Prof. Encke on the Orbits of Double Stars. 



41 



join both systems, with their mean errors, of which the last is 

 founded on 32"'23, Messier's above-mentioned mean error of 

 right ascension observed in the equator. 



Finally, I developed the changes of the ephemeris for the 

 elements obtained from all the observations, and thence de- 

 duced the following errors of the rectified ephemeris from the 

 observations employed. 



\^Here the author gives a coinparison of the calailated places 

 of the comet, according to the elements given p. 40, with the ob- 

 servatio7is bj/,!. Messier ; 2. Maraldi; S.Cassini; A;. Bradley; 

 5. Hell; 6. Various observers, ^r.] 



All the calculations, except the sums {a a), (ae), &c. have 

 been made twice, and I have taken every possible care to be 

 certain of the results given in this essay. 1 hope soon to pub- 

 lish a similar investigation of the observations in 1682, of the 

 comet of Halley. O. A. Rosenbergf.r. 



VI. On the Calcidation of the Orbits of Double Stars. By 

 Professor Encke. 



[Continued from vol. x. page 284.] 



TF we denote the rectangular coordinates of the centre of 

 ■*- the projection-ellipsis with respect to the star at rest by X 

 and Y, and the angle which its semi-axis major forms with 

 the axis of the ^ by co, we have 



0, — X= a cos Ej cos w — Z> sin E, sin w 

 ^2 — X = « cos E2 cos ui — b sin Eg sin w 



03 — X= fl cos Eg cos o) — 6 sin E3 sin w 



04 — X= « cos E4 cos 0) — 6 sin E4 sin w 

 »j, — Y = a cos El sin o) + 6 sin E, sin w 

 >].2 — Y = a cos Eg sin CO + i sin E^ sin » 

 )j3 — Y = « cos E3 sin a; + i sin E3 sin « 

 >j4 — Y =- a cos E4 sin w + Z> sin E4 sin w 



By the above notation, we have 



E, =s — y — /3 + a 

 E2 = 5 — y + /3-« 



K3 = « + r — /3 - « 



E4 = s + y + |3 + « 

 MS. Vol. 11. No. 61. Jan. 1832. G siu 



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