directed by a nozzle against one of the circles of holes. As each hole passes the nozzle, a puff of air rushes through and sends out a wave. The succession of waves produces a musical note, which must be tuned to the given note. This may be done more readily by fixing behind the rotating disc a "resonator," i.e. a vessel shaped so as to sound the given note when blown into. The air in this is set vibrating sympathetically by the waves issuing through the holes, and sends out a loud and clear note when the disc is going at the right speed. If an attached counter shows N revolutions in t seconds, and if the holes in the circle are n in number, then the frequency of the note sounded is as with the toothed wheels Nn/t.

The instrument shown in Fig. 6 is a combination of Savart's and Seebeck's instruments. Neither would be now used for any exact experiment.

Cagniard de la Tour's Siren.-A common form of this instrument is represented in Fig. 16. A small horizontal circular disc, ss, with a circular row of holes in it, is mounted on a vertical axis, so that it turns close to the top, but just clear of a hollow box, A, having a similar row of holes in its top cover. Air is blown into the box from a bellows, and when the holes in the disc coincide with those in the box, a puff issues through each. These separate puffs all coincide to give one big wave. Each time, therefore, that a hole in the disc moves one place on, a wave is sent out; and if n is the number of holes, and N the number of revolutions in t seconds, Nn/t is the frequency of the note sounded. A screw thread, t, on the spindle turns the mechanism which counts N. By cutting the holes in the box and disc slanting in opposite ways, as shown in the section in the lower right-hand side of Fig. 16, taken through nn in the upper righthand figure, the stream of air is made to drive the instrument as well as to give the note. This device was adopted by the inventor, and has been followed since by instrument-makers, but it detracts very much from the exactness of the instrument. With the air blast as motive power it is exceedingly difficult to maintain a constant speed, the tendency being to a gradual increase.

The counter, too, in the ordinary arrangement with an impulse on the slow wheel after every revolution of the quick wheel, is objectionable as making the running jerky. Helmholtz, who used a modified form of the instrument in his celebrated researches, drove it by an electric motor, and used the stream of air merely as a sound producer. No doubt this plan would be always followed, if the instrument were required for exact work, now that good electro motors are so easily obtained.

As a matter of curiosity, we must mention the fact that the siren sounds under water if entirely immersed and driven by a stream of water.

Dove modified the instrument by having several circles of holes in the disc, any one of which can be used at will. Helmholtz1 used a double siren with this modification, in which two discs were mounted on the same vertical spindle with one wind-chest below the lower disc, and the other above the upper disc. The upper wind-chest could be turned about the axis into any re

FIG. 16.-Cagniard de la Tour's Siren, about scale.

A. Wind-chest perforated with a circle of holes at the top; s, rotating disc perforated with an equal circle of holes. The slope of the holes in chest and disc is shown in the lower right-hand figure, which is a section tnrough n n in the upper right-hand figure.

quired position by means of a pinion gearing with a toothed wheel attached to the top of the chest. By this arrangement, if the two sirens were sounding the same note, the difference of phase could be made zero or anything desired by making the opening of the upper holes coincide with those of the lower holes,

1 Sensations of Tone, 1st Eng. ed., p. 243.

or by making them lag behind by the proper amount. The air stream was produced by a stiff paper turbine attached to the disc. Helmholtz succeeded in producing extremely constant notes with this siren, and with a good device for recording the number of revolutions in a given time, it would probably be as good as any other instrument for the determination of absolute frequency.

Scheibler's Tonometer.-This consists of a series of tuningforks spread over an exact octave and ascending by equal steps in frequency from the lowest to the highest. The steps are so short that the beats between two consecutive forks can be easily counted. When the series is exactly adjusted the number of beats between all the consecutive pairs is the same. It is then easy to calculate the pitch of any one fork. For suppose that there are in all sixty-five forks, and that the lowest makes n vibrations per second; the highest, being its octave, makes 2n vibrations per second. The adjustment of these two with each other directly is possible, since, for a reason to be given later (Chapter X., Combination Tones, p. 155), any inaccuracy in tuning would lead to beats of frequency equal to the difference between 2n and the frequency of the higher fork. Let the steps in frequency of the intermediate forks be four per second, each adjusted exactly by means of the beats. This can be done, since four beats per second can be counted easily for a long time. Then the series of forks, which we may represent by

Thus the frequency of every fork is known.

64

n+64 × 4

The tonometer, though extremely troublesome to adjust, is, when once made, not only an exceedingly accurate, but also an exceedingly constant register of absolute frequency, for the physical properties of forks remain practically constant. The effect of temperature change is the only variable element, and this is only slight, being, according to M'Leod and Clarke, a decrease of frequency of about 00011 per 1° rise in temperature (see p. 129).

Of course, any other source of frequency within the range of the tonometer may be determined by counting its beating frequency with the fork nearest in pitch to it. If all the forks are available, it is easy to find whether the source is sharp or flat with regard to the nearest fork, and therefore whether the beats

are to be added to or subtracted from the frequency of the fork. For, if sharp, it will beat more with the lower than with the higher neighbour of the given fork; if flat, the reverse will hold. If there is only the one fork available, then either the frequency of the fork or that of the source must be slightly altered. In the case of the fork, this may be done by loading one prong with wax. The effect on the beats is obviously opposite in the two cases, reducing them if the source is flat, and increasing them if it is sharp.

Appunn substituted free harmonium reeds for forks to form a tonometer, but with a loss of accuracy; for Lord Rayleigh has shown that the consecutive reeds affect each other's frequencies, so that a reed has different frequencies when sounding with each of its two neighbours. He was thus able to explain certain discrepancies found by Ellis between the stated frequencies of some forks made by Koenig and these as determined by the reed tonometer.1

GRAPHIC METHOD OF DETERMINING FREQUENCY.

In this method either a vibrating source or a receiver affected by waves from it is made to write its vibrations on a prepared moving surface. The simplest device is illustrated by Fig. 17, where a light style affixed to one prong of a fork writes its vibrations on the surface of a drum covered with smoked paper.

To measure the number of vibrations in a given time, the fork and drum may form part of the secondary circuit of an induction coil, and through the primary of this short currents may be sent by a clock, which makes the circuit at definite known intervals. There will then be a spark from the style to the drum, which will mark the paper at each signal, and the number of vibrations between two successive marks may be counted. Another method of marking known intervals consists in placing a second style level with the first and working it by the currents from the clock.

The source to be determined is to be sounded with the fork and the difference of frequencies determined by the beats.

This arrangement of fork and drum is really more often used as a chronograph, i.e. as an instrument for measuring intervals of time, assuming the frequency of the fork to be known. For instance, suppose that it is desired to know the exact time of fall of a body through a certain height, it may be made to break a circuit at the start and again at the arrival at the lowest point. If this circuit is the primary of a coil, the interruptions of current may be made to give sparks from style to drum by including them in the secondary circuit; then, on counting the vibrations between the marks made on the drum by the sparks, the time of fall is known.

Electric Maintenance of Tuning-forks. For chronographic and other purposes it is often necessary to keep a fork, such as 1 Nature, xvii. 1877, p. 13.

that used with the revolving drum, in vibration for a long time together. The general principle of electric maintenance will be, perhaps, most easily understood from a description of the mode of action of a fork used by Helmholtz, and represented diagrammatically in Fig. 18.

If the fork is held in position, it will be seen that the circuit is completed through the upper prong of the fork, the mercury cup, and the electro-magnet coils. But the poles N. and S. tend to draw the prongs apart, and if the fork is released, they fly outwards; contact is broken in the cup, and the poles are demagnetised; the prongs fly back, make contact again, and so

on. During the outward motion of the prongs, the magnet is doing work on the fork, and during the inward motion the fork is doing work on the magnet. If these quantities of work were equal, on the whole no energy would be drawn from the electrical system, and the vibrations would die away. But for two reasons the former quantity of work is the greater, viz. (1) that the break of contact is delayed by the adhesion of the mercury to the platinum tip of the wire, while the make is delayed as the point does not at once break through the film; and (2) that the effect of self-induction is to delay the full magnetisation at make during the motion inwards, and to sustain the magnetisation by the