i 



\ 



/ 



BowJUch on the elements of the orbit of a comet. 



6a 



rt\ 



prod 



second and third ob= 

 uilar to the two just 



ould 



lluucd. and 



I 



there mi^lit he cases where it would be advaninseous to use this 

 last one rather than the others, as for example, when the first ob- 

 servation was not made under so favourable circumstances, or was 

 not so accurate, as the second and third ; in which case it would 

 be better to use the first and third etjuations, rather than the first 

 and second. In this way with n observations we niiirht obtain 



n. 



n 



t 



2 



h 



equations, by the combination of the observations two 



two : all these equations are not however equally proper for the 

 calculation of the values of u, t. For, when the interval between 

 the two observations is small, the errors, to Avhich they are liable, 

 night have a very sensible effect on the equation deduced from 



them. 



Such equations being rejected, the rest may be combined 

 together in the manner pointed out by La Place in Pag. 230, Tol. 

 4, of his *^ Mecanique Celeste/' so as to obtain a more accurate 



i 



result than when two equations only are used. 



This method is simple and elegant, with a small number of ob- 

 servations ; but when the number is large, there is an objection 

 to this and to other similar methods, (like that of Newton, before 

 mentioned,) arising from the great number of the equations, and 

 the difficulty of selecting the most accurate, and those best adapt- 

 ed to the purpose of the calculation ; because the errors of the two 



observations are so combined with each other, that it is difficult to 

 appreciate the degree of accuracy of the resulting equation. Thus 

 if the first observation was suspected not to be perfectly good, but 

 ihe second and third were known to be accurate, the first and sec- 

 ond equations would partake of the error of the first observation : 

 but to how great a degree would not be very evident. This diffi- 

 culty seems to balance in some degree ihe simplicity produced by 



' 10 



V 



