Astronomical andNatitical Collections. 177 



published in the Connaissance des Terns for 1812, have been 

 rendered, by some omission in the calculation, completely er- 

 roneous throughout. The volume for 1823 Appears to be in- 

 comparably more accurate than those of the preceding years, 

 and the editors appear to have profited very laudably by the 

 example of- diligence, which has been set them in this country. 



iv. An Essay on the easiest and most convenient Method of 

 calculating the Orbit of a Comet from Observations. By 

 William Olbers, M. D. 8vo. Weimar, 1797. 



Section II. 



On some Equations of the First and Second Order, ivhich have 



been proposed for determining the Equations of Comets. 



[Continued from Vol. X. p. 426] 

 ^ 35. 

 Upon this supposition, it will be easy to determine, what 

 would have been the apparent place of the comet at the time 

 of the middle observation, if the earth had been in d, and the 

 comet in D. For first, all the appaient places in ADC, viewed 

 from adc, lie in a great circle of the sphere : and, secondly, 

 the points b b SDB are all in one plane, so that all the points 

 of the line BS, seen from any part of b S, are in the same great 

 circle. We have therefore only to determine the place of these 

 two circles on the sphere, in order to find the position of the 

 line d D. The first great circle will pass through the first and 

 third places of the comet; the second through the middle place 



and that of the sun. Hence, if we make -: rr. -, ; — 



sm (a — a ) tang ^ — 



cot {a!" — a,') = cot 7r, the longitude of the point of 



intersection of the former circle with the ecliptic will 



be a" — it; and the angle of intersection will be », to 



l>e found by the equation tang » = — r-2 — The longitude 



of the point of intersection of the other circle with the ecliptic 

 must obviously be A", or that of the sun at the time of the mid- 

 dle observation, and its inclination S will be determined by the 

 Vol. XI. N 



