HEAT.
We see also from the formula that the velocity is inversely as the square root of the density of the gas—the pressure being the same. Thus a sound-wave travels about loin times faster in hydrogen than in air.
Also we see that, within the limits of approximation we have used, the velocity does not depend upon the intensity, pitch, or quality of the sound (q.v.). The investigations which seem to lead to slight modifications of this conclusion are too recondite to be intro (limed here. We can only mention, also, the beautiful investigations of Stokes (q.v.) connected with the extinction of a sound-wave as it proceeds, partly by fluid friction, partly by radiation. And we may conclude by stating that the result of a completely general investigation of the velocity of a sound-wave gives, to a first approximation, the result we have deduced from the study of a simple particular case.
We now come to the consideration of waves in water. Of these, there are several species. One, however, we may merely mention, as its theory is the same as that just briefly discussed. This is a sound-wave, or wave of compression, in water. Its velocity is considerably greater than that of sound in air (see SouND). The others, which are commonly observed on the surface of water, depend on mere changes of level, and their effects; and in studying them, we may consider water as incompressible.
The first of these is what is called a long or solitary wave. Its essential characteristic is, that its length is great compared with the depth of the liquid in which it moves. To this class belong the tide-wave (see TIDES), and the long wave which accompanies a canal-boat, and which we see slowly traversing the canal when the boat is stopped. Scott Russell has made many interesting observations on this wave, all of which accord 'well with the results of the mathematical theory of its propagation. The velocity of this wave depends solely on the depth, not on the density of the liquid in which it moves —and in a uniform canal the velocity is that which would be acquired by a stone falling freely through a space equal to half the depth of the water, Another characteristic of this wave is that, after it has passed, it leaves the water bodily transferred through a small space along the bed of the canal—forward or backward, according as it consists of an elevation or a depression of the water-surface. Scott Russell has shown that the most favorable rate at which a canal-boat can be drawn is when its velocity is such that it rides on the crest of the solitary wave. If drawn at any other speed, it leaves the solitary wave behind, or is left by it; and in either case, part of the horse's work is expended in producing fresh solitary waves. An excellent mode of observing these waves is to tilt slightly a rectangular box containingsbme water, and restore it to its origi nal position. A long wave is thus formed, which is reflected repeatedly at the ends of
the box, and whose rate of motion may be accurately observed by watching the image of a candle reflected at the surface of the water. If the sides of the box he made of glass, and some light particles be dispersed through the water, their motions enable us to dis cover all the circumstances of the propagation of this wave.
We next come to what are called oscillatory waves in water or other liquids. To this class belong all waves whose length from crest to crest is small compared with the depth of the liquid; from ripples on a pool to the lona. roll of the Atlantic. They are never as solitary waves, their general characteristic being their periodical recurrence. And, by watching a piece of cork floating on the surface, we see that it moves forward when at the crest of the wave, and backward through an equal amount when in the trough. Also it rises while passing from the trough to crest, and sinks from crest to trough. Mathematical investigation, confirmed by experiments with floats at sea, and with short waves in the glazed box before described, shows that each particle of the water describes a circle about its position of rest in the vertical plane in whtch the wave is advancing. Particles at greater and greater depths describe smaller and, smaller circles. The diameters of these circles diminish with extreme rapidity. At a depth equal to the distance from crest to crest (i.e., the length of the wave), the displae-ment of the water is already only of that at the surface. At the depth of two wave lengths, it is about Taismy of that at the surface. Thus we may see to how small a depth the ocean is agitated even by the most tremendous wind-waves; for, according to Scoresby, 43 ft. is about the utmost difference of level between crest and trough in ocean waves. if the wave-length be 300 ft. (which is a large estimate), then at a depth of 300 ft. the water-particles describe circles whose radii are only the 24.2 of a foot, or about four-tenths of an in.; and at 600 ft. this is reduced to of an in.; while the depth Of the Atlantic is in many parts more than three or four miles. In this case, the velocity of propagation of the wave has been shown to be 27r where g is, as before, 32.2 ft.; 1 is the wavelength in feet; and is the ratio of the circumference of a circle to its diameter (see QUADRATURE ON TIIE CIRCLE). Thus the velocity of an oscillatory wave in deep water is proportional to the square root of its length. This fact has been of use as an analogy in helping us to account for the disper sion (see REFRACTION) of light, where, by experiment, we know that the waves of red light are longer than those of blue light, and also that they travel faster in refracting media.