

i68 



M A 1' H E M A T I C A L and 



*' Let S (plate III. fig. 6) be the center of the Sun and of 

 the circle ABC, whofe radius==:975'' the fum of thefemidi- 

 ameters of the Sun and Venus, Let D L o be the true tran- 

 fit line, and D the place of Venus'* s center at the time of the 

 external contadl, as feen from the earth's center; and B 

 its place as feen from any part on the furface of the earth, 

 fuppofe Greenwich. MakeB E perpendicular to Do; then 

 will D E be the parallax in longitude, andEB in latitude; 

 and D Liliall be the whole fpacebywhicli Venus is brought 

 fooner into contact with the Sun to a fpedator at Green- 

 wich, than as feen from tlic center of the earth. 



" Now if the parallax of longitude only took place, the 

 center of Venus would be removed thereby only along her 

 true path from D to E, and fo the tranfit would not yet 

 be begun. But the parallax of latitude EB makes her cen- 

 ter appear to be removed in another diredion from Eto B, 

 and brings her to touch the Sun*s limb by the fpace E L 

 fooner than if only the parallax of longitude took place. 

 The length of this fpace E L, (which Is here lefsthanE B) 



may be determined as follows. 



" Having affumed the Sun's horizontal parallax as be- 

 fore it follows from the Norriton obfervations, that the 

 leaft diftance of the centers of the Sun and Venus, as feen 



from the earth's center, was 610 



// 



Make therefore, o S 



6 1 o^', perpendicular to D o r ; and o m := half the parallax 



of latitude BE, calculated as above for the given place. 

 Drawn m I, parallel to o L; join S I, which fliall be per- 

 pendicular to B L. Make S p, perpendicular to S I, or 

 parallel to BL. Then the triangles BEL, 1 m S, arefimi- 

 lar; for they are both fimilar to S m p; whence I m : m 



S : : B E. : E L. But m S, "61 — m o, h alf the parallax 

 of latitude already found; and Vsi 1 mS.^m L Thus, 

 the three firft terms of the proportion being known, the 

 fourth EL is known alfo. 



" In like manner let F be the geocentric place of Venus's 

 center, and H its jilace as feen at Norriton at the time of 

 the external contadt. Draw H G perpendicular to D Lo, 



Then 



