parallax.-And the longer this line is, the sooner will her total ingress be, and the later will be her beginning of egress; and just the contrary, if the line be shorter.-But to all places situate on the north side of the plane of her orbit, in the hemisphere VHO, the parallax in lines perpendicular to her orbit is south; and to all places situate on the south side of the plane of her orbit, in the hemisphere VIO, this parallax is north. Therefore, the line of the transit will be shorter to all places in the hemisphere VHO, than it will be, as seen from the Earth's centre, where there is no parallax; and longer to all places in the hemisphere V10. So that the time answering to this parallax must be added to the time of total ingress, as seen from the Earth's centre, and subtracted from the beginning of egress, as

seen from the Earth's centre, in order to have the true time of total ingress and beginning of egress as seen from places in the hemisphere VHO: and just the reverse for places in the hemisphere VIO.—It was proper to mention these circumstances, for the reader's more easily conceiving the reason of applying the times answering to these parallaxes in the subsequent part of this article: for it is their sum in some cases, and their difference in others, which being applied to the times of total ingress and beginning of egress as seen from the Earth's centre, that will give the times of these phenomena as seen from given places on the Earth's surface.

52. The angle which the Sun's semidiameter subtends, as seen from the Earth, at all times of the year, has been so well ascertained by late observations, that we can make no doubt of its being 15' 50" on the day of the transit; and Venus's latitude has also been so well ascertained at many different times of late, that we have very good reason to believe it will be 9' 43" south of the Sun's centre at the time of her conjunction with the Sun.-If then her semidiameter at that time be 37" (as mentioned by Dr. HALLEY) it appears by the projection (Fig. 2.) that her total ingress on the Sun, as seen from the Earth's centre, will be at 28 minutes after two in the morning (40.), and her beginning of egress from the Sun will be 20 minutes after VIII, according to the time reckoned at London.

53. As the total ingress will not be visible at London we shall not here trouble the reader about Venus's parallax at that time.—But by projecting the situation of London on the Earth's disc (Fig. 4.) for the time when the egress begins, we find it will then be at , as seen from the Sun.

Draw Id parallel to Venus's orbit VCO, and lu perpendicular to it: the former is Venus's eastern parallax in the direction of her path at the beginning of her egress from the Sun, and the latter is her

southern parallax in a direction at right angles to her path at the same time. Take these in your compasses, and measure them on the scale AB (Fig. 3.) and you will find the former parallax to be 103", and the latter 214".

54. As Venus's true motion on the Sun is at the rate of four minutes of a degree in 60 minutes of time (See No. XI. of 31.) say, as 4 minutes of a degree is to 60 minutes of time, so is 103" of a degree to 2 minutes 41 seconds of time; which being added to VIII hours 20 minutes (because this parallax is eastward, § 49.) gives VIII hours 22 minutes 41 seconds, for the beginning of egress at London as affected only by this parallax.-But as Venus has a southern parallax at that time, her beginning of egress will be sooner; for this parallax shortens the line of her visible transit at London.

55. Take the distance Ct (Fig. 2.), or nearest approach of the centres of the Sun and Venus in your compasses, and measure it on the scale (Fig. 1.), and it will be found to be 9' 36"; and as the parallax of Venus from the Sun in a direction which is at right angles to her path is 213′′ south, add it to 9' 36", and the sum will be 9' 58"; which is to be taken from the scale in Fig. 1. and set from C to L in Fig. 2. And then, if a line be drawn parallel to tl, it will terminate at the point p in the arc T, where Venus's centre will be at the beginning of her egress, as seen from London*.-But as her centre is at when her egress begins as seen from the Earth's centre, take Lp in your compasses, and setting that extent from t toward on the central transit-line, you will find it to be 5 minutes shorter than tl: therefore subtract 5 minutes from VIII hours 22 minutes 41 seconds, and there will remain VIII

The reason why the lines oLp, a Bb, ct, and th, which are the visible transits at London, the Ganges mouth, Bencoolen, and St. Helena, are not parallel to the central transit-line ktl, is because the parallaxes in latitude are different at the times of ingress and egress, as seen from each of these places. The method of drawing these lines will be shown by-and-by.

hours 17 minutes 41 seconds for the visible beginning of egress in the morning at London.

56. At V hours 24 minutes (which is the middle of the transit, as seen from the Earth's centre) London will be at L on the Earth's disc (Fig. 4.) as seen from the Sun. The parallax La of Venus from the Sun in the direction of her path is then 12"; by which, working as above directed, we find the middle of the transit, as seen from London, will be at V hours 20 minutes 53 seconds.-This is not affected by Lt the parallax at right angles to the path of Venus.-But Lt measures 27" on the scale AB (Fig. 3.): therefore take 27′′ from the scale in Fig. 1. and set it from t to L, on the axis of Venus's path in Fig. 2. and laying a ruler to the point L, and the above-found point of egress p, draw oLp for the line of the transit as seen from London.

57. The eastern mouth of the river Ganges is 89 degrees east from the meridian of London; and therefore, when the time at London is 28 minutes after II in the morning (§ 40.) it is 24 minutes past VIII in the morning (by § 47.) at the mouth of the Ganges; and when it is twenty minutes past VIII in the morning at London (§ 40.) it is 16 minutes past II in the afternoon at the Ganges. Therefore, by projecting that place upon the Earth's disc, as seen from the Sun, it will be at G (in Fig. 4.), at the time of Venus's total ingress, as seen from the Earth's centre, and at g when her egress begins.

Draw Ge and gr parallel to the orbit of Venus VCO, and measure them on the scale AB in Fig. 3. the former will be 21" for Venus's eastern parallax in the direction of her path, at the above-mentioned time of her total ingress, and the latter will be 161" for her western parallax at the time when her egress begins. The former parallax gives 5 minutes 15 seconds of time (by the analogy in § 54.) to be added to VIII hours 24 minutes, and the latter parallax gives 4 minutes 11 seconds to be subtracted from II hours 16 minutes; by which we have VIII

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