248 • PHILOSOPHICAL TRANSACTIONS. [aNN0 171(5. 



And supposing, for trial sake, the difference of the horizontal parallaxes of 

 Venus and the sun to be 3 1^ such as it is on the supposition of the sun's parallax 

 being 12^- Therefore let a small circle, as aebd, fig. 3, pi. 5, be described 

 from the centre c, whose semi-diameter let be SI''', representing the earth's 

 disk, and in it drawing nabE and cde the ellipses of the parallels of ll and 56° 

 N. lat. in the same manner as is now used by astronomers for constructing solar 

 eclipses: and let bca be the meridian in which the sun is, to which let be 

 inclined the right line fhg, representing the path of Venus, in an angle of 

 2° 18', whose distance from the centre c let be 240 such parts as bc is 31 ; and 

 from c let fall the right line ch perpendicular upon fg. Then supposing the 

 planet in h at 17*' 55™, or 5*^ 55"^ in the morning, let the right line fhg be 

 divided into the horary spaces iii; iv, iv; v, v; vi, &c. equal to ch, that is, 

 4 minutes. Let the right line kl be also equal to the difference of the apparent 

 semi-diameters of the sun and Venus, or 15' \3±". Then the circle, described 

 with the radius kl, and from any point within the small circle, representing the 

 earth's disk as a centre, will meet the right line fg in the point denoting what 

 o'clock it is at London, when Venus shall touch the sun's limb in an angle of 

 internal contact, in that place of the earth's superficies that lies under the 

 assumed point on the disk. And if a circle, described from the centre c and 

 with the radius kl, meet fg in the points f and g, the right lines fh, hg will 

 be = 14' 41''', which Venus will appear to pass over in 3^ 40"^. Therefore p 

 will fall upon 2** 15"^ at London, and g upon Q^ 35™ in the morning. Whence 

 it is evident, that if the earth's magnitude should vanish, as it were, into a 

 point, by reason of the immense distance; or if, divested of its diurnal motion, 

 it should always have the sun vertical to the same point c, the entire mora of 

 this eclipse would continue for 75 hours. But in the mean time while the 

 earth revolves with a contrary motion to that of Venus through 1 10° of long, 

 and consequently the duration of the said mora is shorter, suppose by 12 minutes, 

 it will be nearly 7^ 8™, or 107*. 



Now in the meridian itself Venus will be near the sun's centre at the eastern 

 mouth of the Ganges, where the elevation of the pole is about 22°. Therefore 

 that place will be equally distant from the sun on both hands, in the moments 

 of the planet's ingress and egress, viz. 53-^°; as the points a, b, in the greater 

 parallel oabE. But the diameter ab will be to the distance ab, as the square of 

 the radius to the rectangle under the sines of 53^° and 68°, that is, as l' 2" is 

 to 46'' 13'"; and on making a due calculation, I find that the circle described 

 with the radius kl, trom the centre a, will meet the right line fh in the point 

 M, at 2*" 20™ 40*; but described from the centre b, it will meet hg in n, at Q^ 

 29™ 22" at London; consequently, the whole body of Venus will be seen from 



