ON THE ELLIPTICITT OF THE EARTH. 455 



nically invariable makes in a certain definite time at 

 the different stations to which it has been successively 

 conveyed,) into combination with another series in which 

 the experimental object has been a different one, viz. 

 to determine, by Borda's method, the absolute length of 

 the seconds pendulum at one or more stations, requires 

 that some assumption should be made, whereby the 

 absolute lengths of the seconds pendulum at the stations 

 where the invariable pendulum has been used may be 

 substituted for that which is the sole and simple ex- 

 perimental result with the latter apparatus ; and, 

 further, that the lengths so substituted shall be such as 

 would have been obtained by Borda's apparatus in 

 particular, had it been employed at those stations in- 

 stead of the invariable pendulum. 



The operation of even a very small error in the 

 requisite assumption may easily be understood when, 

 as in the present case, the one series viz. that of 

 the invariable pendulum has furnished the results 

 in both the polar and the equatorial latitudes, and the 

 other series viz. that of the absolute lengths measured 

 by Borda's apparatus those in the middle latitudes. 

 1st, By the combination of the polar and equatorial 

 results we obtain the ellipticity unaffected by the sup- 

 posed error, because they form parts of one and the 

 same experimental series, and require no substitution 

 in lieu of the direct experimental results. They have 

 also the very great and independent advantage of com- 

 prehending between them an arc of such extent (and 

 consequently an acceleration of such amount), that 

 minor errors of other kinds, whether observational, or 

 due to local variations of the gravitating force as ill- 



