236 



CAPTAIN SABINE ON THE REDUCTION TO A VACUUM 



Whence we obtain 10.36 vibrations per diem, as the reduction to a vacuum 

 of the invariable pendulum, vibrating- in air of 45°, under a pressure of 30 inches 

 of mercury at 32°. 



To exhibit the degree of approximation, with which the result of each of the 

 experiments, combined in producing this mean determination, is represented by 

 it, we may compute the several retardations corresponding to the circumstances 

 of each experiment, and place the computed retardations in comparison with 

 the results of actual observation. 



r incii ■ vibrations. 



Exp. I. Computed 7.42 



Vibrations. 



Observed 7-38 



Computed + or — 



Vibrations. 



+ 0.04 



. II. 9.08 ; 9.065 ; + 0.015 



in. 9.66 ; 9.54 ; + 0.12 



IV. 9.26 ; 9.17 ; + 0.09 



y. 10.24 ; 10.38 ; —0.14 



;.Y^jf,=-- 5.65 ; 5.705; —0.055 



VIL.- rrrrr 10.575 ; 10.525 ; + 0.05 



VIII. 10.48 ; 10.56 ; — 0.08 



Hence we may perceive, that were the reduction to a vacuum separately de- 

 rived from each of the eight experiments, it would in no instance differ more 

 than 0.14 of a vibration from the adopted determination. In other words, the 

 greatest difference that would be occasioned, by deriving the reduction, which 

 it was the object of these experiments to obtain, from any single experiment, 

 instead of from the mean of the whole, would in no case exceed 75th part of 

 the amount of the reduction. 



The " correction for buoyancy," or the reduction that would have been pre- 

 viously computed, for the vibrations of a pendulum in air of 45°, under a pres- 

 sure of 30 inches, is 6.26 vibrations per diem. The actual retardation is there- 

 fore 4.1 vibrations per diem greater than had been supposed ; and the propor- 

 tion, which the experimental reduction bears to that which is now shown to 

 have been erroneous, is as 1.655 to 1. 



In considering the modifications, which the substitution of the true for the 

 erroneous reduction to a vacuum will introduce, in the results obtained with 



