178 



I'HrLOSOPHICAL TRANSACTIONS. 



[anno 1787. 



In order to reduce the observed geocentric longitude to the sun, or by obser- 

 vation to find the heliocentric longitude, it is required to know the angle at the 

 planet = p. If this angle be calculated in the common way only by the tables, 

 there will arise some difference, according to the different elements and the differ- 

 ent constructions of the tables. Thus, at the time of Saturn's culmination, this 

 angle is found the 12th of July, by the tables of Dr. Halley = 0° 3' 13'', and by 

 the tables of M. de la Lande = 0° l' Q"\ the 8th of August by Halley. = 2° 43' 

 Zb", and by M. de la Lande = 2° 42' 34'^; the 27th of August after Dr. Halley 

 = 4° 14' \b", and after M. de la Lande = 4° 13' 47'^ To avoid those differ- 

 ences, which often may alter the heliocentric longitude more than 1 or 2', the 

 following method may be useful. The heliocentric longitude of the earth, cal- 

 culated after the tables of M. Mayer, is to be depended on to 8 or 1 0''. From 

 the heliocentric longitude of the earth, and from the observed geocentric longi- 

 tude of the planet, corrected for the aberration and nutation, is deduced the angle 

 at the earth = t, or the distance between the sun and the planet seen from the 

 earth. The dimensions of the elliptic orbit of the planet are so far ascertained, 

 that the logarithms of the distance from the sun have not any material difference 

 in the different tables. From the angle t, the distance of the earth from the 

 sun, and the distance of the planet from the sun, the angle p is calculated to a 

 sufficient degree of accuracy. Thus, the 12th of July, by the distances of Dr. 

 Halley, /> = 0° 2' b^\ and by the distances of M. de la Lande = 0° 2' b^" ; 

 the 8th of August after Dr. Halley j& = 2° 43' 1b\ and after M. de la Lande 

 j& = 2° 43' 36'/; the 27th of August after Dr. Halley /> = 4° 14' 10^ and after 

 M. de la Lande/) = 4° 14' 28'^ The difference very seldom will amount to 20 

 seconds, and is of no consequence in this matter. From the observed geocentric 

 latitude of the angle at the sun =. 5, and the angle at the earth = t, the helio- 

 centric latitude of the planet is found = ^^"S- g^°^; ^ • ^ ^'"- '^ , 

 * sin. t 



