inference when an experiment to verify or contravene it is possible. The foregoing argument is clinched by bringing the radiative power of atmospheric air to a direct test. When this is done, experiment and reasoning are found to agree; air being proved to be a body sensibly devoid of radiative and absorptive power.23
But here the experimenter on the transmission of sound through gases needs a word of warning. In Laplace’s day, and long subsequently, it was thought that gases of all kinds possessed only an infinitesimal power of radiation; but that this is not the case is now well established. It would be rash to assume that, in the case of such bodies as ammonia, aqueous vapor, sulphurous acid, and olefiant gas, their enormous radiative powers do not interfere with the application of the formula of Laplace. It behooves us to inquire whether the ratio of the two specific heats deduced from the velocity of sound in these bodies is the true ratio; and whether, if the true ratio could be found by other methods, its square root, multiplied into the calculated velocity, would give the observed velocity. From the moment heat first appears in the condensation and cold in the rarefaction of a sonorous wave in any of those gases, the radiative power comes into play to abolish the difference of temperature. The condensed part of the wave is on this account rendered more flaccid and the rarefied part less flaccid than it would otherwise be, and with a sufficiently high radiative power the velocity of sound, instead of coinciding with that derived from the formula of Laplace, must approximate to that derived from the more simple formula of Newton.
§ 13. Velocity of Sound through Gases, Liquids, and Solids
To complete our knowledge of the transmission of sound through gases, a table is here added from the excellent researches of Dulong, who employed in his experiments a method which shall be subsequently explained:
Velocity of Sound in Gases at the Temperature of 0° C.
| Velocity | ||
| Air | 1,092 | feet |
| Oxygen | 1,040 | ” |
| Hydrogen | 4,164 | ” |
| Carbonic acid | 858 | ” |
| Carbonic oxide | 1,107 | ” |
| Protoxide of nitrogen | 859 | ” |
| Olefiant gas | 1,030 | ” |
According to theory, the velocities of sound in oxygen and hydrogen are inversely proportional to the square roots of the densities of the two gases. We here find this theoretic deduction verified by experiment. Oxygen being sixteen times heavier than hydrogen, the velocity of sound in the latter gas ought, according to the above law, to be four times its velocity in the former; hence, the velocity in oxygen being 1,040, in hydrogen calculation would make it 4,160. Experiment, we see, makes it 4,164.
The velocity of sound in liquids may be determined theoretically, as Newton determined its velocity in air; for the density of a liquid is easily determined, and its elasticity can be measured by subjecting it to compression. In the case of water, the calculated and the observed velocities agree so closely as to prove that the changes of temperature produced by a sound-wave in water have no sensible influence upon the velocity. In a series of memorable experiments in the Lake of Geneva, MM. Colladon and Sturm determined the velocity of sound through water, and made it 4,708 feet a second. By a mode of experiment which you will subsequently be able to comprehend, the late M. Wertheim determined the velocity through various liquids, and in the following table I have collected his results:
Transmission of Sound through Liquids
| Name of Liquid | Temperature | Velocity | |
| River-water (Seine) | 15° C. | 4,714 | feet |
| River”water (S” | 30 | 5,013 | ” |
| River”water (S” | 60 | 5,657 | ” |
| Sea-water (artificial) | 20 | 4,768 | ” |
| Solution of common salt | 18 | 5,132 | ” |
| Solution of sulphate of soda | 20 | 5,194 | ” |
| Solution of carbonate of soda | 22 | 5,230 | ” |
| Solution of nitrate of soda | 21 | 5,477 | ” |
| Solution of chloride of calcium | 23 | 6,493 | ” |
| Common alcohol | 20 | 4,218 | ” |
| Absolute alcohol | 23 | 3,804 | ” |
| Spirits of turpentine | 24 | 3,976 | ” |
| Sulphuric ether | 0 | 3,801 | ” |
We learn from this table that sound travels with different velocities through different liquids; that a salt dissolved in water augments the velocity, and that the salt which produces the greatest augmentation is chloride of calcium. The experiments also teach us that in water, as in air, the velocity augments with the temperature. At a temperature of 15° C., for example, the velocity in Seine water is 4,714 feet, at 30° it is 5,013 feet, and at 60° 5,657 feet a second.
I have said that from the compressibility of a liquid, determined by proper measurements, the velocity of sound through the liquid may be deduced. Conversely, from the velocity of sound in a liquid, the compressibility of the liquid may be deduced. Wertheim compared a series of compressibilities deduced from his experiments on sound with a similar series obtained directly by M. Grassi. The agreement of both, exhibited in the following table, is a strong confirmation of the accuracy of the method pursued by Wertheim:
| Cubic compressibility | ||
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