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XIX. On the Correction of a Pendulum for the Reduction to a Vacuum : 
together with Remarks on some anomalies observed in Pendulum experiments. 
By F. Baily, Esq. F.R.S. fyc. fyc. 8$c. 
Read May 31, 1832. 
The great importance which has, of late years, been attached to experiments 
on the pendulum, is evinced not only by the repeated and valuable labours of 
several of the most distinguished mathematicians and experimentalists of the 
present age, but also by the numerous scientific voyages that have been un- 
dertaken by several of the European Governments, with a view to ascertain 
and compare the results of different pendulum experiments made in various 
parts of the globe ; and thence to determine the true figure of the earth. 
These results, or the number of vibrations which are made in a mean solar 
day, whether made by the same, or by different pendulums, were considered, 
till within these few years, as strictly comparable with each other by means of 
certain well known corrections ; whereby they were reduced 1° to arcs inde- 
finitely small, 2 ° to a common standard of temperature, 3 ° to a vacuum, and 
lastly to the level of the mean height of the sea. 
M. Bessel, however, has recently proved that the formula for the reduction 
to a vacuum is very defective : and Dr. Young has shown that the formula for 
the reduction to the level of the sea is, in many cases, too great : whilst Cap- 
tain Sabine has, in a paper recently published in the Transactions of this So- 
ciety*, shown that there is reason to suspect the accuracy of the usual formula 
for the reduction to indefinitely small arcs. This latter gentleman had pre- 
viously, in another workf, pointed out the discordant results arising from the 
use of different agate planes with the same knife edge : and had also stated 
his decided opinion on the powerful effect of certain geological strata in the 
* Phil. Trans, for 1831, pages 467 — 469. 
t An Account of Experiments to determine the figure of the earth ; 4to, London 1825 ; pages 190 
and 371. 
3 F 2 
