Table 116. 



LENGTH OF THE SECONDS PENDULUM/ 



Range of latitude included by 

 the stations. 



From + 67° 05' to — 33" 56' 



+ 74° 53' 

 + 3^° 40' 

 + 79° 50' 

 + 79° 50' 

 0° o' 



+ 79^51' 



+ 79° 50' 

 + 79° 50' 

 + 79° 50' 



— 51"" 21' 

 -60° 45' 

 -i2°59' 



-51° 35 

 + 67° 04' 



-51^35' 



— 51° 35' 



— 62° 56' 



— 62° 56' 



Combining the above results 



Length of pendulum in metres 

 for latitude ifi. 



0.990631 + 



0.990743 + 

 0.990880 + 



0.990977 4- 

 C.991026 + 



0-990555 + 

 0.991017 + 

 0.990941 -j- 

 0.990970 + 

 0.991011 + 

 0.990918 -j- 



.005637 

 .005466 

 •005340 

 .005142 

 .005072 

 .005679 

 .005087 

 .005142 

 .0051S5 

 .005105 

 .005262 



sin'^ ^ 

 sin- ^ 

 sin- <l> 

 sin- <p 

 sin-^ 

 sin-^ 

 sin- (p 

 sin- 

 sin- (p 

 sin- <p 

 sin- <l> 



0.990910 -\- .005290 sin^^ 



Correspond- 

 ing length 



of pendulum 

 forlat. 45 . 



0.993450 

 0.993976 

 0.993550 

 0.993548 

 0.993562 



0-993395 



0.993560 



0.993512 



o-993554t 



o-9935'J3 



0-993549 



0-993555 



Refer- 

 ence. 



I 

 2 



3 

 4 



5 

 6 



7 

 8 



9 

 10 

 II 



12 



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

 /= 0.9927 1 48 metre 



+ 0.0050890 p~* (sin- (p — I) 



-\- 0.0000979 p"* cos- (/> cos (2ft)' -j-29°04') 



— 0.0001355 p~^ (sin^ (p — f sin )(p 

 -f- 0.0005421 p-^ (sin- (p — ^) cos (p cos (u + 217° 51') 

 -|- 0.0002640 p~^ sin (p cos- (p cos (2a»' + 4° 49') 

 -j- 0.0001248 p~^ cos^ tp cos (3&>' -j- iio^ 24') 

 -f- 0.00014S9 p-" (.sin-* <p — I sin- <;!' + ^) 

 + 0.00073S6 p~'^ (sin'' <p — f sin (p) cos (p cos (w' -\- 3° 02') 

 -f- 0.0002175 p-° (sin- (p — }) cos- (p cos (201' + 262° 17') 

 -j- 0.0003126 p~° sin (p cos^ ^ cos (30?' -f 148° 20') 

 -|- 0.0000584 p"" cos"* (p cos (4ft>' + 248° 19') 

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

 with the latitude, such that the radius of the earth at latitude <p 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 1S16," 

 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 k 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. 



1 1 Helmert : " Die mathematischen und physikalischen Theorieen der hoheren Geo- 

 dasie, von Dr. F. R. Helmert," IL.Theil. Leipzig, 18S4, 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 from a logarithmic expression given by Unferdinger. 



Smithsonian Tables. 



105 



