VOL. XXIX.] I'HILOSOPHICAL TRANSACTIONS. 24gi 



the banks of the Ganges, within the sun's disk, for 7^ 8"" 42^ Therefore we 

 have rightly supposed its duration ^^ S'", since here a part of a minute is incon- 

 siderable. 



But adapting the calculation to Nelson's harbour, I find that Venus shall pass 

 over the sun's disk, when he is just about to set, and emerge out of his disk 

 immediately after his rising, that place in the mean time being carried through 

 the hemisphere opposite to the sun from c to d, with a motion conspiring with 

 that of Venus. Therefore the mora of Venus within the sun's disk will become 

 longer by reason of the parallax, suppose by 4 minutes, so as entirely to be 

 7^ 24"^ or 1 ] 1° of the equator. And since the latitude of the place is 56°, it 

 will be as the square of the radius is to the rectangle under the sines of 55^ 

 and 34°, so is ab = l' 1", to cd = 28" 33'".' And on duly making the calcu- 

 lation, it will appear, that the circle, described from the centre c, with the 

 radius kl, will meet the right line fh in o, at 1^ J 2"^ 45^; but described from 

 the centre d, it will meet hg in p, at p^ 3&^ 37^ Therefore the duration of 

 the mora at Nelson's harbour will be ^^ 23"^ 52% viz. greater than at the mouth 

 of the Ganges by \5^ 10* of time. But if Venus should pass without latitude, 

 the said difference will become 18'"40^; and if she shall be 4 minutes more 

 northerly than the sun's centre, the difference will be increased to 21"^ 40% and 

 will be still greater by increasing the planet's N. lat. 



From the above hypothesis it follows, that at London Venus will rise when 

 entered into the sun, and at Q^ 37*^ in the morning in her egress touch inter- 

 nally the sun's limb, and quite leave his disk not before g^ 56*". 



It is evident from the same hypothesis, that Venus should touch with her 

 centre the extreme northern limb of the sun on May 23, 11^, 1769, so that, 

 by reason of the parallax, her whole body may be seen in the northern parts of 

 Norway, within the sun's disk; while on the coast of Peru and Chili she will 

 seem to ride on the disk of the setting sun with a small segment of her body ; 

 as in like manner in the Molucca islands, and the neighbouring parts, at sun- 

 rising. But if the nodes of Venus be found to have a retrocession, as there is 

 reason to suspect from some later observations, then her whole body being every 

 where seen within the sun's disk, the greatest differences of these eclipses will 

 afford a still more evident proof of the sun's parallax.* 



* " The transit of Venus in 1761 proved much less favourable to the proposed purpose than Dr. 

 Halley expected. The motion of Venus's node not being well known, she passed much nearer the 

 sun's centre than he supposed she wouldj which made the places he pointed out for observing the 

 total duration not proper for the purpose j indeed the entrance of Venus on the sun could not be seen 

 at Hudson's Bay. He made a mistake too in the calculation, in taking the sum instead of the differ- 

 ence, of the angle of the ecliptic with the parallel to the equator, and the angle of Venus's path 

 VOL. VI. K K 



