your compasses, and set it both ways from K. to VI. and VI. These hours will be just in the edge of the disk at the equinoxes, but at no other time in the whole year. With the extent K. VI. taken into your compasses, set one foot in K. in the black line below the occult one as a centre, and with the other foot describe the semi-circle VI. 7. 8. 9. 10. &c. and divide it into 12 equal parts; then from these points of division,draw the occult 7. p. 8. 0. 9. n. parallel to the Earth's axis, C. XII. P. With the small extent K. XII. as a radius, describe the quadrantal arc XII. f. and divide it into six equal parts, as XII. a. a. b. bc. cd. de. ef. and through the division points a. b. c. d. e. draw the occult lines VII. e. V.VIII. d. IV. IXC. III. X. b. II. and XI. a. I. all parallel to VI. K. VI. and meeting the former occult lines 7. p. 8. 0. &c. in the points VII. VIII. IX. X. XI. V. IV. III. II. and I. which points will mark the several situations of LONDON on the Earth's disk at these hours respectively, as seen from the Sun, and the elliptic curve VI. VII. VIII. &c. being drawn through these points, will represent the parallel of latitude, or path of LONDON on the disk as seen from the Sun from its rising to its setting. If the Sun's declination had been south, the diurnal path of LONDON would have been on the upper side of the line VI. K, VI. and would have touched the line D. L. E. in L. It is necessary to divide the hourly spaces into quarters, and if possible into minutes also. Make C. B. the radius of a line of chords on the sector, and taking therefrom the chord of 5 degrees and . 35 minutes, (the angle of the Moon's visible path with the ecliptic ;) set it off from H. to M. on the left hand of C. H. (the axis of the ecliptic,) because the Moon's latitude in this case is north ascending. Then draw C. M. for the axis of the Moon's orbit, and bisect the angle M. C. H. by the right line C. Z. If the Moon's latitude had been north descending, the axis of her orbit would have been on the right hand from the axis of the ecliptic. The axis of the Moon's orbit lies the same way when her latitude is south ascending, as when it is north ascending, and the same way when south descending, as when north descending. Take the Moon's latitude (40 minutes and 18 seconds,) from the scale C. A. in your compasses, and set it from i. to x. in the bissecting line C. Z. making i. x. parallel to C. y. and through x. at right angles, to the Moon's orbit, (C. M.) draw the straight line N. w. x. y. s. for the path of the penumbra's centre over the Earth's disk. The point w. in the axis of the Moon's orbit, is, that, where the penumbra's centre approaches nearest to the centre of the Earth's disk, and consequently is the middle of the general Eclipse. The point x. is where the conjunction of the Sun and Moon falls, according to equal time, as calculated by the Tables, and the point y. is the ecliptical conjunction of the Sun and Moon. Take the Moon's true horary motion from the Sun, (27 minutes and 54 seconds,) in your compasses, from the scale C. A. (every division of which is a minute of a degree,) and with that extent, make marks along the path of the penumbra's centre, end divide each space from mark to mark, into 60 equal parts, or horary minutes by dots, and set the hours to every 60th minute in such manner, that the dot signifying the instant of new Moon by the Tables, may fall into the point x. half way between the axis of the Moon's orbit, and the axis of the ecliptic; and then the remaining dots will be the points on the Earth's disk, where the penumbra's centre is at the instants denoted by them, in its transit over the Earth. Apply one side of a square to the line of the penumbra's path, and move the square backwards and forwards, until the other side of it cuts the same hour and minute, (as at m. and m.) both in the path of the penumbra's centre, and the particular minute, or instant which the square cuts at the same time in both paths, will be the instant of the visible conjunction of the Sun and Moon, or the greatest obscuration of the Sun at the place for which the construction is made, (namely, LONDON in this Example,) and this instant is at 47 minutes and 29 seconds past 10 o'clock in the morning, which is 17 minutes, 5 seconds later than the tabular time of true conjunction. Take the Sun's semi-diameter, (16 minutes and six seconds,) in your compasses, from the scale C, A. and setting one foot in the path of LONDON, at m. viz. at 47 minutes and thirty seconds past 10, with the other foot describe the circle U. Y. which will represent the Sun's disk as seen from LONDON at the greatest ob scuration. Then take the Moon's semi-diameter, fourteen minutes and 57 seconds in your compasses from the same scale, and setting one foot in the path of the penumbra's centre at m. in the 47 and 1 minute after 10, with the other foot describe the circle T. Y. for the Moon's disk, as seen from LONDON, at the time when the Eclipse is at the greatest, and the portion of the Sun's disk, which is hidden, or cut off by the disk of the Moon, will show the quantity of the Eclipse at that time, which quantity may be measured on a line equal to the Sun's diameter, and divide it into 12 equal parts for digits, which, in this Example,is nearly eleven digits. This Eclipse was annular at PARIS. Lastly, take the semi-diameter of the penumbra, 31 minutes and 3 seconds from the scale A. C. in your compasses, and setting one foot in the line of the penumbra's path, on the left hand, from the axis of the ecliptic, direct the other foot towards the path of LONDON, and carry that extent backwards and forwards, until both the points of the compasses fall into the same instants in both the paths, and these instants will denote the time when the Eclipse begins at LONDON. Proceed in the same manner on the right hand of the axis of the ecliptic, and where the points of the compasses fall into the same instants in both the paths, they will show at what time the Eclipse ends at LONDON. |