A table of corrections accompanies the instrument, showing how much should be added or subtracted from the observed readings to get the true distance.

Interesting results may be attained with this instrument on the velocity of the wind, especially during gales, the air currents in buildings from registers, ventilators or doors slightly open. This forms one of the most efficient means of studying the ventilation of large halls and churches.

SOUND.

61. SIRENE.

Apparatus. An organ bellows capable of giving a perfectly constant current of air under various pressures. One of the best forms is that made by Cavaillé Coll (sold by König) with regulator attached. If preferred, a large gas-regulator may be attached to any bellows. A set of organ-pipes well tuned, giving the notes of the scale from Cg to C, two or three tuning forks, one giving the French normal pitch, etc. and a sirene. The latter need not be of large size, as good results may be obtained with a single moving disk with one circle of holes.

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Experiment. Place the organ-pipe, C, in its hole on the bellows, and connect the sirene so that the air shall pass through it. Work the bellows, and the perforated disk will begin to revolve, at first slowly, giving a rustling or humming sound, and then faster, producing a note of low musical pitch. As the speed increases the pitch rises, until it is about that of the pipe. Sound the latter, and increase or diminish the pressure of the air, so that they shall be precisely together. A slight deviation produces beats, that is, an alternate increase and diminution in the intensity of the sound for every vibration gained or lost by the sirene. By a little practice these beats may be made to take place very slowly, or not at all. The wheelwork of the sirene may be thrown in or out of gear with the revolving shaft, so that the hands may or may not register the number of turns of the perforated disk. Throw it out of gear, and read the position of the hands. Bring the two sounds in unison, and keep them together for a minute, during which time the shaft is thrown in gear, and the hands are moving. The difference of the readings before and after, gives the number of turns, and this multiplied by the number of holes in the perforated disk, give the number of complete vibrations. Dividing

122

by 60 gives the number per second. Repeat with the other pipes, and see if this ratio is that given by theory. Do the same with the tuning forks. This is more difficult as they cannot be sounded continuously. The best method of sounding a tuning fork is by means of a violin bow. The latter should be held near the end of the fork, nearly parallel to the two prongs, but touching only one, and drawn with considerable pressure, and not too rapidly To prevent slipping it should be well rubbed with resin.

62. KUNDT'S EXPERIMENT.

Apparatus. Several glass tubes two or three inches in diameter, and six feet long, one open at both ends, the others closed and filled with different gases, and also containing a little lycopodium powder. A number of rods of brass, steel, glass and wood, and a clamp by which they may be held at the centre. Three of the rods should be of the same material, but one of double diameter, the second half the length, of the third. Cloths which may be wet or covered with resin should be provided to set them in vibration, also some lycopodium powder.

Experiment. Place a little lycopodium powder in the open tube, hold it horizontally by the middle, and rub it lengthwise with a wet cloth. A clear musical note of high pitch is at once produced, and the powder arranges itself in about fifteen to twenty groups at regular intervals along the tube. The reason is, that the air in the interior of the tube vibrates with the same rapidity as the glass, but as the velocity of sound in it is much less, the wave-length is less in the same proportion. Hence dividing the length of the tube by the distance apart of the lycopodium groups gives the relative velocity of sound in glass and air, or multiplying this number by 333 gives the velocity of sound in glass in metres.

If the tube is filled with any other gas than air the interval will be proportional to the velocity. Thus knowing the velocity in glass, the velocity in the gas may be obtained. Make this measurement with the other tubes, and see if the law holds that the velocity is inversely proportional to the square root of the density.

This same method may be applied to the accurate determination of the velocity of sound in solids. One of the rods is clamped at the centre, and the end inserted in the open glass tube. The air

in the latter is confined by a cork at one end, and a disk somewhat smaller than the tube is attached to the rod. The latter is now set in vibration by a cloth moistened with water, for glass, or covered with resin, for wood or metal. The vibrations of the rod are transmitted to the air, and the heaps of sand formed. In general these will not be clearly defined, because the whole length of the air space is not an exact multiple of half a wave-length. The rod should therefore be moved in or out until the heaps are distinctly marked. The velocity of sound in the rod is then obtained by the following calculation. If I is the length of rod, 7 the distance between the heaps of lycopodium, and V 333 (1 + .0037 t), the velocity of sound in air at any temperaᏞᏙ ture t, then the velocity in the rod The temperature t may be taken as equal to that of the room, and measured with a Centigrade thermometer.

63. MELDE'S EXPERIMENT.

Apparatus. A tuning-fork projecting horizontally from a vertical wall, and tuned to give a low note, as C. Four weights in the ratio 1,4,,, made of brass rods cut to these lengths respectively, some fine silk thread, and a millimetre scale. A piece of brass with a hole in it should be fastened to the end of one prong of the fork, and a fine wire hook attached to the silk to support the weights. A violin bow is also needed to excite the fork, or bette, ran electro-magnetic attachment, by which the vibrations may be maintained continuously.

Experiment. By this apparatus the various laws for the vibrations of cords may be proved. 1st. The time of vibration is proportional to the length. Place the fork so that its two prongs shall lie in the same vertical plane, and suspend the largest weight from it by the silk thread. Sound the fork, as described in Experiment 61, and vary the length of the thread until its time of vibration corresponds with that of the fork. When this is the case it will form a loop or spindle, fixed at the ends and swelling out at the centre through several inches. As this occurs only when the cord is very nearly the right length it may be tuned quite accurately by the eye alone. Make three or four observations in this way, measuring the length in each case with the mil

limetre scale. Next turn the fork 90°, so that the prongs shall lie in the same horizontal plane. The cord will now make as many vibrations as the fork, while in the former case it made but half as many. This is evident if the relative positions of the prong and cord are compared. When the prong is in its highest position the cord is straight or central. As the prong descends it moves to the right, and as it ascends again becomes central. At the next descent of the prong it moves to the left, becoming central a second time, when the prong has reached the top. It thus makes only one complete vibration, while the fork makes two. Accordingly when the fork is turned around 90°, the cord will be set vibrating exactly twice as fast as before. On trying the experiment it will be found that the new length of cord required will be just one half that in the first case. That is, a double length requires a double time.

2d. The time of vibration is inversely proportional to the square root of the tension. Applying the four weights in succession, the corresponding lengths are proportional to 1, 2, 3 and 4, or since for equal tensions the times are proportional to the lengths, the law is proved.

3d. The time is proportional to the diameter of the cord. A second cord of precisely twice the diameter of the first, may be made by twisting four strands of the former. It will be found that the length must be reduced one half to obtain the same effect as before.

All these laws may also be proved by preparing a string of such a length that it will vibrate as a whole, when the larger weight is applied, then attaching the other weights it divides into 2, 3 or 4 loops, separated by fixed points or nodes, and corresponding to the harmonics of the cord. A second string of double thickness serves to prove the 3d law. A simple proof of the first law may also be obtained by a second fork an octave higher than the other.

64. ACOUSTIC CURVES.

Apparatus. In Fig. 47, A is a large tuning-fork capable of giving out at least one harmonic besides its fundamental note, and carrying on the end of one of its prongs a piece of sheet brass cut to a point. B is a little carriage on which a piece of smoked