VOL. XVII,] PHILOSOPHICAL TRANSACTIONS. 451 



Hence, by following the method of the preceding calculus, it is evinced that 

 Mercury after 13 years 3d. 7h. 37m. revolves to its conjunction with the sun; 

 but if the preceding jear be the 3d after bissextile, in that case 2d. 7h. 37 m. 

 are only to be added ; and then Mercury will be found to advance l6' 55" more 

 southerly. After 46 years, with 12 intercalations, add 7h. 14m. and Mercury 

 will be in conjunction with the sun 2' 53" more southerly; but if the former 

 year be bissextile, or the first after it, id, 7h. 14m, are to be added, in order 

 to have the conjunction accurately. In like manner, after 263 years, in which 

 Mercury declines 22" to the south, either id. 1 1 h. 49m. or 1 1 h. 49m. are to 

 be added, according to the rule prescribed in the former case. 



But in 6 or 7 years, because of the nearness of the earth and that planet, 

 and therefore on account of the enlarged arches at this node, it does not return 

 to the sun, so as to be seen within its disk. -After 33 years it passes over the 

 sun 14' 2" more northerly; and the .iioment of the conjunction is had by sub- 

 tracting from the time of the former, 3d. Oh. 23m. if it be the 3d year after 

 bissextile; otherwise subtract 2d. Oh, 23m. only. 



Having found these, it will be easy to continue the calculus for all the con- 

 junctions of Mercury with the sun, and that with the greatest certainty ; by 

 addition only, the moments of the conjunctions, and the distances of the 

 planet from the centre of the sun are obtained, whence also by the help of a 

 table, the durations of these eclipses are discovered ; so that nothing seems to 

 be wanting in this affair. 



As to the epocha, these are with more safety had from the industry of ob- 

 servers than by the subtilest calculations ; therefore I chose for the first case, 

 that remarkable transit of Mercury which I fully observed at St. Helena, Oct. 

 28, 1677, O. S. and whose middle I determined there at 4 m. p. m. but at Lon- 

 don 28m. p. m. The way in which the planet seemed to advance was 4' 40^' 

 more northerly than the sun's centre ; in the other case, viz. when Mercury was 

 in conjunction with the sun, April 23, l66j, O, S. he appeared at his least dis- 

 tance from the sun's centre at Dantzic 6h. 8m. p. m, and at London 4h, 52 m. 

 being then in the middle of his transit, and at the same time was distant from 

 the centre 4' 27" to the north. Hence, according to the above rules, it was 

 easy to exhibit in order all the visible conjunctions of Mercury with the sun. 



A series of the times wherein Mercury, being in conjunction with the sun, 

 is seen within his disk, calculated for the present and ensuing century, with the 

 distances of the planet from the sun's centre. 



3 M 2 



