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Art. XV. ASTRONOMICAL AND NAUTICAL 

 COLLECTIONS, No. I. 



[The astronomical ephemerides of foreign countries have commonly contain- 

 ed, in addition to the tables for the year, a variety of novelties relating 

 to the mathematical sciences, which are often of great interest to the 

 practical astronomer, and sometimes of great utUity to the seaman 

 The limited bulk of the Nautical Almanac, and the arrangement of the 

 department by which it has been conducted, have not admitted a 

 similar extension of the plan of that highly valuable publication; and 

 there seems to be a particular opening, considering the zeal with which 

 astronomy is now pursued in tliis country, for some periodical com- 

 munication of a similar nature, through a more private channel. Upon 

 these grounds the editor of this work has made an arrangement by 

 which a certain porUon of its pages will in future be regularly devoted 

 to astronomical and nautical subjects, not excluding the more refined 

 investigations, but more peculiarly seeking such as are capable of being 

 immediately applied to practical astronomy, or to nautical calcula- 

 tions." He hopes in future to be favoured with some /articles from 

 the highest possible nautical authorities ; and the first of the series 

 is a translation of a memoir of one of the most justly celebrated astro- 

 nomers and philosophers of the present day, with some supplementary 

 demonstrations, which have been added by the translator.] 



i. An Essay on the easiest and most convenient Method of calculat- 

 ing the Orbit of a Comet from Observations. By William 

 Olbers, M.D. 8vo. Weimar, 1797. Translated from the Ger- 

 man. With Notes. 



Section I. General Observations. 

 ^ ^■ 

 To determine the orbit of a comet by means of geocentric 

 observations was considered, even by the great New°ton him- 

 self, as far from an easy problem; he calls it, indeed, fon^e 

 difficillimum ; and he had attempted its solution in various 

 ways, before he discovered the elegant construction which he 

 has laid down in his Principia. This construction is, indeed 

 worthy of the gctiius of its inventor ; it is, however, laborious' 

 and requires a number of conjectural trials. Since the time of 

 Newton, many of the greatest mathematicians have employed 

 themselves in the investigation ; and having satisfied themselves 

 of the impossibility of an accurate direct solution, have subsfi- 



