rest. The space through which the cord oscillates, or the amplitude of the oscillations, diminishes, but the

D

Fig. 1.

time required for a small oscillation is the same as that required for a large one.

Amplitude of Vibration in Air.-In like man-ner during the passage of the sound-wave through the air, each particle of air oscillates to and fro, giving motion to neighbouring particles in all directions, and these again in their turn impart motion to the surrounding air; just as, in a large crowd of people, we see the agitation of the centre gradually spread to the outer circles by the motion passing from one person to another. Although sound may be heard at great distances, yet each particle of air makes only a short journey to and fro, called its amplitude of vibration.

Elasticity and Density. The velocity of sound depends upon the elasticity of the air, and also upon its density or weight. The elasticity of air is measured by the pressure which it can sustain. At the sea-level this pressure is equal to that of a column of mercury 30 inches in height; on a high mountain the pressure is less in proportion to the height.* In this case the air would be said to have less elasticity on the top of

*For a rise of 590 feet the mercury column falls one inch. (See Exercise I.)

the mountain than at the sea-level. If air be heated in a closed vessel its elasticity increases, whilst the weight remains the same; the velocity of sound passing through such air is increased. If the air of the open atmosphere be heated it expands, its elasticity remains the same, while the weight is lessened, and, as before, the velocity is increased. The velocity of sound in a warm temperature is therefore greater than in a cold one. Now we see the reason for saying that at a freezing temperature the velocity of sound is 1,090 feet per second, and the increase for rise in temperature is about 2 feet for every degree centigrade. It is common to take the velocity of sound at 1,120 feet per second, the temperature being at 62° F. When this is the case, a rise of 13 inches for every degree Fahrenheit must be allowed.

From this it is easy to calculate the velocity of sound when the temperature is given, and with a given velocity to ascertain the temperature of the air. (See Exercise I.)

From the known velocity of sound, it is not difficult to calculate the distance between two places. Let a pistol be fired at the distant place, and note the time carefully between seeing the flash and hearing the report. Let this interval of time be expressed in seconds and multiplied by (1,090 + 2 t). This will give the distance in feet, and the value will be given by the centigrade thermometer. In this calculation the direction and velocity of the wind are neglected. (See Exercise I)

It must be borne in mind that it is neither the elasticity nor the density alone that affects velocity, but the two together, according to the relation which exists between them, and in accordance with the following laws:

1. The velocity of sound is proportional to the square root of the elasticity of the medium.

2. The velocity is inversely proportional to the square root of the density.

Thus, in the example of the air heated in a closed vessel, if the elasticity be increased four times, the velocity will be doubled. The velocity would also be doubled if the density in the second case were reduced to; so that if the two vary alike they act upon the velocity in contrary directions, and exactly neutralize each other. The law of Mariotte and Boyle shows that they do thus neutralize each other if the temperature be the same in the substances under experiment. The law may be demonstrated by an instrument known as Mariotte's tube (Fig. 2). It consists of a long glass tube, bent at the end and open at the top of the long limb only; both the limbs are graduated. A small quantity of mercury is put into the tube, so as to mark off a certain volume of air which is now under ordinary atmospheric pressure. Reduce the volume of the air one-half by adding more mercury, and it will be found that the mercurial column is exactly the height of the barometer column of mercury; that is, you have doubled the pressure to obtain half the volume. Other similar experiments will still further demonstrate the law that, "temperature remaining the same, the volume of a gas is inversely as the pressure."

Fig. 2.

A beautiful illustration of the law as applied to density, elasticity being the same, is shown in the velocities of sound in the gases hydrogen and

oxygen :

Hence the density is as 1 to 16, therefore velocity is in the case of oxygen against 1 in hydrogen.

The Air-pump.-Perhaps the instrument known as Tate's is at the same time the simplest and most efficient, Fig. 3. It consists of a cylinder and double

piston, a b, in the form of a syringe, placed horizontally on a wooden foot c. At each end the air is expelled as it passes from the receiver d down the tube e. In this tube stopcocks are placed to pre

serve the vacuum when obtained, or to readmit the air. The syringe at the base may be used for compressing air if the vessel to be filled is attached to the end a.

EXPERIMENTS.-Remove the receiver, and attach by a screw, which enters the plate f, a globe provided with a stopcock; exhaust the air, then carefully weigh the globe; readmit the air, and weigh again. The difference between the two weights will show the weight of the volume of air contained by the globe.

Again close the end a of the syringe, cut off communication with the receiver. Force the air in the syringe to the end a, remove the pressing force, and it will be found that the piston will return to its former position with a force equal to the pressure formerly applied. This demonstrates the elasticity of the air compress a bladder containing any gas, remove the force, and it will return to its former volume. Many other simple experiments to demonstrate this elasticity of gases will occur to the thoughtful reader.

Again that air is necessary for the passage of sound is easily proved by the experiment of enclosing a bell within the receiver of an air-pump. As the exhaustion of the air proceeds, the sound of the bell grows fainter and fainter, until at last it nearly dies away. The hammer is seen to strike the bell, but there is no sound, because there is no medium to convey these undulations to the ear. The experiment is never quite successful, owing to the impossibility of obtaining a perfect vacuum, and insulating the bell from the metallic plate of the air-pump. Sound is also transmitted through water, wood, metals, &c., but with different velocities. Through water it moves more rapidly than through air, and with increased velocity as the temperature of the water increases. At