Transit of Mercury over the Sun. 293 



Olservatidns. 1st, 1 Ith &c 12th 



- 1st, llt1i & I6th 



- 1st, nth & 15th 



- 1st, 11th & 14th 



- 1st, lOlh & 18th 



Mean 60-137 21 14 405 



Tf S'^'S be taken for the mean parallax of the Sun, the 

 horizontal parallax of Mercury from the Sun on the rlay of 

 the transit is 4^'' 1221 3, and at 21*^ 14^ 40'-5, the parallax in 

 longitude will' be — 2"-6775, and the parallax in latitude 

 + 2".9923 to be applied to the apparent place : therefore the 

 geocentric nearest distance of their centres was 62''- 7 1 at 

 21^' U*" 10' apparent time. 



From the above data several theorems have been given for 

 computing the effect of parallax in accelerating or retarding 

 the time of the beginning or end of a transit. The follow- 

 ing method, which is here employed, is as simple as any, 

 and will be found sufficiently accurate. 



Let O (Fig. 4.) represent the centre of the Sun, M D the 

 relative path of Mercury, M its geocentric place at .egress, 

 and D at the nearest approach to the Sun's cehlfe : joih O D, 

 O M, and in D O take D 0, equal to the parallax at the egress 

 perpendicular to the path ; draw ^'jx, meeting the Sun's limb 

 in |Lc and parallel to D M, and ^ p perpendicular to D M, 

 and take p m in D M produced equal to the parallax at the 

 egress in^ the path ; then will ^u, be the apparent place of 

 Mercury at the egress, and m its place seen from the 

 P^arth's centre, as is manifest from the construction. Now 

 the egress is accelerated or retarded by the time Mercury 

 takes to describe M w, which is = mp +, pM; and as the: 



M O D -h a O D, 



angle |u. M p is = ~ — — p M = ftp x cot } 



(MOD + ju^OD), and M 7?i = M p + y. p x cot i 



(MOD + jw, O D) ; but if m C the parallax in longitude 

 be put = TT, ftC the parallax in latitude = |S, and the angle 

 M m C or the angle which the relative path makes with the 



T 3 ecliptic 



