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. 
Vibrations. Vibrations. Vibrations. 
Exp. I. Computed 7-42 ; Observed 7-38 ; Computed + or — ; + 0.04 
II. 9.08 ; 9.065 ; + 0.015 
III. 9.66 ; 9.54 ; + 0.12 
IV. 9.26 ; 9.17 ; + 0.09 
V. 10.24 ; 10.38 ; — 0.14 
VI. 5.65 ; 5.705 ; — 0.055 
VII. 10.575 ; 10.525 ; -f 0.05 
VIII. 10.48 ; 10.56 ; — 0.08 
I lence 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 T ^th 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 
