554 GENERAL WALKER ON PENDULUM OPERATIONS FOR DETERMINING 
It will be seen that the mean value is fairly in accordance with the values derived 
from Colonel Hersghel’s observations with pendulums No. 4 and No. 6 (1821). His 
swings with those pendulums, at Kew, were made in the basement of the Kew 
Observatory, within a few feet of the spot at which the revisionary swings, with all 
three pendulums, were made; but he swung pendulum No. 11 in a shed outside the 
Observatory, under circumstances of great disadvantage as regards the stability and 
firmness of the support of tlie stand of the invariable pendulum and also of the support 
of the clock. Thus liis observations at Kew, with pendulum No. 11, though generally 
very accordant inter se, are very jjrobably burdened with a large constant error, and 
must therefore l)e reiected. 
On the Reduction to a Vacuum. 
In all pendulum experiments—even those of a purely differential character, as with 
invariable pendulums—it has been generally customary to apply a correction for the 
retardation which is caused by the air, in order to obtain results such as would have 
been obtained if the pendulum had been swung in a vacuum. This correction was 
originally determined by calculating the influence of the buoyancy of the atmosphere 
in diminishing the weight—and consequently the accelerating force—of the pendulum. 
Afterwards Bessel showed that the correction thus obtained was too small, for the 
pendulum is accompanied in its oscillation by a certain amount of air, varying with its 
form, which increases the mass in vibration and the moment of inertia. Thus the 
buoyancy correction has to be multiplied by a factor, 1 + ^, which can be computed 
mathematically for pendulums of certain simple forms, but must be determined ex¬ 
perimentally, by swings at high and low pressures, when the form is not susceptible 
of being brought under mathematical treatment. Tlie buoyancy correction, thus 
augmented, is usually called the pressure correction. 
The buoyancy correction and the pressure correction have been investigated for 
pendulums No. 4 and No. 6 (1821) by special and laborious series of operations which 
are fully set forth in vol. 5 of the ‘ Account of the Operations of the Great Trigno- 
metrical Survey of India.’ Nothing of the kind is known to have been done for 
No. 11 ; but the results obtained for the two first pendulums are so closely accordant 
that they may be applied without objection to the third, which is almost identical 
with them in foi-m and construction. 
/3 
The buoyancy correction = '23 j qq.^io which yS is the pressure m 
inches, and t the temperature in degrees of Fahrenheit. 
The pressure correction was found to be ’32 
1 + -0028 (t - 32°) 
by experimental 
swings which were made specifically for the purpose at Kew, under extreme high 
and low pressures, immediately before the pendulums were sent out to India. Cor¬ 
rections determined by this formula were applied, provisionally, to the whole of the 
