MATHEMATICAL PAPERS 





For 5 's scinirliamcter Ly tlio obscr\ 



of 



contacts, 



and also his latitude, together with the time of the ecliptici 

 conjunction : Tn fig, 8, Plate i. let E S K represent the southern 

 half of the Sun's disc j the diameter E O K a portion of the 

 ecliptick, or rather a line parallel to it, being removed from 



it 



= the Sun's parallax in latitude ; C ^ Mercury's visible 

 geocentrick latitude at the time of the first external contact ; 

 L M his visible geocentrick latitude, at the time of the second 



external contact; the line M U drawn from the point M 

 parallel to K E == Mercury's visible motion upon the Sun's 

 disc, between the two external contacts, reduced to the eclip- 

 tick ; consequently, ^ U = liis visible motion in geocentrick 

 latitude, during the time which passed between the two ex- 

 ternal contacts. Therefore, ^ M is the visible transit line; 

 and ^ M U, the angle Avhich this line makes with the eclip- 



ft 



tick. The point 



the Sun 



app 



of the visible conjunction of centres ; O N perpendicular to 



^ M, the visible least distance . of centres ; O D perpendicular 

 to the eclijDtick, the visible distance of centres, at the time of the 



■the 



sum 



visible ecliptick conjunction ; S O and M O ^ 



the semidiameter of the Sun and Mercury, the distance of ccn- 



of • 



the 



ires, at the time of the external contacts ; O i and O r 

 Sun's semidiameter, the distance of' centres, at the time of the 



contacts of Mercury's centre with the Sun's limb ; C U 



UF, 



the visible difference of longitude of the centres, at the time of 

 the first external contact, and O L the visible diilerence, at the 

 time of tlie second. 



The 



