Astronomical and Nautical Collections. 95 



the sun's horizontal parallax may be thus determined from obser- 

 vations of the transits of Venus. 



If the sun's horizontal parallax be supposed known, the hori- 

 zontal parallax of Venus is ascertained from the ratios of the dis- 

 tances of Venus and the sun from the earth. By means of these 

 parallaxes, the observed times of ingress and egress at those places 

 where the beginning and end of the transit have been observed, 

 and other astronomical data, the nearest distance of Venus from 

 the sun, as seen from the earth's centre, is to be computed in the 

 same manner as the moon's latitude is determined from observa- 

 tions of an occultation. See La Lande's Astronomy, third edition, 

 Arts. 1970-1976. In this calculation the orbital and perpendicular 

 parallaxes are to be adopted, instead of the parallaxes in longitude 

 and latitude employed by La Lande, and the motions are to be 

 referred to Venus's relative orbit in place of the ecliptic. If the as- 

 sumed parallax, the observations, and other data, be correct, the 

 nearest distances, deduced from the observations at the respective 

 places, ought to be equal. But if they turn out to be different, 

 that value of the sun's parallax should be preferred which gives 

 for the nearest distance quantities agreeing best with each other. 

 This is to be determined by repeating the calculation upon a second 

 hypothesis of the sun's parallax, observing that all the parallaxes 

 will undergo a proportional variation. 



For an illustration of this method, the transit of 1769 is assumed. 

 The times of observation at the different places, and the other 

 data, are taken from De Lambre's Astronomy. 



At Otaheite, the total ingress was observed at 21 h 43 m 55*, and 

 the beginning of egress at 3 h 14 m 3 s , apparent time. The sun's 

 horizontal parallax at his mean distance from the earth being 

 assumed 8"*7, Venus's nearest distance is found to be 606"*122 ; 

 but the sun's parallax being assumed 8"-5, the same distance is 

 found to be 606"*728. Hence an increase of one second upon the 

 sun's mean horizontal parallax produces a diminution of 3"-030 

 upon the nearest distance, deduced from these observations. If D 

 denote the nearest distance, P the number of seconds by which the 



