65. Statement of the principal modern results for the velocity of Sound.

We confine ourselves, in the following table, to the most trustworthy experiments made since the year 1820.

Phil. Trans. 1824 Moll and Van Beek 57839

1089.4 32

The best of these experiments give results somewhat larger than those in our theoretical table, Article 63; some, however, give results rather smaller. It seems not impossible that we ought to have taken for n a value very slightly exceeding 12, and also that there is some uncertainty in the experiments.

It is to be remarked that, except in M. Regnault's experiments, there are no observations sufficient to enable us to apply a correction for the effect of moisture in the air.

M. Regnault's experiments shewed clearly that the greatest disturbance produced by a violent solitary wave travelled rather more rapidly than that of a feeble wave: as may be inferred from the theory of Article 33.

We ought not here to pass over a curious remark of Captain Parry and Mr Fisher, in observations made in Captain Parry's second voyage. The stations were so near that the human voice could be heard; and the remark was, that the officer's word of command "fire," was heard about one beat of the chronometer (or of a second of time, we believe) after the report of the gun. The instance is quite singular. Mr Earnshaw has supposed it possible that the phenomenon has some relation to that acceleration of the wave which occurs when the displacement of particles is very large (see Articles 32, 33, 34). But we cannot imagine that the acceleration could ever amount to a space of 200 feet; and in any case we imagine that when the accelerated large disturbance came up with the small disturbance, the two disturbances would be merged into one.

It appears to us more probable that the phenomenon is physiological. We have often remarked that, when the report of a gun or any other violent and sudden noise is heard, it is preceded by the perception of a shock through the bodily frame, the interval in time being a large fraction of a second. From the voice, there would be no sensible shock: but the shock from the cannon-explosion might be sensible, and might precede the auditory perception of the report by a time sufficiently long to present itself to the observer's mind before the auditory perception of the voice.

66. Comparison, with theory, of the observed pressure accompanying an atmospheric wave: the pendulum.

The only experiment which is sufficiently delicate to give a measure of the pressure of a wave is the observation of its influence on the movement of a pendulum whose bob is a sphere. And the reason why this experiment is so delicate is, that the effect of the pressure of the wave is to lengthen the time of every vibration; and though its effect on the time of a single vibration would be undiscoverable, yet its aggregate effect on the total time of a great number of successive vibrations is very conspicuous, and very little doubt exists as to the accuracy of the results found from it.

Referring to books on Mechanics for descriptions of the methods by which the length of a pendulum to its center of oscillation is accurately measured and its time

of vibration is accurately observed, it is only necessary here to remark: that for different pendulums swinging in a vacuum, whatever be the materials of which they are composed, an invariable relation exists (at a given locality) between the length of the pendulum and its time of vibration: but that, in the far greater number of experiments, the vibrations have been observed not in a vacuum but in air; and that therefore a numerical correction to the observed time of vibration of each is necessary, in order to produce the time of vibration which would have been observed in vacuum. In the reduction of all the earlier pendulum-observations, the numerical correction was computed on the supposition that the sole effect of the air was, to diminish the active weight of the bob by an absolute quantity equal to the weight of the displaced air, and therefore to diminish the effect of gravity by a proportional part represented by a fraction, whose numerator is the specific gravity of air and whose denominator is the specific gravity of the pendulum-bob.

But it was found in the present century (in the first instance, we believe, by Bessel) that when different pendulums composed of different metals were treated in this way, they gave discordant results: the relation between the pendulum's length and its corrected time of vibration did not hold uniformly. In all cases it was necessary to apply a larger numerical correction than that given by the rule which we have just stated.

Experiments therefore were made, principally by

M. Bessel in Prussia, and Mr F. Baily in England, in order to discover how much the original correction ought to be increased. (Observations, not applying to the spherical form, were also made by Captain Sabine.) › In some instances, spheres of different substances were used in the same state of air; in other instances, the spheres were not varied, but the density of the air was varied by conducting the experiments in a close case from which the air was partially exhausted by an airpump. The results were the following;

Bessel, by comparing the vibrations of a sphere of brass and a sphere of ivory, in common air, found that the old correction ought to be multiplied by 1.95.

Baily, by comparing the vibrations of a sphere in common air with the vibrations of the same sphere on the same mounting in vacuum, and applying the same process to different spheres, found for the factor: with spheres 1 inch in diameter, platinum 1881, lead 1·871, brass 1834, ivory 1872; with spheres 2 inches in diameter, lead 1-738, brass 1·751, ivory 1.755.

Now, in Article 54, corrected by the considerations cited in the latter part of Article 57, we have found, as the theoretical result of considering the spherical wave with oscillating centre, that the old correction ought to be multiplied by 1.72.

We consider the agreement of the observed and the theoretical results as being as good as, under all the experimental circumstances (especially with the limitation of the surrounding space of air), could be expected.