London, is on the 6th of June 1761, at 46 minutes 17 seconds after V in the morning, according to Dr. HALLEY'S tables.

II. The geocentric latitude of Venus at that time, 9′ 43′′ south.

III. The Sun's semidiameter, 15' 50".

IV. The semidiameter of Venus (from the Doctor's Dissertation), 374".

V. The difference of the semidiameters of the Sun and Venus, 15' 12".

VI. Their sum, 16' 27".

VII. The visible angle which the transit-line makes with the ecliptic 8° 31'; the angular point (or descending node) being 1° 6' 18" eastward from the Sun, as seen from the Earth; the descending node being in 14° 29′ 37′′, as seen from the Sun; and the Sun in 15° 35′ 55′′, as seen from

the Earth. VIII. The angle which the axis of Venus's visible path makes with the axis of the ecliptic, 8° 31'; the southern half of that axis being on the left hand (or eastward) of the axis of the ecliptic, as seen from the northern hemisphere of the Earth, which would be to the right hand, as seen from the Sun.

IX. The angle which the Earth's axis makes with

the axis of the ecliptic, as seen from the Sun, 6°; the southern half of the Earth's axis lying to the right hand of the axis of the ecliptic, in the projection which would be to the left hand, as seen from the Sun.

X. The angle which the Earth's axis makes with the axis of Venus's visible path, 14° 31'; viz. the Sum of No. VIII. and IX.

XI. The true motion of Venus on the Sun, given by the tables as if it were seen from the Earth's centre, 4 minutes of a degree in 60 minutes of time.

32. These elements being collected, make a scale of any convenient length, as that of Fig. 1. in Plate XVI, and divide it into 17 equal parts, each of which shall be taken for a minute of a degree, then divide the minute next to the left hand into 60 equal parts for seconds, by diagonal lines, as in the figure. The reason for dividing the scale into 17 parts or minutes is, because the sum of the semidiameters of the Sun and Venus exceeds 16 minutes of a degree. See No. VI.

33. Draw the right line ACG (Fig. 2.) for a small part of the ecliptic, and perpendicular to it draw the right line CvE for the axis of the ecliptic on the southern half of the Sun's disc.

34. Take the Sun's semidiameter, 15' 50" from the scale with your compasses; and with that extent, as a radius, set one foot in C as a centre, and describe the semicircle AEG for the southern half of the Sun's disc; because the transit is on that half of the Sun.

35. Take the geocentric latitude of Venus, 9' 43", from the scale with your compasses; and set that extent from C to v, on the axis of the ecliptic: and the point v shall be the place of Venus's centre on the Sun, at the tabular moment of her conjunction with the Sun.

36. Draw the right line CBD, making an angle of 8° 31' with the axis of the ecliptic, toward the left hand; and this line shall represent the axis of Venus's geocentric visible path on the Sun.

37. Through the point of the conjunction v, in the axis of the ecliptic, draw the right line qtr for the geocentric visible path of Venus over the Sun's disc, at right angles to CBD, the axis of her orbit, which axis will divide the line of her path into two equal parts qt and tr.

38. Take Venus's horary motion on the Sun, 4' from the scale with your compasses; and with that extent make marks along the transit-line qtr. The equal spaces, from mark to mark, show how

much of that line Venus moves through in each hour, as seen from the Earth's centre, during her continuance on the Sun's disc.

39. Divide each of these horary spaces, from mark to mark, into 60 equal parts for minutes of time; and set the hours to the proper marks in such a manner, that the true time of conjunction of the Sun and Venus, 46 minutes after V in the morning, may fall into the point v, where the transit-line cuts the axis of the ecliptic. So the point v shall denote the place of Venus's centre on the Sun, at the instant of her ecliptical conjunction with the Sun, and t (in the axis CtD of her orbit) will be the middle of her transit; which is at 24 minutes after V in the morning, as seen from the Earth's centre, and reckoned by the equal time at London.

40. Take the difference of the semidiameters of the Sun and Venus, 15' 12", in your compasses from the scale; and with that extent, setting one foot in the Sun's centre C, describe the arcs N and T with the other crossing the transit-line in the points k and ; which are the points on the Sun's disc that are hid by the centre of Venus at the moments of her two internal contacts with the Sun's limb or edge, at M and N: the former of these is the moment of Venus's total ingress on the Sun, as seen from the Earth's centre, which is at 28 minutes after II in the morning, as reckoned at London; and the latter is the moment when her egress from the Sun begins, as seen from the Earth's centre, which is 20 minutes after VIII in the morning at London. The interval between these two contacts is 5 hours 52 minutes.

41. The central ingress of Venus on the Sun is the moment when her centre is on the Sun's eastern limb at u, which is at 15 minutes after two in the morning and her central egress from the Sun is the moment when her centre is on the Sun's western limb at w; which is at 33 minutes after VIII in

the morning, as seen from the Earth's centre, and reckoned according to the time at London. The interval between these times is 6 hours 18 minutes.

42. Take the sum of the semidiameters of the Sun and Venus, 16' 27", in your compasses from the scale; and with that extent, setting one foot in the Sun's centre C, describe the arcs Q and R with the other, cutting the transit-line in the points q and r, which are the points in open space (clear of the Sun) where the centre of Venus is, at the moments of her two external contacts with the Sun's limb at S and W; or the moments of the beginning and ending of the transit as seen from the Earth's centre; the former of which is at 3 minutes after II in the morning at London, and the latter at 45 minutes after VIII. The interval between these moments is 6 hours 42 minutes.

43. Take the semidiameter of Venus 37", in your compasses from the scale: and with that extent as a radius, on the points q, k, t, l, r, as centres, describe the circles HS, MI, OF, PN, WY, for the disc of Venus, at her first contact at S, her total ingress at M, her place on the Sun at the middle of her transit, her beginning of egress at N, and her last contact at W.

44. Those who have a mind to project the Earth's disc on the Sun, round the centre C, and to lay down the parallels of latitude and situations of places thereon, according to Dr. HALLEY'S method, may draw Cf for the axis of the Earth, produced to the southern edge of the Sun at f; and making an angle ECf of 6° with the axis of the ecliptic CE: but he will find it very difficult and uncertain to mark the places on that disc, unless he makes the Sun's semidiameter AC 15 inches at least: otherwise the line Cf is of no use at all in this projection.-The following method is better.

45. In Fig. 3. of Plate XVI make the line AB of any convenient length, and divide it into 31 equal parts, each of which may be taken for a second

of Venus's parallax either from or upon the Sun (her horizontal parallax from the Sun being supposed to be 31"); and taking the whole length AB in your compasses, set one foot in C (Fig. 4.) as a centre, and describe the circle AEBD for the Earth's enlightened disc, whose diameter is 62", or double the horizontal parallax of Venus from the Sun. In this disc, draw ACB for a small part of the ecliptic, and at right angles to it draw ECD for the axis of the ecliptic. Draw also NCS both for the Earth's axis and universal solar meridian, making an angle of 6° with the axis of the ecliptic, as seen from the Sun; HCI for the axis of Venus's orbit, making an angle of 8° 31' with ECD, the axis of the ecliptic; and lastly, VCO for a small part of Venus's orbit, at right angles to its axis.

46. This figure represents the Earth's enlightened disc, as seen from the Sun at the time of the transit. The parallels of latitude of London, the eastern mouth of the Ganges, Bencoolen, and the island of St. Helena, are laid down in it, in the same manner as they would appear to an observer on the Sun, if they were really drawn in circles on the Earth's surface (like those on a common terrestrial globe) and could be visible at such a distance.-The method of delineating these parallels is the same as already described in the XIXth chapter, for the construction of solar eclipses.

47. The points where the curve-lines (called hour-circles) XI N, XN, &c. cut the parallels of latitude, or paths of the four places above mentioned, are the points at which the places themselves would appear in the disc, as seen from the Sun, at these hours respectively. When either place comes to the solar meridian NCS by the Earth's rotation on its axis, it is noon at that place; and the difference, in absolute time, between the noon at that place and the noon at any other place, is in proportion to the difference of longitude of these two places, reckoning one hour for every 15 degrees of