as deduced from Experiments made with the Pendulum. 97 



expressed in millimetres, and it refers to the decimal division 

 of the day. The total variation of the decimal pendulum be- 

 tween the extreme stations is 1'74 mm., and to this quantity 

 the unavoidable errors of observation bear too great a propor- 

 tion to admit of many safe determinations of the ellipticity by 

 different combinations of the experiments. In order to com- 

 bine these experiments with that of Captain Sabine at Maran- 

 ham, it is necessary to reduce the sexagesimal pendulum in 

 English inches, or rather the equatorial pendulum 39-01175 

 in. deduced from it, to millimetres and the decimal division 

 of the day. Now when the sexagesimal pendulum is 39*01 1 75 

 in., it will be found that the decimal pendulum is 739 mm .6885, 

 which is therefore the value cf L in the formula ( 1 ) when it is 

 applied to the French experiments. The resulting ellipti- 

 cities are contained in the following table. 



Stations. 



Latitude. 



Pendulum. 



Ellipticity. 



Formentera . 





38 39 56 N. 

 44 36 45 



44 50 26 



45 46 48 

 48 50 14 

 51 2 10 

 55 58 37 

 60 45 25 - 



mm. 

 741-2520 

 741-6122 

 741-6087 

 741-7052 

 741-9175 

 742-0770 

 742-4134 

 742-7231 



Mean 



•00324 

 •00338 

 •00343 

 •00334 

 •00333 

 •00331 

 •00329 

 •00326 



•00332 



Bourd^aux . 

 Clermont . . . 



Dunkirk . . . 

 Leith Fort . . 

 Unst 



The result of all these calculations stands thus : 



Mean of Captain Sabine's experiments . . . '00333 



of Captain Kater's -00329 



ofM. Biot's -00332 



2. We next proceed to the other method of determining 

 the earth's ellipticity. As before, let L represent the equatorial 

 pendulum ; f the whole increase from the equator to the pole ; 

 V the observed length of the seconds pendulum at the latitude 

 A f , and V + e the true length, s being the error of observa- 

 tion : then we have 



V + e = L-r-/sin 2 A', 



/=(-?. -«)xL. 



Again, let I be another observed pendulum at the latitude A, 

 and I + e + x, the true pendulum, x being the difference of 

 the errors at the latitudes A and A' ; then, 



I + E + x = L +/sin 2 A. 

 Vol. 68. No. 340. Aug. 1826. N Thus 



