568 



PHILOSOPHICAL TRANSACTIONS. 



[anno 1761. 



^_T1 A 



Let the circle llRirc represent the sun's 

 disk: in which let ec be a portion of the 

 ecliptic, TLtt its axis, ma a parallel to the 

 equator, pp its axis, tvv the visible path of 

 Venus on the sun, and ab the perpendicular 

 to that path. The angle qsc = psfl = the 

 inclination of the axis of the equator to the 

 iaxis of the ecliptic, is given by calculation; 

 ,then at the internal contact, the side sv, be- 

 ing the semidiameter of the sun, lessened 

 by the semidiameter of Venus, is given, and S tt P 



also vl, the observed difference of declination; whence may be found by plain trigo- 

 nometry the angle v si ; from which, if the angle qsc be subtracted, there will 

 remain the angle vsd ; whence, with sv, may be found sd, the difference of lon- 

 gitude, and vd, the difference of latitude from the sun's centre. In any oth&r 

 position, as at u, there will be given sh, the difference of right ascension, and 

 uli, the difference of declination ; whence may be found the angle ush, and the 

 side su: if from the angle ush the angle qsc be subtracted, there will remain the 

 angle usn: which, with the side su, before found, will give sn, the difference of 

 longitude, and un, the difference of latitude from the sun's centre. At the con- 

 junction in right ascension sv is the observed difference of declination, and the 

 complement of the angle qsc is = the angle vsa: whence will be found the 

 difference of longitude sa, and the difference of latitude va, from the sun's 

 centre. 



1. If a mean be taken of the 4th, 5th, 6th, and 7th of Mr. Hornsby's ob- 

 'servations, and also of the times at 17^ 50™ 46% the right ascension of the 

 centre of Venus will be 1 ".2 before the sun's centre, and the declination of it 

 '10' 10''.6; whence the visible conjunction in right ascension was at 17*^ 56"™ 31% 

 and the visible declination south of the sun's centre lO' 10"A; the visible longi- 

 ■ tude was therefore l' S^'.S before the sun's centre, and the visible latitude south 

 'of it 10' 6 '.9. From the computed visible motion in longitude and latitude, by 

 ^making the proper proportion, the visible ecliptic conjunction will be found at 

 '^17^ 40^" 3* apparent time, at Shirburn, or at 17*^ 44™ 4* apparent time, at Green- 

 wich, when the visible latitude was 9' 57''.6 south of the sun's centre. At 17** 

 56™ 46% the parallax in longitude (supposing as above the horizontal parallax of 

 the sun to be 10^') will be 14% to be added to the visible longitude of Venus, to 

 give her true longitude before the sun's centre, and 20''.5 to be subtracted from 

 the visible latitude, to give the true latitude, as seen from the centre of the 

 earth. The true ecliptic conjunction therefore was at 17^ 36™ 25' apparent time 



