rot. XVII.] PHILOSOPHICAL TRANSACTIONS. 44Q 



each other, those conjunctions, that happen in different nodes, are also to be 

 considered separately. 



Let Mercury, when retrograde, be in a central conjunction with the sun in 

 the ascending node, in the month of October, and from the above hypothesis 

 we shall have as follows : 



Longitude of the sun from the first star of Aries 6' 15° 44' 0* 



Longitude of Mercury seen from the sun O 15 44 O 



Distance of Mercury from the sun 31365 

 Ditto from the earth 67591 



Angle of the inclination of Mercury's orbit O 6 54 O 



Mercury's motion seen from the sun, in 6 hours O 1 30 58 



Sun's motion in the same, 6 hours O 15 5 



Hence Mercury's motion from the sun, in 6 hours I 15 53 



The same as seen from the earth, in fi hours O O 35 12 



Angle of Mercury with the ecliptic seen in the sun O 8 15 O 



Hence Mercury's motion in his visible orbit, in 6 hours o O 35 40 



Therefore Mercury's motion in a sidereal year, besides 4 revolu- 

 tions, is 1 24 4» 8 



And therefore in 1 3 years 11 21 46 44 



Therefore less than 54 entire revolutions, by O 8 13 16 



Which space Mercury runs over in 2'' O'' 1 1" O' 



In which the sun's place is advanced, and Mercury, in the node, 



is as much distant from the conjunction of the earth O' 2° 1' O" 



But that arch seen from the earth is O o 56 10 



Hence from the given angle of the visible way, 8° 15', arises the 



base, or distance from the visible conjunction o O 45 34 



Which arch is run over by Mercury in 0"* 9'' 2 1 '" O' 



But 13 sidereal years exceed so many Julian ones, with 3 inter- 

 calations, by O 8 O O 



Therefore Mercury returns to the sun after 13 Julian years, and 



besides 2 1 7 34 O 



Or with 4 intercalations, if the preceding year be the third after 



Bissextile 1 17 34 o 



But from the arch 56' 10', and the given angle, the perpendicu- 



»;lar, or Mercury's nearest distance from the sun, is o' 0° 8' 3" 



Therefore Mercury, after seen in the sun, in 13 years advances 



more northerly by ''. .... O 8 3 



Likewise in 46 sidereal years Mercury moves 1 1 28 36 8- 



Therefore wanting of 191 entire revolutions .'Jt'i*.^\ i*!*!^.*^.'* '5"" 1, 23 52 



VOL. III. 3 M 



