284- Prof. Encke on Olbers's Method of 



quantity, while by Olbers this quantity is not used analyti- 

 cally, but only according to its approximate value at the first 

 amendment of the result. Whether in this case the method 

 of Olbers is more convenient for calculation I do not dare to 

 decide, as, in order to give an opinion on a matter of mere 

 practical convenience, one ought to have had an equal experi- 

 ence in the use of both of them, and Olbers's method has been 

 almost exclusively used by me. But that in all other cases, 

 which in general are so predominant, the calculation by this 

 latter method is, without comparison, more easy and more 

 quick in leading to the result, appears, in the opinion of all 

 astronomers who know both methods, to be subject to no 

 doubt. 



The course which M. de Pontecoulant takes in his own me- 

 thod is essentially this : 



By the series above given, x, t/, *, x", y", #", may be ex- 

 pressed as functions of #', y\ *', —j— , -~, —,— , r 1 , its dif- 

 ferential quotients and the intervals of time. The same may 

 be done with the heliocentric coordinates of the earth (let them 

 be designated by X, Y, &c.) with regard to the coordinates of 

 the middle place of the sun. If now from these expressions 

 the nine equations for the geocentric coordinates are formed, 

 three more unknown quantities, p, p', p", are introduced. The 

 author then eliminates from these nine equations the five un- 

 known quantities, p, p", #', y\ %', and besides a quantity of the 

 third order, which is indeed known, but very small, the quan- 

 tity (0.1.2) in Gauss's Theoria Motus, lib. i. sect. 4, which, on 

 account of the errors of observation, might too much affect the 



accuracy of the result, and then expresses —.— , -.- , -f-, 

 as functions of/. His values have this form : 

 dx f dX' _ 



-dT = lit+ Y t' 



dy> _ dY' 



dt dt 



dt 



It is, however, essential to remark, that F, G, H are quite 

 known. The quantity r' with its differentials has likewise dis- 

 appeared by the other eliminations. He substitutes these va- 

 lues in the equation for the parabola : 



