\ 



68 



JSowditch on the elements of the orhit of 



putation is restricted 

 To render this evide 

 calculation. 



whicli that number 



small 





iefly the principles of his 



It is founded upon the supposition that the angular distance V 



between the heliocentric places of 



of 



d 



observations is computed by two different methods^ the one 

 pending chiefly upon the observations actually made upon the 

 comet, and the other upon the mean anomalies computed by means 

 of the approximate elements 1), T, above mentioned. 



If the V al 



ue of V resulting from both these calculations is the same, we may 

 generally infer that the elements D, T, are correct ; but if they do 

 not agree, as will almost always be the case, their diiference must 

 be put equal to m. This operation is repeated a second time, 

 using the elements D + B', T, instead of D, T, respectively ; D 



being a very small quantity or part of D, as for example 



/ 



n 



oO 



by 



this means the error m in the angle V is cbanged into rf. In a 



third operation the ele 



D and T + T', T' being a small 



time, as for example, half a day, and in this operation the differ- 



1 



ence of the angle V is equal top. Supposing then the corrected 



J ^ 



elements to be D + « D', T +^ T', we easily deduce from these ex- 

 pressions the following equation 



(m 



n) . « -j- (m — ji) .t = m 



0) 



By the combination of the second and third observations, in a sim- 

 ilar manner we obtain another equation of the same form 



( 



') • w + C 



V) 



m 



p', being the values of m, ??, p, correspond 



C^) 



case 



From these two equations the values of u and t may be found 



and thence the corrected elements D + uD , T + * 1 



If 



18 obtained are very small, and the observations are ac- 

 result wiU in general be nearly correct. 



otherwise . the 



peraiion must he repeated 



V 



