84 RELATIONS PERTAINING SIMPLY [BOOK I. 



of the earth as rectilinear and its velocity as uniform : so also A, a, a will lie in a 

 straight line, and the parts Aa, aa will likewise be proportional to the intervals 

 f T, t t. Hence it is readily inferred, that the right lines AP, I d are paral 

 lel, and therefore that the first and third places are identical. 



The time t T, within which the light traverses the mean distance of the 

 earth from the sun which we take for unity, will be the product of the distance 

 Pa into 493&quot;. In this calculation it will be proper to take, instead of the dis 

 tance Pa, either PA or pa, since the difference can be of no importance. 



From these principles follow three methods of determining the apparent place 

 of a planet or comet for any time t, of which sometimes one and sometimes 

 another may be preferred. 



I. The time in which the light is passing from the planet to the earth may be 

 subtracted from the given time ; thus we shall have the reduced time T, for which 

 the true place, computed in the usual way, will be identical with the apparent 

 place for t. For computing the reduction of the time t T, it is requisite to 

 know the distance from the earth ; generally, convenient helps will not be want 

 ing for this purpose, as, for example, an ephemeris hastily calculated, otherwise it 

 will be sufficient to determine, by a preliminary calculation, the true distance for 

 the time t in the usual manner, avoiding an unnecessary degree of precision. 



II. The true place and distance may be computed for the instant t, and, 

 from this, the reduction of the time t--T, and hence, with the help of the daily 

 motion (in longitude and latitude, or in right ascension and declination), the re 

 duction of the true place to the time T. 



III. The heliocentric place of the earth may be computed for the time t; and 

 the heliocentric place of the planet for the time T : then, from the combination 

 of these in the usual way, the geocentric place of the planet, which, increased 

 by the aberration of the fixed stars (to be obtained by a well-known method, or 

 to be taken from the tables), will furnish the apparent place sought. 



The second method, which is commonly used, is preferable to the others, 

 because there is no need of a double calculation for determining the distance, 

 but it labors under this inconvenience, that it cannot be used except several 

 places near each other are calculated, or are known from observation ; otherwise 

 it would not be admissible to consider the diurnal motion as given. 



