58 ASTRONOMICAL TABLES. SECT. VIII. 



hours, at the rate of 15 in an hour, time becomes a 

 measure of angular motion and the principal element in 

 astronomy, where the object is to determine the exact 

 state of the heavens, and the successive changes it under- 

 goes in all ages, past, present, and to come. Now the 

 longitude, latitude, and distance of a planet from the 

 sun, are given in terms of the time, by general analytical 

 formulae. These formulae will consequently give the 

 exact place of the body in the heavens, for any time as- 

 sumed at pleasure, provided they can be reduced to 

 numbers. But before the calculator begins his task, the 

 observer must furnish the necessaiy data, which are, 

 obviously, the forms of the orbits, and their positions 

 with regard Jo the plane of the ecliptic (N. 57). It is 

 therefore necessary to determine by observation for each 

 planet, the length of the major axis of its orbit, the ec- 

 centricity, 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 great- 

 est 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 eccentricity. The longitude of the 

 planet, when at its least distance from the sun, is the 

 same with the longitude of the perihelion ; the greatest 

 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 toward the north, is the longitude 

 of the ascending node, and the periodic time is the in- 

 terval between two consecutive passages of the planet 

 through the same node, a small correction being made 

 for the precession of the node, during the revolution of 

 the planet (N. 135). Notwithstanding the excellence of 

 instruments and the accuracy of modern observers, una- 

 voidable errors of observation can only be compensated 

 by finding the value of each element from the mean of 

 a thousand, or even many thousands of observations. 

 For as it is probable that the errors are not all in one 



