For water at 8°.1 C. (the temperature of the Lake of Geneva in Colladon's experiment) we have E = 2.08 x 1010, D= 1 sensibly; the velocity as determined by Colladon was 143500. 94. For the propagation of sound along a solid, in the form of a thin rod, wire, or pipe, which is free to expand or contract laterally, E must be taken as denoting Young's modulus of elasticity.* The values of E and D will be different for different specimens of the same material. Employing the values given in the Table (§ 64), we have 95. If the density of a specimen of red pine be 5, and its modulus of longitudinal elasticity be 1.6 x 106 pounds per square inch at a place where g is 981, compute the velocity of sound in the longitudinal direction. *Strictly speaking, E should be taken as denoting the elasticity for sudden applications of stress-so sudden that there is not time for changes of temperature produced by the stress to be sensibly diminished by conduction. This remark applies to both §§ 93 and 94. For the amount of these changes of temperature, see a later section under Heat. By the table of stress, at the beginning of this volume, a pound per square inch (g being 981) is 6.9 × 101 dynes per square centim. Hence we have, for the required velocity, 96. The following numbers, multiplied by 105, are the velocities of sound through the principal metals, as determined by Wertheim : : The following velocities in wood are from the observations of Wertheim and Chevandier, Comptes Rendus, 1846, pp. 667 and 668 :— Musical Strings. 97. Let M denote the mass of a string per unit length, F دو stretching force, length of the vibrating portion; then the velocity with which pulses travel along the For the four strings of a violin the values of M in grammes per centimetre of length are 00416, 00669, 0106, 0266. The values of n are 1955; 660, 440, 293, and the common value of L is 33 centims. Hence the values of v or 2Ln are 43560, 29040, 19360, 12910 centims. per second; and the values of F or Mv2, in dynes, are 7.89 × 10o, 5·64 × 10o, 3.97 × 10, 4·43 × 106. Faintest Audible Sound. 98. Lord Rayleigh (Proc. R. S., 1877, vol. xxvi. p. 248), from observing the greatest distance at which a whistle giving about 2730 vibrations per second, and blown by water-power, was audible without effort in the middle of a fine still winter's day, calculates that the maximum velocity of the vibrating particles of air at this distance from the source was 0014 centims. per second, and that the amplitude was 8.1 x 10-8 centims., the calculation being made on the supposition that the sound spreads uniformly in hemispherical waves, and no deduction being made for dissipation, nor for waste energy in blowing. F 82 vacuo. CHAPTER VIII. LIGHT. 99. ALL kinds of light are believed to have the same velocity in vacuo. The absolute index of refraction for light of given refrangibility in a given medium is equal to the quotient obtained by dividing the velocity of that kind of light in the medium into the velocity of light in The frequency of vibration (that is the number of vibrations per second) is unchanged when a ray passes out of one medium into another; but the wave-length changes in the inverse ratio of the index of refraction. The product of the wave-length in any medium by the index of refraction for that medium is equal to the wavelength in vacuo. 100. The best determinations of the velocity of light are those of Michelson and Newcomb, by the method of the revolving mirror, and of Cornu, by the method of the toothed wheel. The resulting velocity in vacuo is about 2.999 × 1010 centims. per sec. X Professor Newcomb remarks that the value 299860 km. per sec. for the velocity of light, combined with Clarke's value 6378.2 km. for the earth's equatorial radius, |