ON THE ELLIPTICITT OF THE EARTH. 461 



buoyancy might be expected to differ widely from each 

 other, as well as from the original, and now known to be 

 erroneous, computation ; and that the results would, with 

 each apparatus, be altered by the whole amount of the 

 difference between the original computation, and the true 

 buoyancy correction as learnt by experiment ; whilst in 

 the case of the invariable pendulum the acceleration 

 would only require to be corrected for a small fraction 

 of that difference, because the greater portion would be 

 a common error at all the stations where the same form 

 of invariable pendulum had been used. 



The kind of experiment best suited to give the true 

 "correction for buoyancy" (or it is sometimes called 

 " the reduction to a vacuum ") for any particular form 

 of pendulum, was sufficiently obvious, and presented no 

 other difficulties than such as might be surmounted by 

 a fitting apparatus, in which the pendulum itself might 

 be vibrated alternately in air of the ordinary tempera- 

 ture and density, and in rarefied air approaching nearly 

 to a vacuum. 



In the same year that Bessel's discovery was an- 

 nounced (1828), I had such an apparatus constructed, 

 and, by experiments recorded in the Phil. Trans, for 

 1829, art. xviii., ascertained that the buoyancy correc- 

 tion for an invariable pendulum of the form employed 

 by Captain Kater and myself, computed by the formula 

 which had been previously in use, required to be multi- 

 plied by the factor 1-65 in order to give the true reduction 

 to a vacuum. The most widely differing buoyancy cor- 

 rections at the 19 stations of Captain Kater and myself, 

 Computed by the original formula, were: + 5 S *75 at 

 Sierra Leone, and + 6 S *27 at Spitzbergen, in a mean 



