Internal Friction of Fluids on the Motion ol Pendu- 

 lums" 7: that was read to the < lambridge Philosophical 

 Society on December 9, 1850, had solved the hydro- 

 dynamical equations to obtain the resistance to the 

 motions of a sphere and a cylinder in a viscous 

 fluid. Peirce had studied the effect of viscous 

 resistance on the motion of his Repsold-Bessel 

 pendulum, which was symmetrical in form but not 

 cylindrical. The mainly cylindrical Form of his 

 pendulums (fig. 19) permitted Peirce to predict 

 from Stokes* theory the effect ol viscosity and to 

 compare the results with experiment. His report 

 ol November 20, 1889, in which he presented the 

 comparison of experiment. d results with the tl 

 of Stokes, was not published. 7, 



Peirce used his pendulums in 1883 to establish 

 .i station .it the Smithsonian Institution that was to 

 serve .is the base station for the Coast and Geodetic 

 Survey for some years. Pendulum Peirce no. 1 

 w.is swung .it Washington in 1881 and was then taken 

 by the party of Lieutenant Greely, U.S.A., on an 

 expedition to Lady Franklin Bay where it was swung 

 in 1882 at Fort Conger, Grinnell Land, Canada. 

 Peirce nos. 2 and 3 were swung by Peirce in 1882 

 .it Washington, D.C.; Hobokcn, New Jersey; 

 Montreal, Canada; and Albany, New York. Assist- 

 ant Preston took Peirce no. 3 on a U.S. eclipse 

 expedition to the Caroline Islands in 1883. Peirce 

 in 1885 swung pendulums nos. 2 and 3 at Ann 

 \ilioi. Michigan; Madison, Wisconsin: and Ithaca, 

 New York. Assistant Preston in 1887 swum* Peirce 

 nos. 3 and 4 at stations in the Hawaiian Islands, 

 and in 1890 he swung Peirce nos. 3 and t at stations 

 on the west coast of Africa. 79 



The new pattern of pendulum designed by Peine 

 was also adopted in France, after some years ol 

 experience with a Repsold-Bessel pendulum. Peirce 

 in 1875 had swung his Repsold-Bessel pendulum at 

 the observatory in Paris, where Borda and Cassini, 



17 Transactions oj the Cambridge Philosophical Society (1856), 

 vol. 9, part 2. p. 8. Also published in Mathematical and Physical 

 Papers (Cambridge, 1901), vol. 3, p. 1. 



7 " IVircc's comparison of theory ami experiment is discussed 

 in a report on the Peirce memoir by William Fbrrel, dated 

 Octobci 19, is 111 Martinsburg, West Virginia. U.S. Coast and 

 Geodetic Ro . Special Reports. MS, National 



Archives, Washington ). 



79 The stations at which observations were conducted with 

 the Peirce pendulums are recorded in the reports of the Super- 

 intendent of the U.S. Coast and Geodetic Survey from 1881 to 

 1890. 



and Biot, had made historic observations and where 

 Sal line also had determined gravity by comparison 

 with Rater's value at London. During the spring of 

 1880, Pence made studies ol the supports for the 



pendulums of these earlier determinations and I 



latcd corrections to those results for hydrodynamic 



effects, viscosity, and llexure. < )n June 14, 



pence addressed the Academy of Sciences, 

 on the value ol gravity at Paris, and compared Ins re- 

 sults with the corrected results ol Borda and Biot and 

 with the transferred value ol K 

 In the same \<-.\\ the I rent h < reographii Si 



Army acquired a Repsold-Bessel reversible 

 pendulum ol the smaller type, and Defforge 

 dmted experiments with it." He introduced the 

 method oi measuring flexure from the movement 

 of interference fringes during mot ion of the pendulum. 

 He found an appreciable difference between dynam- 

 ical and statical coefficients of flexure and 

 concluded that the "correction formul 

 and ( i suited perfectly to practici 



represents exactly the variation of period I 

 l.v swaying ol the support, on the condition that one 



Uses the statical Coefficient." Defforges developed a 



theory for the employment of two similar pendulums 

 of the same weight, but of different length, and hung 



by the same- knives. This theory eliminated the 



flexure of the support and the cui vature of the knives 



from the reduction of observations. 



Pendulums of 1 -meter and of '.-meter di 

 between the knife edges were constructed from 

 Defforges' design by Brunner Brothers in Paris 

 (fig. 21). These! tefforges pendulums were ev lindrical 

 in form with hemispherical ends like the Peirce 

 pendulums, and were hung Oil knives that pn 

 from the sides of the pendulum, as in some unfinished 

 dauber pendulums designed by Pence in 1 

 Paris. 



I mces (Paris, 1880), 



vol. 90, p. 14ul. Herve I vm \ report, dated June 21, 1880, is 

 in the same Comptes-rendus, p. 1463. 



c ommandani ( '.. Defforges, "Sur I'Intensite .ibsoluc de 

 la pesanteur," Journal de Physique (.1888 ), vol. 17, pp. 239, 34". 

 453. Sec also, Defforcfs, "Observations du pendule." 

 Memorial du Dep&l general de la Guerre tParis, 1894). vol. 15. 

 In the latter work, Defforges described a pendulum "reversible 

 iuv risible." which he declared to be truly invariable and 

 therefore appropriate for relative determinations. The knives 

 remained fixed to the pendulums, and the effect of interchang- 

 ing knives was obtained by interchanging weights within the 

 pendulum tube. 



PAPER 44: DEVELOPMENT OF GRAVITY PENDULUMS IN THE 1 9TH CENTURY 





