ORBIT ELEMENTS COMET I., 1899, (SWIFT). 



191 



Equations for Co-ordinates 



x = [9-9877050] r sin (v + 77 30 48-56) 



y = [9-9962456] r sin (v + 165 41 13-03) 



z = [9-4292320] r sin (v + 47 25 44-35) 



RESIDUALS— Elements III. 



RESIDUALS— Elements IV. 



Equations. 



Elements. 



1 



- 79 



- 7-8 



2 



+ 9-9 



+ 9-8 



8 



+ 120 



+ 12 



4 



+ 17-9 



+ 17-8 



5 



- 140 



- 142 



6 



+ 5-2 



+ 5-2 



7 



+ 22-4 



+ 22-5 



8 



+ 25-0 



+ 251 



9 



+ 23 3 



+ 23-3 



10 



- 9-4 



- 95 



11 



- 10-7 



- 10-7 



12 



+ 24-6 



+ 24-5 



13 



+ 26-1 



+ 26-0 



14 



- 7-4 



- 73 



15 



- 6-6 



- 65 



16 



+ 53 



+ 5-4 



Equations. 



Elements. 



1 



- 1-4 



- 1-4 



2 



+ 1-2 



+ 1-3 



3 



+ 1-3 



+ 1-3 



4 



- 2-5 



-2-7 



5 



+ 1-5 



+ 1-4 



6 



+ 01 



+ 0-2 



7 



+ 0-2 



+ 0-4 



8 



+ 0-9 



+ 1-0 



9 



- 0-4 



- 0-4 



10 



+ 0-3 



+ 0-2 



11 



+ 1-0 



+ 1-0 



12 



- 0-2 



- 03 



13 



+ 2-7 



+ 2-8 



14 



- 0-9 



- 0-8 



15 



- 2-9 



- 2-8 



16 



+ 8-7 



I + 8-9 



[vvl = 10 4 x 0-41332 

 "" = 4133-2 



[w] = 108-12 



The agreement between the residuals, computed from the equa- 

 tions of condition and those found from the corrected elements, is 

 satisfactory in each case. The residual of the final equation, 

 Elements IV., is somewhat large in comparison with the others 

 but unaccountable, the number of observations employed in find- 

 ing this normal is small, but the measures are consistent, and to 

 reject this normal would be unjustifiable. 



The agreement of the residuals would seem to indicate, that the 

 higher order of differentials, neglected in the calculation of the 

 coefficients, will have little or no effect on the result. If the 

 residuals found from the Elements IV. are again introduced into 

 the equations of condition, the corrections obtained are small and 

 will not alter the residuals to the extent desired. 



Before concluding the calculation the residuals from 

 Elements IV. were assumed to be in the form 



& = v + /(efe) a 2 



the 



