J 94 



The coefficients of the unknown quantities in these equations would 

 be correct, if we had the elements correct ; but, as the elements are 

 only approximate, so these coefficients are only approximate, and their 

 degrees of accuracy depend on the influence of the errors of the 

 elements on these coefficients. 



Thus, if in computing dx, SCT should be nearly a right angle, the 

 corresponding error of d^ would be great, compared to what it would 

 be, if SCT were nearly 45° — In the former case, therefore, the 

 elements would require to be much more correct than in the latter — 

 If SCT should be so near a right angle, that it was uncertain whether 

 it were actually greater or less tlian a right angle, that observation 

 could not be used for the correction of the elements ; and so in similar 

 cases. The magnitude of the angles SCT, CST, and TSP, will 

 therefore point out the fitness of the observations used, and the degree 

 of exactness required in the approximate elements. 



When Elliptic Elements are required, equations (^a) and (h) are 

 to be adapted to an elliptic orbit. Then another unknown quantity 

 viz., dm, m being = axis major, 



will be introduced ; and so four observations at least must be used, 

 as there will be three equations witii three unknown quantities. 



