1*" 



JBowditch on lli8 elements of the orhlt of a comctr^ 71 



ibt»tJiird. V into ¥ -hiO laihc four tli, N intsN — i;0'intlie//^/t; 

 aud I into I -f 10 in the sixth. Then rcpiTsenting' the longitudfl 

 (»r latitude') ctim-;)ute(l in these successive operations by E', L",L"', 

 L'% L% L''', respectively, and the conespoiuling observation by L; 

 also the true elements of the orbit by D + . 004. (f ; T + .05, t, 



P + IO. 2», N-^l0.7i, l-^iOfTy each observed longitude 

 and latitude will furnish an equation of this fdrniy 



0=(1 — t')+(l«'~L">.r/4 (L'— L"')./+(L'-"L'0.p+CT/— L' ).w+(L'— I. ).i (3) 



so that n observations vvouhl furnish 2w equations, each of which 

 would be wholly independent of the others, and from this circum- 

 stance we are better able to judge of the probable degree of accu- 

 racy in each of them, and the propriety of retaining and using any 

 one of the in in the subsequent calculati(>n«,^wljich is a tery great 

 advautasie in this method. It has however the inconvenience of 





requiring more labour when the number of observations is small, 

 than the method of l<ii Place does,, because it takes more time 

 or labour to compute an equation of the form (3) IbaO of the fortii' 

 (1). But as the number of observations iucreases, this difference, 

 decreases, and by still increasing the num!>er the method (3) final- 

 ly becomes the most simple. Suppose for example that the labour 



of computing one equation of the form (3; was greater than that of 

 the form (i) in the ratio of /to 1 ; the labour of computing all the 



w. ~Y~ equations of the fonn ((} would be to that of the 3 n equa- 



tions of the form (3) as «. ^ to 2 n ?, or as jz ^ 1 : 4 /. The 

 value of I varies with the number of observations. When that 

 number is small it does not exceed 1 or ^, and never exceeds 

 so that when n = I7, or even much less, the labour of comput- 

 ing the equations^ (3) will not exceed that of the equations (1), and 

 when n exceeds that quantity, it will be the least laborious to com- 

 pute the equation* (3) j and these last mentioned equations will have 



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