Figure 9. — Friedrich Wilhelm Bessel (1784- 1846), 

 German mathematician and astronomer. He be- 

 came the first superintendent of the Prussian ob- 

 servatory established at Konigsberg in 1810, and 

 remained there during the remainder of his life. 

 So important were his many contributions to precise 

 measurement and calculation in astronomy that he 

 is often considered the founder of the "modern" age 

 in that science. This characteristic also shows in 

 his venture into geodesy, 1 826-1 830, one product 

 of which was the pendulum experiment reported in 

 this article. 



The latter effect had been discovered by Du Buat in 

 1786, 23 but his work was unknown to Bessel. The 

 length of the seconds pendulum at Konigsberg, 

 reduced to sea level, was found by Bessel to be 

 440.8179 lines. In 1835, Bessel determined the 

 intensity of gravity at a site in Berlin where observa- 

 tions later were conducted in the Imperial Office of 

 Weights and Measures by Charles S. Peirce of the 

 U.S. Coast Survey. 



Katcr's Convertible and Invariable 

 Pendulums 



The systematic survey of the gravity field of the 

 earth was given a great impetus by the contributions 

 of Capt. Henry Kater, F.R.S. In 1817, he designed, 

 constructed, and applied a convertible compound 

 pendulum for the absolute determination of gravity 

 at the house of Henry Browne, F.R.S., in Portland 

 Place, London. 24 Katers convertible pendulum (fig. 

 11) consisted of a brass rod to which were attached a 

 flat circular bob of brass and two adjustable weights, 

 the smaller of which was adjusted by a screw. The 

 convertibility of the pendulum was constituted by the 

 provision of two knife edges turned inwards on 

 opposite sides of the center of gravity. The pendulum 

 was swung on each knife edge, and the adjustable 

 weights were moved until the times of swing were the 

 same about each knife edge. When the times were 

 judged to be the same, the distance between the 

 knife edges was inferred to be the length of the 

 equivalent simple pendulum, in accordance with 

 Huygens' theorem on conjugate points of a compound 

 pendulum. Kater determined the time of swing by 

 the method of coincidences (fig. 12). He corrected 

 for the buoyancy of the air. The final value of the 

 length of the seconds pendulum at Browne's house in 

 London, reduced to sea level, was determined to be 

 39.13929 inches. 



The convertible compound pendulum had been 

 conceived prior to its realization by Kater. In 1792, 

 on the occasion of the proposal in Paris to establish 

 the standard of length as the length of the seconds 

 pendulum, Baron de Prony had proposed the employ- 

 ment of a compound pendulum with three axes of 

 oscillation. 25 In 1800, he proposed the convertible 

 compound pendulum with knife edges about which 

 the pendulum could complete swings in equal times. 

 De Prony's proposals were not accepted and his 

 papers remained unpublished until 1889, at which 

 time they were discovered by Defforges. The French 

 decision was to experiment with the ball pendulum, 

 and the determination of the length of the seconds 



23 L. G. du Buat, Principes d'hydr antique (Paris, 1786). See 

 excerpts in Collection de memoires, pp. B-64 to B-67. 



24 Capt. Henry Kater, "An Account of Experiments for 

 Determining the Length of the Pendulum Vibrating Seconds 

 in the Latitude of London," Philosophical Transactions of the 

 Royal Society of London (1818), vol. 108, p. 33. [Hereinafter 

 abbreviated Phil. Trans.] 



25 M. G. de Prony, "Methode pour determiner la longeur 

 du pendule. simple qui bat les secondes," Collection de vi< 



vol. 4, pp. 65-76. 



314 



BULLETIN 240: CONTRIBUTIONS FROM THE MUSEUM OF HISTORY AND TECHNOLOGY 



