268 DETERMINATION OF AN ORBIT FROM [BOOK II. 



p 0-|-2r = 3 



?+4r=21, 



but from a fourth observation, to which is to be assigned one half the same 

 accuracy only, there results 



We will substitute in place of the last equation the following : 



-P + 3 1 + 3 r = 14 &amp;gt; 



and we will suppose this to have resulted from an observation possessing equal 

 accuracy with the former. Hence we have 



Pr=27/&amp;gt;-f 60 88 



Q= 6^+15^4-r 70 

 R= ? + 54 r _i07, 



and hence by elimination, 



19899jo = 49154 + 809 P 324 Q -\- Q Jt 



737?= 2617- 12 P+ 540 7? 

 6633 r = 12707+ 2P- 9 -f 123 /?. 



The most probable values of the unknown quantities, therefore, will be 



p = 2.470 

 q = 3.551 

 r = 1.916 



and the relative precision to be assigned to these determinations, the precision of 

 the original observations being put equal to unity, will be 



19899 



- 



=3.69 



