SECT. 3.] ANY NUMBER OF OBSERVATIONS. 273 



to small variations of the distances D, I/, as well as of the geocentric places 

 computed from them, we can assume, that the geocentric places computed from 

 the fourth system of elements, based on the distances from the earth D-\-xd. 

 D -f y &amp;lt;T, are respectively M-\- a x -f /ty, M 1 -f a x -\- (t y, M&quot; -f a&quot;x -f &amp;gt;, etc. 

 Hence, x, y, will be determined, according to the preceding discussions, in such a 

 manner (the relative accuracy of the observations being taken into account), that 

 these quantities may as far as possible agree with N, N , N&quot;, etc., respectively. 

 The corrected system of elements can be derived either from L, L and the dis 

 tances D -\- x d, D -\- x , or, according to well-known rules, from the three first 

 systems of elements by simple interpolation. 



189. 



This method differs from the preceding in this respect only, that it satisfies 

 two geocentric places exactly, and then the remaining places as nearly as possi 

 ble ; while according to the other method no one observation has the preference 

 over the rest, but the errors, as far as it can be done, are distributed among all. 

 The method of the preceding article, therefore, is only not to be preferred to the 

 former when, allowing some part of the errors to the places L, L , it is possible to 

 diminish considerably the errors in the remaining places : but yet it is generally 

 easy, by a suitable choice of the observations L, L , to provide that this difference 

 cannot become very important. It will be necessary, of course, to take care that 

 such observations are selected for L, L , as not only possess the greatest accuracy, 

 but also such that the elements derived from them and the distances are not 

 too much affected by small variations in the geocentric places. It will not. there 

 fore, be judicious to select observations distant from each other by a small inter 

 val of time, or those to which correspond nearly opposite or coincident heliocen 

 tric places. 



35 



