182. Experiments for determining the Length of the Penduluit.- 
Of the Correction for the Buoyancy of the Atmosphere. 
The Jength of the pendulum thus found, differing from what - 
it would have been had the vibrations den made in vacuo, it is 
necessary to apply to it a correction for the buoyancy of the at- 
mosphere. 
For this correction, the weight of the pendulum, compared 
with that of air, at the time of observation, must be known. 
The pendulum being compased of different kinds of brass, the 
specific gravity of each part was carefully determined, and from 
thence the specific gravity of the whole mass. 
Part of the Pendulum. bad iN! Specific gravity. 
i eeaprermareuban: a Sa aioe Wa MEA: 
3 weights (cast brass)....| 3-14 8-417 
4 knee pieces (cast brass) | 0°13 7°S16 
Bar (plate brass) . ......| 3°30 8-532 
\ 
From the above data, the specific gravity of the pendulum is 
8469 ; or the weight of the pendulum compared with water is 
as 8-469 to i, 
It has been determined by Sir George Shuckburgh (Phil. Trans, 
for 1777) that water is 836 times heavier than air, when the 
thermometer is at 53°, and the barometer at 29°27 inches. But 
the specific gravity of air veries directly as the height of the ba- 
rometer, and inversely as its expansion, which is known to be 
zigth part of its bulk for each degree of Fahrenheit: conse- 
quently, for any other state of the barometer and thermometer, 
the number 836 will may inversely as the height of the baro- 
meter, and directly zt,th part for each degree of the therma-. 
meter above 53’, 
Thus the specific gravity of water, compared with that of air, 
may be known for the temperature and altitude of the barometer 
at the time of observation ; and multiplying this by the specific 
gravity of the pendulum, the ratio of the weight of the pendulum, 
compared with that of air will be obtained. 
This ratio will express the diminution of the farce of gravity 
arising from the bueyanev of the atmosphere ; and in order that 
the number of vibrations may be the same in vacuo as in air, the. 
Jength of the pendylum must be increased in the proportion of 
this ratio to 1, the lengths of pendulums vibrating in the same. 
time, varying directly as the force of gravity, 
[To be continued. ] 
XXVIII, Ox 
