TABLE 116. 



LENGTH OF THE SECONDS PENDULUM.* 



In 1884, from the series of observations used by Ur. Fischer, Dr. G. W. Hill 1S found 

 /= 0.9927148 metre 



+ 0.0050890 p~ 4 (sin 2 | 



51') 



-- 0.0000979 p~ 4 cos 2 cos (2w' +29 04') 



00001355 p~ 5 (sin 3 ^ f sin )0 



+ 0.0005421 p~ 5 (sin 2 ^ |) cos $ cos (' + 217 



-j- 0.0002640 p~ 5 sin (f> cos 2 <}> cos (2ta + 4 49') 



-j- 0.0001248 p~ 5 cos 8 <j> cos (30)' -j- 1 10 24') 



-j- 0.0001489 p- 6 (sin 4 <t> f sin 2 <j> + ^) 



-j- 0.0007386 p~ 6 (sin 3 f sin <j>) cos <j> cos (' -(- 3 02') 



-f- 0.0002175 p~ 8 (sin 2 <j> |) cos 2 <t> cos (2' -f 262 17') 



-j- 0.0003126 p~ 6 sin <t> cos 3 ^ cos (30*' + 148 20') 



-f- 0.0000584 p~ 6 cos 4 cos (40)' + 248 19') 



where <f> is the geocentric latitude, ' the geographical longitude, and p a factor, varying 

 with the latitude, such that the radius of the earth at latitude <t> is ap where a is the equa- 

 torial radius of the earth. 



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, 1825, 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;" 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. 



13 Hill, Astronomical paper prepared for the use of the "American Ephemeris and 

 Nautical Almanac," vol. 3, p. 339. 



* 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, 1891). 

 t Calculated frm a logarithmic expression given by Unferdinger. 



SMITHSONIAN TABLES. 



105 



