shown in Fig. 43. Then put into a piece of India-rubber tube a glass tube having its interior about the diameter of the holes in the card disk. We are now ready for our experiments.

EXPERIMENT 77.-Rotate the disk slowly, and, placing the glass tube before a ring of holes, blow through the tube. You will observe that whenever a hole comes before the tube a puff of air goes through the disk. If the disk is revolved faster the puffs become more frequent, and soon, on increasing the velocity of the disk, they blend into a sound. Not very pure, it is true; but yet, in the midst of the whizzing, your ear will detect a smooth note. Fixing your attention on this note, while the rotator is urged with gradually increasing velocity, you will hear the note gradually rising in pitch. This again shows us that the pitch of a sound rises with the frequency of the vibrations causing it.

Two bodies make the same number of vibrations in a second when they give forth sounds of the same pitch. Therefore, if we can measure how many vibrations the disk makes in a second while it gives the exact sound of one of the forks, we will have measured the number of vibrations which the fork makes in a second. If we count with our watch the number of turns the crank C makes in one minute, we can from this knowledge calculate the number of puffs or vibrations the disk makes in one second, as follows: One revolution of the crank of the rotator makes the disk go round exactly five times. Now, suppose that the tube is before the third circle, having 36 holes, and that in one minute the crank C turns round 100 times. Then in one minute the disk turned 5 times 100 times, which is 500 times. But for each turn of the disk 36 puffs or vibrations were made on the air; there

fore, 36 times 500, or 18,000, puffs or vibrations were made by the disk in one minute, and of 18,000, or 300,

in one second.

But it is difficult to know just when the disk gives the same sound as the fork, and it is yet more difficult to keep the disk moving so that it holds this sound, even for a few seconds. To do this, very expensive apparatus has heretofore always been needed. But I did not wish to banish from our book such an important experiment, so I found out a cheap and simple way of doing it, which I will show you.

EXPERIMENT WITH THE SIREN, IN WHICH IS FOUND THE NUMBER OF VIBRATIONS MADE BY A TUNING-FORK IN ONE SECOND.

EXPERIMENT 78.-Get a glass tube (the same we used in the experiment on page 50 of "Light") 4 inch (19 millimetres) in diameter and 12 inches (30.5 centimetres) long, and a cork 1 inch thick, which slides neatly in the tube. Put the cork into one end of the tube, and holding a stick upright press the cork down on it. The fork is now vibrated and held over the open end of the tube, while the cork is forced up the tube with the stick till the column of air in the tube is brought into tune with the fork. This you will know by the tube sending out a loud sound. Try this several times till you are sure of the exact place where the cork should be to make the tube give the loudest sound.

Now lay the fork aside, and with small pieces of wax stick the tube on the top of a block, or on a pile of books, with its mouth near the disk and facing one of the circles of holes, as shown in Fig. 43. On the other side

of the disk, and just opposite the mouth of the resonant tube, hold the small tube through which you blow the air.

Turn the crank at first slowly, then gradually faster and faster. Soon a sound comes from the tube. This gets louder and louder; then, after the disk has gained a certain speed, the sound grows fainter and fainter, till no sound at all comes from the tube.

When the sound from the tube was the loudest, the disk was sending into the tube the same number of vibrations in a second as the fork makes; for the tube was tuned to the fork, and can only resound loudly when it receives from the disk of the siren the same number of vibrations in a second as the fork gives.

It is, then, quite clear that, to find out the number of vibrations per second given by the fork, we first have to bring the disk to the velocity that makes the tube sound the loudest, and then to use this sound as a guide to the hand in turning the crank of the rotator. Practice will soon teach the hand to obey the check given by the ear; and if the student have patience, he will be rewarded when he finds that he can keep the tube sounding out loudly and evenly for 20 or 30 seconds. Then we count the number of turns made by the crank-handle C of the rotator in 20 or 30 seconds of the watch. If we have succeeded in this, we can at once calculate the number of vibrations the fork makes in one second.

The following will show how this calculation is made: EXPERIMENT 79.-The cork was pushed to that place which made the air in the tube resound the loudest to the A-fork. The tube was then placed facing the circle of 36 holes. After we had succeeded in making the tube resound loudly and evenly to the turning disk, I counted the number of turns I gave to the handle C in 20 seconds,

and I found this number to be 49. For one revolution of the handle C, the disk makes exactly five. Hence 5 times 49, or 245, is the number of turns the disk made in 20 seconds. But in one turn of the disk 36 puffs or vibrations entered the tube; therefore, 245 times 36, or 8,820, is the number of vibrations that went into the tube in 20 seconds; and of 8,820, or 441, is the number of vibrations which entered the tube in one second.

The experiment, therefore, shows that the tube resounds. the loudest when 441 vibrations enter it in one second. But the tube also resounded its loudest when the vibrating A-fork was placed over it. Hence the A-fork makes 441 vibrations in one second.

EXPERIMENT 80.—Let the student now try to find out by a like experiment the number of vibrations made by the C-fork in one second. Repeat these trials many times till numbers are found which do not differ much from one another.

FINDING THE VELOCITY OF SOUND BY AN EXPERIMENT WITH THE TUNING-FORK AND THE RESONANT TUBE.

EXPERIMENT 81.-Our experiment (78) with the glass tube has taught us that the tube must have a certain depth of air in it to resound loudly to the A-fork. Let us measure this depth. We find it to be 7 inches (19.47 centimetres) when the air has a temperature of 68° Fahr.

From this measure, and from the knowledge that the A-fork makes 441 vibrations in one second, we can compute the velocity of sound in air.

It is evident that the prong of the fork over the mouth of the tube, and the air at the mouth of the tube, must swing to and fro together, otherwise there will be a strug

gle and interference between these vibrations, and then the air in the tube cannot possibly co-vibrate and strengthen the sound given by the fork.

We have already learned that the prong of the fork in going from a to b, Fig. 45, makes one half wave-length in the air before it. This may be represented by the curve b c d above the line b d. Now the tube T' must be as long as from b to c, or one-quarter of a wave-length; so that, by the time the prong of the fork has gone from a to b, and is just beginning its back-swing from b to a,

the half-wave b c d has just had time to go to the bottom of the tube T, to be reflected back, and to reach the prong b at the very moment it begins its back-swing. If it does this, then the end of this reflected wave (shown by the dotted curve in the tube T') moves backward with the back-swing of the prong b, and thus the air at the mouth of the tube and the prong of the fork swing together, and the sound given by the fork is greatly strengthened.

If the depth of the quarter of the wave made by the A-fork is 7 inches (19.47 centimetres), the whole wave is