402 
MR. BAILY ON THE CORRECTION OF 
the convertible pendulum (except perhaps in that particular instance when it 
makes the least number of vibrations possible,) the correction will not be the 
same for the two knife edges : and consequently that a pendulum, which has 
been made convertible in air, will no longer be so when tried in a vacuum. 
It becomes therefore of importance to know how far the differently con- 
structed pendulums, made use of by various experimentalists, are affected by 
this newly discovered principle, in order that their results may be strictly 
comparable with each other. The amount of the required correction, how- 
ever, cannot (according to our present knowledge of the subject,) be deter- 
mined by calculation, but must, in every case, be ascertained by actual expe- 
riment. The most direct method of effecting this appears to be, as M. Bessel 
states (page 37), by swinging the pendulum in a vacuum : although he him- 
self, on account of some doubts which he entertained of this method, but 
which he has not explained, adopted another and a very different plan. 
The mode adopted by M. Bessel was of two kinds. The first and principal 
one was by swinging in air two spheres of equal diameter (about 2T4 inches) 
but of very different specific gravity, viz. brass and ivory, suspended by a fine 
steel wire : the other, which was not commenced till the subsequent year, was 
by swinging the same sphere (brass) first in air and afterwards in water. The 
result of the experiments, by both these methods, showed that the usual cor- 
rection for the reduction to a vacuum was much too small ; and that the true 
correction was nearly double what has been generally assumed. The first 
method gave T946*, and the second 1625, as the factor by which the old 
correction must be multiplied in order to obtain the true correction. These 
values differ materially from each other; but M. Bessel prefers the former, 
as his investigations are founded on the theory that the vibrations are made in 
a medium of very small density f. 
Being desirous of ascertaining, by a different process, the true value of the 
correction for the numerous and various pendulums in my possession, as accu- 
rately as experiments of this kind will decide the fact, and considering the 
* In a paper, subsequently inserted in the Astronomische Nachrichten, No. 223, M. Bessel has in- 
creased this value to 1956. 
t M. Bessel also swung a hollow brass cylinder alternately in air and in water, and has deduced 
some results which appear to be astounding : but, I shall show in the sequel that the discordancy in 
the results stated by him, will be removed by the assumption of a different specific gravity of the 
moving body, from that which he has adopted. 
