ON  THE  MOTION  OF PENDULUMS.                           7/
The object of these experiments was, to determine by actual observation the correction to the time of vibration due to the presence of the air in the case of a great number of pendulums of various forms. This was effected by placing each pendulum in succession in a vacuum apparatus, by which means the pendulum, without being dismounted, could be swung alternately under the full atmospheric pressure, and in air so highly rarefied as nearly to approach to a vacuum. The paper, as originally presented to the Royal Society, contained the results obtained with 41 pendulums, the same body being counted as a different pendulum when swung in a different manner. Out of these, 14 are of such forms as to admit of comparison with theory. An addition to the paper contains the results obtained with 45 pendulums more, of which 24 admit of comparison with theory. The details of these additional experiments are omitted, the results only being given.
Baily has exhibited the results obtained with the several pendulums in each of two ways, first, by the value of the factor n by which the correction for buoyancy must be multiplied in order to amount to the whole effect of the air as given by observation, and, secondly, by the weight of air which must be conceived to be
the effect of the air was supposed to be arrived at by increasing the observed difiperence in the times of vibration in the ratio of the difference of densities to the atmospheric density. As the effect of the air at the lower density was too large to be neglected, it was necessary, in order to compare with sufficient accuracy the results of experiment with the formulae of this paper, to know the relation between ac and p. As already mentioned, I assumed in accordance with what appeared to be indicated by a single experiment of Sabine's that ac varies as p, or in other words that fjJ is independent of the density. The results of the experiments when thus reduced seemed to indicate a most remarkable accord with theory.
When it became known that the law of nature is that p and not /// is independent of p, it seemed very strange that the experiments when reduced on the assumption of a wrong law as to the relation of ac to p should have led to such a remarkable agreement with theory. I contemplated at one time undertaking the re-computation of the whole series of Baily's experiments here discussed in accordance with Maxwell's law, and it was this that delayed the reprinting of the present paper. The value of the result at the present time would however hardly repay the labour of the calculation, more especially as the remarkable agreement between theory and observation notwithstanding the employment of a wrong law as to the relation between p and p admits of being readily explained, and the value of fj. obtained as in the text of being very approximately corrected, in a very simple manner. As however this would be too long for a footnote, I must reserve it for an addition to be made at the end of the paper.]