242 Mr. Ivory on the Methods proper to be used for deducing 



plication. But no rule, however general, can be safely ap- 

 plied without attending in some degree to the particular cir- 

 cumstances of the case. And if we compare the results ob- 

 tained by this method, we shall find that they often vary greatly, 

 when no adequate reason can be assigned ; which must raise 

 our suspicions of its fitness for this particular investigation. 

 Thus Captain Sabine, at p. 334- of his work, deduces from his 

 1 3 stations, by the method of the least squares, the equatorial 

 pendulum x, the total increase from the equator to the pole y, 

 and the ellipticity of the earth, viz. 



x — 39-01568 



y — -20213 

 ellipticity = -00346. 

 But if we leave out the experiments at St. Thomas and Ascen- 

 sion, we shall obtain by calculating in the same manner from 

 the 1 1 remaining stations, 



x = 39*01374 



y — 0-20463 

 ellipticity = -003405. 

 And, further, if we leave out the experiments at St. Thomas, 

 Ascension, Sierra Leone, and Jamaica, the remaining 9 sta- 

 tions will give us, 



x = 39-01257 



y — 0-206 

 ellipticity = -00337. 

 Now in every one of the three calculations the experiments 

 employed, being both numerous and extending from the 

 equator to 80° of latitude, ought to be sufficient for an accu- 

 rate determination. No reason, therefore, can be alleged 

 for the great variations, except inaccuracy in the experiments 

 themselves, or the irregular deviation of the earth's surface 

 from the elliptical figure, or some fault in the mode of investi- 

 gation by which the unavoidable errors of the experiments 

 are greatly aggravated. 



It seems necessary, from what has been said, to examine 

 the method of the least squares in its application to the , pen- 

 dulum experiments. Let I, /', /", &c. denote the pendulums 

 found experimentally ; A, A', A", &c. the latitudes of the expe- 

 riments; L the equatorial, and L +ythe polar, pendulum: 

 then, e, e 1 , e", &c. being the respective errors of the experi- 

 mental quantities, we shall have, 



L +/sin 3 A -I -e 



L -f /sin 9 A' - V = e' 



L+fsm 2 \"-l"=e tl 



&c. 

 As the seconds pendulum from the equator to the pole con- 

 sists 



> inches 



.,, > inches 

 >3j 



V inches 



