TRANSLATOR S PREFACE. 



Ix 1852, a pamphlet, entitled The Computation of an Orbit from Three Complete 

 Observations, was published, under the authority of the Navy Department, for the use 

 of the American Ephemeris and Nautical Almanac, the object of which was to excerpt 

 from various parts of GAUSS S Theoria Motus, and to arrange in proper order the numer 

 ous details which combine to form this complicated problem. To these were added an 

 Appendix containing the results of Professor EXCKE S investigations, Ueber den Avsnah- 

 mefall einer doppelten Bahnbestimmung aus denselben drei geocentrischen Oertern (Ab- 

 handlungen de.r Akademie der Wisse.nschaften zu Berlin, 1848), and also Professor PEIRCE S 

 Graphic Delineations of the Curves showing geometrically the roots of GAUSS S Equa 

 tion IV. Article 141. 



After this pamphlet was completed, the opinion was expressed by scientific friends 

 that a complete translation of the Theoria Motus should be undertaken, not only to meet 

 the wants of the American Ephemeris, but those also of Astronomers generally, to whom 

 this work (now become very rare and costly) is a standard and permanent authority. 

 This undertaking has been particularly encouraged by the Smithsonian Institution, 

 which has signified its high estimate of the importance of the work, by contributing to 

 its publication. And by the authority of Hon. J. C. DOBBIN, Secretary of the Navy, this 

 Translation is printed by the joint contributions of the Nautical Almanac and the Smith 

 sonian Institution. 



The notation of GAUSS has been strictly adhered to throughout, and the translation 

 has been made as nearly literal as possible. No pains have been spared to secure typo 

 graphical accuracy. All the errata that have been noticed in ZACH S Monatliche Corre- 



spondenz, the Berliner Astronomisches Jahrbuch, and the Astronomische Nachrichten, have 



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