VOL. LXXX.] 



PHILOSOPHICAL TRANSACTIONS. 



623 



Let the difference between two heliocentric longitudes, one before and the 

 other after the passage through the node, be = a, the northern heliocentric 

 latitude = h, and the southern = P ; let the arc of the ecliptic from the node to 

 the longitude, answering to the southern latitude, be = j?; then tang, x = 



By this formula the distance from every longitude with a 



sin. a . tang. 



Observations compared. 



tang, b + cos. a tang. /3 



southern latitude to the node may be found ; and hence the heliocentric longitude 



of the node. 



Heliocentric Hence the heliocentric longi- 



of 8 ? . ^^^^ ^^ ^^ descending node of 



the planet Venus was, 1786, 

 August 25, at S^ 39™ = 8« 14° 

 44' 38'^, which is to be depended 

 on to 10 or IS^''. According to 

 Cassini's tables, the longitude of 

 the node is 8^ 14° 48' 31'-', the 

 difference, or the error, — 3' 53", 

 According to Halley's 8^ 14° 42' 

 3Q", the difference -f l' 59^^ 

 From De la Lande's 8^ 14° 45' 

 15'''', the difference only — ^y". 



In order to ascertain the an- 

 nual motion of the node, this 

 observation is to be compared 

 with the observations of other 



astronomers. The numbers in the column a are found by setting out from my 



