Mechanical /Science. 603 



answer for an error of less than J oscillation. The latitudes were de- 

 termined by numerous sets of circummeridian altitudes of the sun and 

 stars, observed with a sextant of Troughton, a reflecting circle by the 

 same artist, and a reflecting repeating circle by Dollond. The follow- 

 ing table contains the number of oscillations of the pendulum at each 

 station in 24 mean solar hours, reduced to the standard temperature 

 of 62 Fahr., to a vacuum, and to the level of the sea. The fourth 

 column contains the corresponding lengths of the seconds' pendulum 

 founded on Captain Rater's measurement of the same at London. 

 With this view the observations at Greenwich were reduced to the 

 station in Portland Place by the difference of oscillations of the two 

 places, as determined by Captain Sabine. 



Numbers of Lengths of 



Stations. Latitudes. Oscillations. Second? Pendulum. 



Ualan 5 21' 16" N 86112.83 39.02756 



Guahan ... ..-.., . . 13 26 21 N 117.98 03242 



St. Helena . . . 15 54 59 S 125.63 03933 



Bonin .... 27 4 12 N 159.24 06980 



Valparaiso ... 33 2 30 S 165.33 07533 



London . . . . 51 31 8 N 235.80 13929 



St Peter's and St. Paul's 53 53 N 245.83 14838 



Sitka 57 2 58 N 257.44 15810 



St. Petersburgh . . 59 56 31 N 269.08 16950 



In order to find the mean value of the ellipticity resulting from all 

 these observations, it is most convenient to combine them by the 

 method of minimum squares. Designating the length of the pen- 

 dulum at the equator by #, its difference from that at the pole by y, 

 the errors of each partial result by E', E", E'", and assuming the 

 hypothesis of an elliptical figure of the earth, for which we have the 

 length of the pendulum in latitude L = x + y sin 8 L, we shall obtain 

 the following equations of condition : 



Ualan 39.02765-a;-0.0087080 . y = E' 



Guahan .;.... 39.03243 a- 0.0540157 . y = E" 



St. Helena . .. . . . 39.03933 -x 0.0752045 . y = W 



Bonin 39.06980 x 0.2070967 . y = E iv 



Valparaiso ..... 39.07533-*- 0.2972962 . y = E v 



London 39. 13929 -a? -0.6 127966 . y = E Tl 



St. Peter's and St. Paul's 39. 14838-*- 0.6380657 . y = E vU 



Sitka 39.15810 .r-0.7041567 . y = E viii 



St. Petersburgh . . . 39.16950-*-0.7491220 . y = E* 



The following values will then be found by the method of mini- 

 mum squares : 



x = 39.02422; y = 0.091787; ellipticity = 



The differences between the observed and calculated lengths of the 

 pendulum and numbers of oscillations will then stand as follows : 



