DETEEMINATION OF ELLIPTIC ORBITS. 



141 



a s =- -07232 

 6 8 =- -00845 

 c 3 =- -04050 



IV. 



The values of a', /3', etc., furnish the basis for the computation of 

 the following quantities : 



<*!= - -01254 a 2 = - -03517 

 6 1= + -01726 6 2 =- -00525 

 c 1= =- -15746 c 2 =- -08526 



For G we get three values sensibly identical. Adopting the mean, 



we set 



G = -01006. 



We also get H= - -00998, L = -02322.* 



V. 



Taking the values of a lt a 2 , etc., from the columns under IIIj, III 2 , 

 III 3 , we form the residuals 



a =--06058, 0=-, -16692, y= -'05557. 

 From these, with the numbers last computed, we get 



<?! = - -65888, <7 2 = - -76983, C 3 = - -79939, 



which might be used as corrections for our values of ft, g 2 , q s . To 

 get more accurate values for these corrections we set 



Ag 2 = a 2 - T VX(A^ 2 ) 2 , or Ag 2 = - -76983 --01393(Ag 2 ) 2 , 

 which gives Ag 2 = '77826. 



The quadratic term diminishes the value of A<? 2 by '00843. Sub- 

 tracting the same quantity from C^ and G 2 we get 



h = - -66731, Ag 3 = - -80780. 



* It would have been better to omit altogether the calculation of H and L, if the 

 small value of the latter could have been foreseen. In fact, it will be found that 

 the terms containing L hardly improve the convergence, being smaller than quantities 

 which have been neglected. Nevertheless, the use of these terms in this example will 

 illustrate a process which in other cases may be beneficial. 



