i'\ employing a long interval of obsert ition !i The 



whole apparatus was enclosed in a box, in order to 

 i\( hide disturbances from currents of air. Corrections 

 were made for buoyancy, lor amplitude of swiny and 

 for variations in length of the wire with temperature. 

 The final result was that the length ol the seconds 

 pendulum .it the observatory in Paris was determined 

 to be 440.5593 Paris lines, or 993.53 nun., reduced 

 to sea level 993.85 mm. Some years later the met lu ids 

 of Boni.i wen- used l,v other French investigators, 

 among whom was Biot who used the platinum ball of 

 Borda suspended by a copper wire 60 cm. long. 



Another historic "simple" pendulum w .is the one 

 swung !>\ Bessel (fig. 7) for the determination of 

 gravity at Ki migsbei ; 1 ["he pendulum 



!1 !•'. W. Bessel, "Untersuchungen Qber die Lar 

 einfachen Secundenpendels," Abhandlungm da Kbniglicht Akade- 

 Wissmschafttn at Berlin, 1828). 



i onsistei I of a »] ipei . or ivorj thai was 



ded by a fine wire, the upper end of which 

 was wrapped and unwrapped on a horizontal 

 cylinder as support The pendulum was swung 

 first from one point and then hum another, exact!) 

 a "toise de Peru" -'-' higher up, the bob being at 

 the same level in each case (fit;. 7). Bessel found the 

 period of vibration ol the pendulum by the method 

 of coincidences; and in order to avoid disturl 

 from the comparison clock, it was placed at Borne 

 distance from the pendulum under observation. 



Bessel's experiments wen- significant in view ol the 

 rare with which lie determined the Corrections H( 

 corrected for the stiffness of the wire and for the lack 

 of ngiditv of connection between the bob md wire. 

 The necessity lor the latter correction had 

 pointed out by Laplace, who showed that through 

 the circumstance that the pull of the wire is now on 

 one side and now on the other side of the center ol 

 gravity, the bob acquires angular momentum 

 its center of gravity, which cannot be accounted for 

 if the line of the wire, and therefore the force tl 

 exerts, always passed through the center. In addi- 

 tion to a correction for buoyancy of the air considered 

 In his predecessors. Bessel also took account of the 

 inertia of the air set in motion by the pendulum. 



i nulaiil of length a toise which had been 

 made by Fortin in Paris and had been compared with the 

 original of the "ti lise i le Pet u" I ij \i 



Figure 8. Mom Ol SUSPENSION of Bessel's pendulum is 



here, ["he iron wire is supported by the thumb- 

 and clamp ai the left, but passes over a pin .n the 

 center, which is actual!) the upper terminal of the pen- 

 dulum B ind this "cylinder of unrolling" superior 

 to the clamps ami knife edges of earlier pendulums 

 counterweight at the right is pan ol a system foi supporting 

 .le in such a way that it is not elongated by us nun 

 weight. 



With this apparatus. Bessel determined the ratio of 



ngths of the two pendulums and their times of vibra- 

 tion. From diis the length of the seconds pendulum n.n 



Ited. His method eliminated the need to lake into 



inaccuracy as flexure ol the pen- 

 dulum wire .md imperfections in the shape of the bob. 

 ion of plate -. \ I nnoires publics par la Socictc Jran- 

 caise dt ol. 4.) 



PAPER 44: DEVELOPMENT OF GRAVITY PENDULUMS IN nil l'TH CENTURY 



313 



