III. (1) Photographic Methods.-Professor Blake of Broner University has recently contributed to the American Journal of Science an ingenious method of photographing vibrations.

It is not necessary to enter into all the details of this valuable contrivance; but it is obvious that as with a tuningfork vibrating at a standard rate, velocities of rotation can be accurately determined, so with a steady standard of rotation, the error of a tuning-fork from its theoretical vibration-number can be immediately detected.

Fig. 50.-Professor Blake's method of photographing vibrations.

From the centre of the vibrating disc, made of thin iron as in the telephone, a wire projects which is connected by a short arm with the back of a small steel mirror capable of rotating in a vertical direction between two steel points. The reflecting surface of the mirror is firmly fixed perpendicular to the vibrating disc. A heliostat sends a beam of sunlight horizontally into a dark closet, and at a distance of several feet falls upon the mirror, which is inclined 45° to the horizon. The rays reflected vertically downwards pass through a lens, at the focus of which they form a luminous image of the opening of entry. A carriage moving smoothly on four wheels travels beneath the lens at such a distance that a sensitized plate laid upon it is at the focus for actinic rays. Uniform velocity is given to the carriage and is measured by a tuning-fork of 512 vibrations fitted with a style. If the carriage be set in motion alone a straight line is photographed. But on causing the disc to vibrate, each of its movements carries the reflected beam from the oscillating mirror through twice the angle of the mirror's motion. Curves are thus recorded on the photographic plate, the abscissæ of which are measured by the known velocity of the plate and carriage, and which serve to determine the pitch; the ordinates representing the amplitude of vibration of the centre of the disc magnified in this case 200 times. With the voice, speaking in an ordinary tone an amplitude of nearly an inch is obtained. This contrivance has been applied more to the analysis of vowel-sounds than to determinations of pitch; though it is obviously a form of graphic determination, and therefore deserving of record in this place.

The beautiful transcript on p. 99 was obtained by this method.

(2) Scheibler's Method. The first person who hit upon a practical method of obtaining exact measurement was Scheibler, of Crefeld, who described it in a pamphlet published in 1834. His system, as modified by Helmholtz's more recent researches, is thus described. If we strike a tuning-fork, with another an octave higher, and hold them both over their proper resonance chambers, we shall hear no beat, even if they are out of tune. But if they are applied to a sounding-board, a beat may be heard between the second partial of the lower, and the lowest of the upper fork. If both be held over the resonance chamber of the upper fork, the beat is heard inore distinctly. Counting the number of beats in a second, they give the difference between the number of vibrations of the upper fork, and double the number of the lower. Suppose

1 Journal of Society of Arts, May 1877.

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the forks P and Q, of which Q is nearly an octave above P, when sounded together beat n times in a second, where n is less than A; then n will be the difference between the number of vibrations in Q, and twice those in P. But the beats do not tell us whether Q is too sharp or too flat. To discover this, tune a third fork R sharper than Q, and making four beats in a second with it. Try the beats of P and R. If they are n + A, then Q was too flat; but if they are 4 n, then Qwas too sharp. Using P, Q, R, to represent the pitches of these notes, we have, when is too flat, 2P Q+n, and when Q is too sharp, 2P : n. Then interpose between P and Q (supposed to be too flat) so many tuning-forks that each beats with its neighbour, or with P or Q, either four times in a second or less. Suppose the sum of these beats to be m. Then QP+ m, and since 2P = Q +n, we have P = m +n ; so that the number of vibrations is the sum of all the beats heard, including those with the imperfect octave. But when P is known, the pitch of all the intermediate forks is also known. In Scheibler's case he tuned Q so as to make no beats with 2P; so that Q = 2P, n = o, and P = m. He then constructed 52 forks, and found P = 2193, Q = 439, and the pitch of the intermediate forks was regulated so as to include the complete equally-tempered scale. In this case P was A on the second ledger-line below the treble staff, and Q was the usual A on the open string of a violin. Scheibler subsequently adopted 440 in place of 4393 for his A. Having this scale complete, he had only to sound another fork beside these in turn to determine, by counting the beats, between which two it lay, and by how many vibrations it was sharper than one, and flatter than the other, the exact pitch of which was known. Very slow beats are difficult of observation, from the difficulty of distinguishing the falling off of the sound which naturally occurs from that which is due to interference. Scheibler, therefore, somewhat modified his plan, by using forks which were intentionally dissonant with the note to be determined, and beating with it some convenient number of times in a second. By reproducing the same number of beats on the instrument to be tuned as existed between the original standard and the intermediate fork, great accuracy could be obtained.

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A still closer approximation has been obtained in counting beats, by the employment of a metronome pendulum, the period of vibration of which can be varied, and against which the beats may be compared. This instrument was originally used by Scheibler, but has been materially improved by Mr. Bosanquet.

(3) Appunn's Reed Tonometer.-Appunn has substituted free harmonium reeds for Scheibler's forks. These, although somewhat more affected by changes of temperature than tuning-forks, have the advantage of producing a louder and more coercive tone. The reed quality is peculiarly rich in upper partials, producing a strong, hard, and somewhat harsh sound, which is of great service scientifically, because it perfectly discriminates all the consonances, allowing a slight error to be immediately detected by dissident beats. The arrangement of Appunn's instrument is as follows:-Sixtyfive reeds are arranged in a long rectangular box, and excited by a steady wind-pressure. The reeds each act in a separate chamber, controlled by a wire which opens a valve fully, or to any smaller amount. By pushing in the valve, the note is flattened up to about 2 vibrations in a second. The reeds are so tuned that each beats exactly four times a second with either of the adjacent reeds. The lowest is numbered 0, and the highest 64. Consequently the highest is four times 64, or 256 vibrations sharper than the lowest. The lowest and highest, sounded together, make a perfect octave. The difference between the numbers of vibrations being 256, it follows from what has been shown above, that the lowest reed makes 256, and the highest 512 vibrations in a second.

Unfortunately this apparatus is materially influenced by the power which the reeds, when vibrating strongly, have of influencing one another. Determinations made with it by Mr. Ellis are disputed by M. Koenig, and Lord Rayleigh has recently added some excellent evidence to the same effect.

IV. (1) Mayer's Electrical Tonometer is described by Mr. Ellis, from an unpublished letter of the inventor. The seconds pendulum of a clock has a wedge of platinum foil attached to its lower extremity, which, at every swing, passes through a globule of mercury, placed vertically under it in the cup of an iron binding-screw connected with one wire of a small battery, of which the other wire is connected to the primary coil of a large inductorium, whence a wire passes to the top of the pendulum. By two other wires the secondary coil of the inductorium is connected with a tuning-fork and a revolving cylinder. The tuning-fork carries a delicate piece of platinum, which, as the cylinder revolves, will mark a curve on its smoked surface. Every time the pendulum leaves the mercury globule, a single spark is projected from the foil on the fork, which pierces the covering of the cylinder, and marks the beginning and end of the second. As the mercury globule may not be truly under the point of suspension, the

length of every two seconds is used. The number of sinuosities of the curve between the spark holes, divided by two gives the pitch of the fork. This method is very accurate, but seems to be slightly influenced by the weight of the platinum on the fork, and also by the friction on the cylinder, as will be noticed further on.

(2) Lord Rayleigh's Experiment.-1A standard fork by Koenig which was supposed to give 128 vibrations in a second was excited by means of a bow, and the object was to compare its frequency with the seconds pendulum of a clock keeping good time. The remainder of the apparatus consisted of an electrically maintained fork interruptor with adjustable weights, making about 12 vibrations per second, and a dependent fork, the frequency of which was about 125. The current from a Grove cell was rendered intermittent by the interruption, and as in Helmholtz's vowel experiments excited the vibrations of the second fork, the period of which was as nearly as possible an exact submultiple of its own. When the apparatus was in steady operation, the sound emitted from a resonator associated with the higher fork had a frequency determined by that of the interruptor and not by that of the higher fork itself; nevertheless an accurate tuning now necessary in order to obtain vibrations of sufficient intensity. This tuning was effected by prolonging as much as possible the period of the beat heard when the dependent fork starts from rest. The beat may be regarded as due to an interference of the forced and natural notes. By counting the beats during a minute of time it was easy to compare the higher fork and the standard with the necessary accuracy; all that remained being to compare the frequencies of the interruptor and of the pendulum. For this purpose the prongs of the interruptor are provided with small plates of tin so arranged as to afford an intermittent view of a small silvered bead carried by the pendulum, and suitably lighted. Under the actual circumstances of the experiment, the bright point of light is visible in general in twenty-five positions, which would remain fixed if the frequency of the interruptor were exactly twenty-five times that of the pendulum. In accordance, however, with a well known principle, these twenty-five positions are not easily observed when the pendulum is simply looked at; for the motion then appears to be continuous. The difficulty is easily evaded by the interposition of a somewhat narrow vertical slit through which only one of the twenty-five positions is visible. In practice

Nature, November 1, 1877.