621 



PHILOSOPHICAL TRANSACTIONS. 



[anno 1790. 



The angle at the planet, or the commutation = p, is not directly to be taken 

 out of the table. The difference between the observed geocentric longitude of the 

 planet and the geocentric longitude of the sun, calculated from M. Mayer's solar 

 tables, is the angle at the earth, or the elongation = t. From this elongation, 

 which is to be depended on to a very few seconds, and from the planet's and the 

 earth's distances from the sun, according to the tables, the commutation is cal- 

 culated, and the geocentric longitude is reduced to the heliocentric longitude. 

 The angles p, t, and s, at the sun, thus found, are likewise used to calculate the 

 heliocentric latitude. According to the different dimensions, given to the orbit 

 of the planet in the different tables, the radius vector at a given time will also be 

 somewhat different. These differences in the tables of Dr. Halley and M. de la 

 Lande are but small : thus, 1784, September 20, at O^ 37' 17" mean time, the 

 observed and apparent geocentric longitude of Venus 6^ 9° 39' 54'", the aberration 

 and nutation + 33'', the corrected and true geocentric longitude 6^ 9° 40' 27'', 

 the sun's geocentric longitude 5^ 28° 5' 51''; hence the elongation t = OMl° 34' 

 36^'. If now the logarithm of the radius vector sp be taken out of Halley's tables 



= 4.858251, then sin. 



p = 



ST X Sin. T 



andp = 16° 11' 52"; but if the loga- 



rithm SP be taken out of M. de la Lande's tables = 4.858168, the angle p will 

 be found = 16" 12' 4", the difference is 12". This uncertainty in the commuta- 

 tion, and consequently in the heliocentric longitude, would have been still greater 

 if the calculations had been made only from the tables, or from the planet's geo- 

 centric longitude by the tables ; thus this angle p is, according to Dr. Halley, 

 = 16° 10' 52"; and from M de la Lande = 16° lO' 13". 



