SECT. 2.] TO POSITION IN SPACE. 85 



The disadvantage with which the first and third methods are incumbered, is 

 evidently removed when several places near each other are to be computed. 

 For, as soon as the distances are known for some, the distances next following 

 may be deduced very conveniently and with sufficient accuracy by means of 

 familiar methods. If the distance is known, the first method will be generally 

 preferable to the third, because it does not require the aberration of the fixed 

 stars ; but if the double calculation is to be resorted to, the third is recommended 

 by this, that the place of the earth, at least, is retained in the second calculation. 



What is wanted for the inverse problem, that is, when the true is to be derived 

 from the apparent place, readily suggests itself. According to method I., you will 

 retain the place itself unchanged, but will convert the tune t, to which the given 

 place corresponds as the apparent place, into the reduced time T, to which the 

 same will correspond as the true place. According to method II, you will retain 

 the time t, but you will add to the given place the motion in the time t T, as 

 you would wish to reduce it to the time t-\- (t T}. According to the method 

 III., you will regard the given place, free from the aberration of the fixed stars, 

 as the true place for the time T, but the true place of the earth, answering to 

 the time t, is to be retained as if it also belonged to T. The utility of the third 

 method will more clearly appear in the second book. 



Finally, that nothing may be wanting, we observe that the place of the sun is 

 affected in the same manner by aberration, as the place of a planet : but since 

 both the distance from the earth and the diurnal motion are nearly constant, the 

 aberration itself has an almost constant value equal to the mean motion of 

 the sun in 493 s , and so 20&quot;.25; which quantity is to be subtracted from the 

 true to obtain the mean longitude. The exact value of the aberration is in the 

 compound ratio of the distance and the diurnal motion, or what amounts to the 

 same thing, in the inverse ratio of the distance ; whence, the mean value must be 

 diminished in apogee by 0&quot;.34, and increased by the same amount in perigee. 

 Our solar tables already include the constant aberration 20&quot;.25 ; on which 

 account, it wih 1 be necessary to add 20&quot;.25 to the tabular longitude to obtain the 

 true. 



