Tables 84-85. 

 LENGTH OF THE SECONDS PENDULUM. 



TABLE 84. — LengUi of Seconds Pendulum at Sea Level for Different Latitudes.* 



107 



* Calculated from force of gravity table by the formula I ^ g /t'. 

 centimeters, or 0.000235 inches, or .ooooig6 feet. 



For each 100 feet of elevation subtract 0.000596 



TABLE 85. — Leng:tli of the Seconds Pendulum.* 



Date of 

 determi- 

 nation. 



1799 

 1816 

 182I 



1825 

 1S27 

 1829 

 1S30 



1S33 

 1869 

 1876 

 1884 



Number 

 of obser- 

 vation 

 stations. 



IS 

 ^8 



25 

 41 



5 

 49 



51 



73 



123 



Range of latitude included by 

 the stations. 



From +67^05' to —33° 56' 



+74° 53' 

 +38^40' 

 +79° 50' 

 +79° 50' 

 0° o' 



+79^51' 



+79° 50' 

 +79° 50' 

 +79° 50' 



51 21' 



—60° 4 5' 

 -12° 59' 



-5i°35' 

 +67^04' 



-5;!° 35' 



-5i°35' 

 — 62=56' 

 -62° 56' 



Combining the above results 



Length of pendulum in meters, 

 for latitude i>. 



0.99063 1 + . 



0-9907 43+- 

 0.990880+ . 

 O.990977+. 

 O.991026-I-. 



0.990555+- 

 0.99IOI74-. 

 0.990941-}-. 

 0.990970-i- , 

 0.9910114-. 

 0.9909 1 8-f-. 



005637s 

 005466s 

 005340s 

 005142s 

 005072s 

 005679s 

 005087 s 

 005142s 

 005185s 

 005105s 

 005262 s 



n> 



n2(|, 

 n2<^ 

 n2,|) 

 n'^ 

 n2<^ 



n^</> 



o.9909io-|-.oo5290sin^<^ 



Correspond- 

 ing length 

 of pendulum 

 for lat. 45° 



0-993450 

 0.993976 



0.993550 

 0.993548 

 0.993562 



0-993395 

 0.993560 

 0.993512 



0-993S54t 



0-993563 

 0-993549 



0.993555 



Refer- 

 ence. 



3 

 4 



5 

 6 



7 

 8 



9 

 10 

 II 



1 Laplace : " Traite de Mecanique Celeste," T. 2, livre 3, chap. 5, sect. 42. 



2 Mathieu : " Sur les experiences du pendule;" in " Connaissance des Temps 1816." 

 Additions, pp. 314-341, p. 332. 



3 Biot et Arago: " Recueil d'Observations geodesiques, etc." Paris, 1821, p. 575. 



4 Sabine : " An Account of Experiments to determine the Figure of the Earth, etc., by 

 Sir Edward Sabine." London, 1S25, p. 352. 



5 Saigey : "Comparaison des Observations du pendule a diverses latitudes; faites par 

 MM. Biot, Kater, Sabine, de Freycinet, et Duperry;" in "Bulletin des Sciences Mathe- 

 matiques, etc.," T. i, pp. 31-43, and 171-184. Paris, 1827. 



6 Pontecoulant : " Theorie analytique du Systeme du monde," Paris, 1829, T. 2, p. 466. 



7 Airy : " Figure of the Earth ; " in " Encyc. Met." 2d Div. vol. 3, p. 230. 



8 Poisson : "Traite de Mecanique," T. i, p. 377; "Connaissance des Temps," 1834, 

 pp. 32-33; and Puissant: "Traite de geodesic," T. 2, p. 464. 



9 Unferdinger : " Das Pendel als geodatisches Instrument j " in Grunert's "Archiv," 1869, 

 p. 316. 



10 Fischer: " Die Gestalt der Erde und die Pendelmessungen ;" in " Ast. Nach." 1876, 

 col. 87. 



11 Helmert: "Die mathematischen und physikalischen Theorieen der hbheren Geo- 

 dasie, von Dr. F. R. Helmert," II. Theil. Leipzig, 1884, p. 241. 



12 Harkness. 



* The data here given with regard to the different determinations which have been made of the length of the 

 seconds pendulum are quoted from Harkness (Solar Parallax and its Related Constants, Washington, iSgi). 

 t Calculated from a logarithmic expression given by Unferdinger. 



Smithsonian Tables. 



