Royal Society. 203 



and it contains all the tables necessary for that purpose as well as for 

 ordinarj' star-reduction, for the century to whifh it applies, founded 

 on elements derived from the comparison of Bradley's with Bessel's 

 own observations, together with the formulae for computation. It 

 is in daily use in every observatory, and has led to the general 

 adoption of a uniform and precise system of astronomical calcula- 

 tion which has been attended with signal advantage to the science. 



The services' rendered to astronomy by Bessel were not con- 

 fined to the observatory and the closet. In the course of a series 

 of experiments, undertaken in 1826, for the determination of the 

 length of the seconds' pendulum, he detected and demonstrated 

 the existence of a cause of error in the usual reduction to a va- 

 cuum, which, though it had long before been clearly pointed out by 

 Du Buat, appears to have been entirely overlooked and forgotten. 

 This consists in the fact that every oscillating body drags along 

 with it a certain portion of air, or of the fluid in which it moves, 

 so that the specific gravity of the actually moving mass is different 

 from that of the body at rest; and as the quantity of dragged air 

 depends on tlie form of the moving body, the specific gravity can- 

 not be determined a iwiori, but must be found by experiment for 

 each particular jiendulum. It followed, therefore, that the results 

 of all the previous pendulum experiments were erroneous to the ex- 

 tent occasioned by the neglect of this circumstance. Bessel's method 

 of conducting the experiment was extremely ingenious ; and it may 

 be asserted that his determination of this important astronomical 

 element — the absolute length of the seconds' pendulum — is the only 

 <me yet given which is deserving of full confidence. The details 

 and results were published in the Berlin Memoirs in 1828. 



Another very important result of the indefatigable activity of 

 Bessel, is the ' Gradniessung in Ost-Preussen,' published in 1838. 

 A series of geodetical measurements, comprehending the measure 

 of an arc of the meridian of the Dorpat Observatory, had been exe- 

 cuted by Struve and Von Tenner in Russia, and it was of great im- 

 portance, in reference to the question of the figure of the earth, to 

 connect them with those of tlie west and soutii of Europe. The 

 operations necessary for this purpose were undertaken by the Prus- 

 sian government in 1830, and executed under the direction of Bes- 

 sel, who seized on tlie opportunity of measuring an arc of the meri- 

 dian of his Observatory. In consequence of the novel methods em- 

 ployed both in the geodetical and astronomical ]iarts of this operation 

 the details are of extreme interest, more particularly with reference 

 to the ingenious a])paratus for measuring the base line, the mode of 

 observing and connecting the terrestrial angles, and the application 

 of a method of computation hy which every geometrical relation sub- 

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

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

 bable errors, deduced by the method of least scpiares. Tlie ' CJrad- 

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

 ' I'lindaiiKHita' did for astronomy ; lioth works exhibiting the apj)li- 

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



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