SECT' viii.] ASTKONOMTCAL TABLES. 67 



consequently give the exact place of the body in the heavens, 

 for any time assumed at pleasure, provided they can be re- 

 duced to numbers. But before the calculator begins his 

 task the observer must furnish the necessary data, which 

 are, obviously, the forms of the orbits, and their positions 

 with regard to the plane of the ecliptic (N. 57). It is t iere- 

 fore necessary to determine by observation, for each planet, 

 the length of the major axis of its orbit, the excentricity, 

 the inclination of the orbit to the plane of the ecliptic, the 

 longitudes of its perihelion and ascending node at a given 

 time, the periodic time of the planet, and its longitude at 

 any instant arbitrarily assumed, as an origin from whence 

 all its subsequent and antecedent longitudes are estimated. 

 Each of these quantities is determined from that position of 

 the planet on which it has most influence. For example, 

 the sum of the greatest and least distances of the planet 

 from the sun is equal to the major axis of the orbit, and 

 their difference is equal to twice the excentricity. The longi- 

 tude of the planet, when at its least distance from the sun, 

 is the same with the longitude of the perihelion j the great- 

 est latitude of the planet is equal to the inclination of the 

 orbit : the longitude of the planet, when in the plane of the 

 ecliptic in passing towards the north, is the longitude of the 

 ascending node, and the periodic time is the interval be- 

 tween two consecutive passages of the planet through the 

 same node, a small correction being made for the procession 

 of the node during the revolution of the planet (N. 135). 

 Notwithstanding the excellence of instruments and the ac- 

 curacy of modern observers, unavoidable errors of observa- 

 tion can only be compensated by finding the value of each 

 element from the mean of a thousand, or even many thou- 

 sands of observations. For as it is probable that the errors 

 are not all in one direction, but that some are in excess 

 and others in defect, they will compensate each other when 

 combined. 



However, the values of the elements determined separately 



F 2 



