266 PHILOSOPHICAL TRANSACTIONS. [aNNO IjGS. 



ments as given in Dr. Halley's tables. According to these numbers, and the 

 Abbe de la Caille's solar tables, the ecliptic conjunction will happen on June 3 

 1769, at 9*" 59™ 24' mean time at Greenwich, the planet's geocentric latitude 

 being lo' 13*.5 N. The log. of the earth's distance from the sun = 5.oo65l66- 

 the log. of Venus's distance from the sun = 4.8610947; and of the planet's t 

 distance from the earth = 4.46o6784; and the equation of the prascession of the 

 equinoctial points = + l7"-7' By computing the geocentric longitude and lati- 

 tude of the planet 3 hours before and 3 hours after the ecliptic conjunction, Mr. 

 H. finds the planet's hourly motion from the sun in the ecliptic ^ 3' 57''''.7 ; the 

 hourly motion in the relative orbit = 4' 0''.3 ; the hourly motion in latitude = 

 0' 35". Ab ; the angle of the planet's path with the ecliptic = 8° 29' 2"; the angle 

 of the ecliptic with the equator = 7° 2' 54"; and therefore the angle made by the 

 planet's visible path with the equator = 15° 3 1' 56'. The geocentric latitude is, 

 as has been observed, = lO' 13*. 5; and hence it is easily determined that the 

 least distance of the centres will be lO' 6''.8, and the interval between the time 

 of the ecliptic conjunction and the middle of the transit ^ 22"" 21* of time. 

 As the planet has not yet passed its node, the middle of the transit will therefore 

 be at 10*" 21'" 45* mean time at Greenwich. In every inferior conjunction the 

 motion of Venus is retrograde, and therefore the effect of the aberration of light 

 in long. = 3''.7j when reduced to time =: 55% is to accelerate the several phases 

 of the transit; the equated mean time of the middle therefore will be at 10'' 20°" 

 50*. But the place of the planet is also affected by the aberration of light in 

 latitude, and as Venus's latitude is decreasing, the least distance of the centres 

 will be increased by l".35. The equated least distance of the centres therefore 

 will be 10' 8". 15. Now, supposing the semidiameter of the sun = 15'45*.6, 

 and of Venus = 29", the semidurations, or intervals between the middle and 

 the external and internal contacts, will be found = 3'' 10™ 8'.5, and 2*' 51'" 13'.2. 

 The equation of time is about 2"^ 14' at the middle of the transit, by which 

 quantity the apparent time is before the mean, and decreases at the rate of about 

 2' in 6 hours. Therefore the apparent times of the several phases of this transit 

 for the meridian of Greenwich are as follow : 



Apparent time. 



First external contact, June 3 7^ 1 2"" 56* 



Total ingress 7 31 52 



Middle 10 23 04 



Beginning of egress 13 14 16 



Last contact 13 33 11 



Hitherto we have had no regard to parallax, and the above times are such as 

 would be observed from the earth's centre. To the British isles, and to the 

 neighbouring parts of the continent, the effect of parallax is nearly at a maxi- 



