406 
MR. BAILY ON THE CORRECTION OF 
well agreed upon. It has generally been taken at ^th of its bulk, or *002083 
for each degree of Fahrenheit : but this value applies more particularly to 
air rendered perfectly dry for the purpose of the experiments from which such 
value has been deduced. The expansion of common atmospheric air, impreg¬ 
nated, as it generally is, with a certain degree of moisture, is supposed by 
M. Laplace to be ^j-oth of its bulk, or *002222 for each degree *. I have as¬ 
sumed this latter value, and consequently make (a + f) = *0023. Whence 
the numerical expression for the formula in question will be 
1 /3 1 
+ 2 (S x 770 — 1) X 29*9218 X 1 + *0023 (t! - 32°) 
If we make (3 = 1, and t' = 32°, we might readily obtain for each pendulum, 
a constant quantity 
r, XT *0000217016 
C — IS x s _ *001299 
for one inch pressure of the atmosphere, at the freezing point of water ; whence 
the value of the correction at any other pressure (3 , and at any other tempera¬ 
ture t, would be denoted by 
( X 1 + *0023 (( — 32°) ( 5 ) 
This is the old correction, which is so far erroneous that no account is taken 
of the effect of the air set in motion by, and accompanying the pendulum, as 
if adhering thereto ; and which is now found to influence the result very ma¬ 
terially. This formula, however, will still be of considerable service to us, 
since not only M. Bessel’s experiments, but also those about to be detailed in 
this paper, have for their object the determination of the factor, by which the 
quantity C must be multiplied (according to the form and construction of the 
pendulum,) in order to produce the true correction : this being one of the most 
convenient forms of showing the relative value and amount of this new in¬ 
fluence. I have already stated that the mode proposed to be pursued in the 
following experiments, for the determination of this factor, was to swing the 
pendulum under the full pressure of the atmosphere and also in a highly rare- 
* Systeme du Monde, 5th edition, 1824, page 89. See also Biot’s Traite d’Astronomie Physique, 
vol. iii. (Mesures Barometriques, page 14.) 
