SECTION VI.

EXPERIMENTS ON THE VELOCITY OF SOUND, AND ON THE PRESSURE ACCOMPANYING ATMOSPHERIC WAVES; AND COMPARISON OF THE EXPERIMENTAL RESULTS WITH THE RESULTS OF THEORY.

63. Recapitulation of the theoretical results for the velocity of Sound in Air.

It has been found, in Article 24, that the velocity of sound in a cylinder is no x 916-2722 feet per second; where n is a constant (Articles 15 and 16) depending on the increase or diminution of the elastic force of the air produced by sudden compression or expansion, to which we have assigned the probable value 1.2; and where is a factor depending on the temperature of the air during the experiment, and represented by √

or

450+ reading of Fahrenheit's thermometer
482

√450

(Articles 14 and 17). Converting the formula into numbers, we have the following table of the theoretical velocities of sound;

Theoretical Velocity of Sound, at different temperatures of the air as indicated by Fahrenheit's Thermometer.

The only source of uncertainty in these numbers is the uncertainty on the value of n, (see Article 16). The numerical coefficients given by different theorists are sensibly different, and we are yet ignorant whether the value of n depends on the temperature of the undisturbed air.

It appears from Article 39 that the velocity of a plane wave of air is the same as that of a wave in a cylinder: and it appears from Article 50 that the velocity of a divergent wave is sensibly the same as that of a wave in a cylinder.

64. Methods used for determining the velocity of Sound.

In the greatest part of the experiments, the observations have been those of the flash and the report of a distant cannon. The flash, and the first disturbance. of air by the emission of gas, occur so nearly or exactly at the same instant, that no sensible error arises from the difference in the nature of these two phenomena. The same observer observes both phenomena with the same watch or clock; and, if the distance of the gun be several miles, there is ample time for the observer to write down the observation of the flash before preparing himself for the observation of the sound. All these circumstances are very advantageous. The gun is usually pointed towards the observer, and it seems probable that this circumstance may slightly accelerate the pulse of air in the beginning of its course, but possibly by a few feet only, corresponding to an imperceptible error of time.

But there is a physiological circumstance, the effects of which have hitherto escaped notice, but which probably produces a sensible error; it is, that two different senses (sight and hearing) are employed in the observation of the two phenomena, and we are not certain that impressions are received on them with equal speed. Indeed we believe that the perception of sound is slower by a measurable quantity, perhaps 0.2, than the per

ception of light; and this may affect the result with an error amounting to some hundreds of feet.

We should much prefer a plan of observation in which two observers observed, in the same manner, the time of the sound passing two stations. By using signals given reciprocally from two stations beyond both the observing stations, it will be easy to obtain a result for the time of passage of the sound, independent of the habits of each observer, independent of the difference of the indications of their time-keepers, and independent of the velocity of the wind. (The reader will verify this without difficulty, by putting algebraical symbols for the different elements just mentioned; when it will be found that, on taking the mean of the two apparent times occupied by the passage of sound, according as the gun at first station or at second station is used, those elements disappear.) A process of this kind is employed in the measurement of higher velocities, as the velocity of the galvanic current in a telegraph-wire.

Difficulties have sometimes been experienced, by persons not familiar with astronomical practices, in the estimation of fractions of a second of time. To avoid these, a timepiece was employed in the Dutch experiments to be mentioned below (perhaps, on the whole, the best which had been made before those of M. · Regnault) in which the motion, being regulated by a pendulum revolving in a conical form, was free from the jerks of a common clock, and the index could be stopped at any fraction of a second.

A most elaborate series of experiments by M. V. Regnault is published in the Mémoires de l'Académie des Sciences, tome XXXVII., occupying 575 pages. The most important were made in tubes prepared for conveyance of gas and water in the neighbourhood of Paris: these tubes varied in diameter from 0·108 mètre to 1.10 mètre, and in length from 961 to 4886 mètres. The general principle in all was, to cover the near end of the tube with a firm plate (excepting in some early experiments), in which was a hole through which a pistol barrel was thrust; and a charge of powder, or somotimes a large percussion cap, was fired. The distant end of the tube was covered with a sheet of caoutchouc, which was made to tremble by the shock of the airwave: sometimes it produced a reflexion to the firm plate, and from it to the caoutchouc again, &c. The pistol-explosion broke a galvanic circuit, and the trembling of the caoutchouc restored it: and these galvanic effects were registered upon a revolving barrel, on which were also registered the beats of a clock and the vibrations of a tuning-fork. In some experiments, laminæ of caoutchouc were applied to apertures in the sides of the tube at different distances. Finally, experiments were made in the same way without tubes, using the explosion of a heavy cannon. Experiments were also made on the velocity of sound through air of different densities, and through various gases. These, we believe, are the only experiments in which there has been no reference to human nerves.