647 



of a method of computation by which ever}' geometrical relation sub- 

 sisting among the angles over the whole triangulated surface is ex- 

 pressed by equations of condition, and the results, with their pro- 

 bable errors, deduced by the method of least squares. The ' Grad- 

 messung' may be described as having done for geodesy what the 

 * Fundamenta' did for astronomy ; both works exhibiting the appli- 

 cation of the best and surest methods of deducing results from ob- 

 servations which science has yet placed within the reach of the 

 computer. 



Several of his minor papers on the subject of geodesy, published 

 in the " Astronomische Nachrichten,' are of great interest and value. 

 He recomputed the French triangulation between Montjouy and 

 Formentera (No. 438), and the sector observations of the English 

 and Indian arcs measured by Mudge and Lambton (334, 336) ; and 

 from the whole of the meridional arcs hitherto measured with ad- 

 missible precision, deduced elements of the terrestrial spheroid which 

 give probably the nearest approximation which has yet been made 

 to the true form and magnitude of the earth. 



In connexion with the measurement of the pendulum and arc of 

 meridian, he also undertook a comparison of the standard measures 

 of Prussia; determined their relation to the unit of the French 

 measures ; and directed the execution of a new standard which will 

 probably become an object of great interest in some future age. 

 The details of these delicate and difficult comparisons are described 

 by him in an interesting work published by order of the Prussian 

 government in 1839. 



The question of the annual parallax of the fixed stars. — a vexed 

 question in astronomy since the days of Bradley, — has of late years 

 acquired an extraordinary interest through the labours of Struve, 

 Henderson, and Bessel. Having previously made some unsuccess- 

 ful attempts, Bessel at length determined to attack the problem in a 

 new way, and to subject one individual star to a scrutiny v/hich 

 would infallibly decide whether any appreciable parallax existed in 

 that particular case. The star which he selected was 61 Cygni, a binary 

 system whose two members had been proved to be physically con- 

 nected, and which, by reason of the very considerable distance be- 

 tween the component bodies, and its large proper motion, afforded 

 strong presumptions of its being one of the nearest to the earth. With 

 the splendid heliometer of the Konigsberg Observatory, an instru- 

 ment peculiarly adapted for such a purpose, he commenced a series 

 of microraetrical measurements of the distances of the star from two 

 others in its vicinity, which were continued from August 1837 to 

 March 1840, and conducted with all the appliances and precautions 

 for attaining extreme accuracy which were to be expected from the 

 importance of the inquiry and the consummate skill of the observer. 

 The results exhibited a periodic and systematic fluctuation of the 

 places of the double star, agreeing exactly in its law and period with 

 the effects of parallax, and referable to no other knqwn cause. The 

 parallax thus indicated was indeed an extremely minute quantity, 

 amounting only to 31-lOOths of a second; but no one in a condition 



