422 Capt. Liietke's Account of Experiments with an 



vibrations made by the pendulum, at each station, in a mean 

 solar day, reduced to the standard temperature of 62° Fahr., 

 to a vacuum, and to the level of the sea. The 4th column 

 contains the corresponding length of the seconds pendulum 

 (in English inches), founded on that determined by Captain 

 Kater in London. For this purpose we ought to reduce the 

 experiments at Greenwich to the station at Portland Place, by 

 the difference in the number of vibrations, found to exist be- 

 tween these two places, by Capt. Sabine. 



In order to find the mean result of the compression of the 

 earth, corresponding to the whole of these experiments, we 

 must adopt the method of least squares. If we denote by x 

 and j/ the length of the pendulum at the equator, and the dif- 

 ference of that at the pole ; by E', E", E'" &c. the errors of 

 each partial result ; and recollecting that in the hypothesis for 

 the elliptical figure of the earth the length of the pendulum for 

 each latitude is h = x + tj x sin - L ; we shall have the fol- 

 lowing equations of condition : viz. 



Ualan .... 39-02765 - x — O-O0870SO xj/ = E'. 



Guam .... 39-03242 — x -0-0540157 Xj/ = E". 



St. Helena . . 39-03933 - x -0-0752045 x?/ = E'". 



Bonine .... 39-06980 - x -0-2070967 xj/ = E'\ 



Valparaiso . . 39-07533 — x -0-2972962 x?/ = E^ 



London . . . 39-1-3929 — x -0-6127966X3/ = E^'. 



Petropaulouski 39-14838 — .r —0-6380657 Xj/ = E^". 



Sitka 39-15810 - x -0-7041567 Xj/ = E^>''. 



St.Petersburgh 39-16950 — x —0-7491220 xj/ = E^''". 



The equation of the minimum, with respect to x, will be the 

 sum of these same equations divided by their number : that is, 



39-095532 —x — 0-3718291 x y = 0. 

 In order to take the equation of the minimum with respect 



