50 cm. long-we get the value of the surface tension. The adjustment for level should be made more than once, and the observations of weight repeated. Experiment.-Determine the surface tension of water by the capillary multiplier. Enter the results thus: Length of strip in contact, given with instrument, 100 cm. A MUSICAL note is the result of successive similar disturbances in the air, provided that they follow each other at regular intervals with sufficient rapidity. Similar disturbances following each other at regular equal intervals are said to be periodic. The interval of time between successive impulses of a periodic disturbance determines the pitch of the note produced-that is, its position in the musical scale. The pitch of a note is therefore generally expressed by the number of periodic disturbances per second required to produce it. This number is called the 'vibration number,' or 'frequency' of the note. It generally happens that any apparatus for producing a note of given frequency produces at the same time notes of other frequencies. The result is a complex sound, equivalent to the combination of a series of simple sounds or tones. The simple tones of which the complex sound may be regarded as consisting are called 'partial tones;' the gravest of these-that is, the one of lowest pitch-is called the 'fundamental tone' of the sounding body, and the others are called 'upper partials.' A note which has no upper partials is called a pure tone. By means of suitable resonators the different partial tones of a complex note may be made very clearly audible. For many musical instruments, as organ-pipes, string instruments, &c., the ratio of the vibration frequency of any upper partial tone to that of the fundamental tone is a simple integer, and the upper partials are then called 'harmonics;' for others, again, as for bells, tuning forks, &c., the ratios are not integral, and the upper partials are said to be inharmonic. 27. To compare the Frequencies of two Tuning-forks of nearly Identical Pitch, and to tune two Forks to unison. A tuning-fork mounted upon a resonator-a wooden box of suitable size-furnishes a very convenient means of obtaining a pure tone; the upper partials, which are generally heard when the fork is first sounded, are not reinforced by the sounding box, and rapidly become inaudible, while the fundamental tone is, comparatively speaking, permanent. When two forks which differ only slightly in pitch are set in vibration together, the effect upon the ear is an alternation of loud sound with comparative silence. These alternations are known as beats, and they frequently are sufficiently well marked and sufficiently slow for the interval of time between successive beats to be determined with considerable accuracy by counting the number occurring in a measured interval of time. It is shewn in text-books on sound that the number of beats in any interval can be inferred from the vibration num 'Deschanel, Natural Philosophy, p. 813: Stone, Elementary Lessons, p. 72; Tyndall, On Sound, p. 261. bers of the two notes sounded together, and that, if N be the number of beats per second, n, n' the frequencies of the two notes, n being the greater, then We have, therefore, only to determine the number of beats per second in order to find the difference between the frequencies of the two notes. This may be an easy or a difficult matter according to the rapidity of the beats. they are very slow, probably only few will occur during the time the forks are sounding, and the observer is liable to confuse the gradual subsidence of the sound with the diminution of intensity due to the beats. If, on the other hand, there are more than four beats per second, it becomes difficult to count them without considerable practice. The difficulty is of a kind similar to that discussed in § 11, and we may refer to that section for further details of the method of counting. In order to determine which of the two forks is the higher in pitch, count the beats between them, and then lower the pitch of one of them by loading its prongs with small masses of sheet lead, or of wax (softened by turpentine), and observe the number of beats again. If the number of beats per second is now less than before, the loaded fork was originally the higher of the two; if the number of beats has been increased by the loading, it is probable that the loaded fork was originally the lower; but it is possible that the load has reduced the frequency of the higher fork to such an extent that it is now less than that of the unloaded second fork by a greater number than that of the second was originally less than that of the first It is safer, therefore, always to adjust the load so that its effect is to diminish the number of beats per second, that is, to bring the two forks nearer to unison; to do so it must have been placed on the fork which was originally of the higher pitch. In order to adjust two forks to unison, we may lower the pitch of the higher fork by weighting its prongs until the beats disappear; the difficulty, already mentioned, when very slow beats are observed occurs, however, in this case, and it is preferable to use a third auxiliary fork, and adjust its pitch until it makes, say, four beats a second with that one of the two forks which is to be regarded as the standard, noting whether it is above or below the standard. The second fork may then be loaded so that it also makes four beats a second with the auxiliary fork, taking care that it is made higher than the auxiliary fork if the standard fork is so. The second fork will then be accurately in unison with the standard-a state of things which will probably be shewn by the one, when sounded, setting the other in strong vibration, in consequence of the sympathetic reso nance. A tuning-fork may be permanently lowered in pitch by filing away the prongs near their bases; on the other hand, diminishing their weight by filing them away at their points raises the pitch. Such operations should, however, not be undertaken without consulting those who are responsible for the safe custody of the forks. Experiment.--Compare the frequencies of the two given. forks A and B by counting the beats between them. Determine which is the higher and load it until the two are in unison. Number of beats per sec. between A and the 3.6 3.6 28. Determination of the Vibration Frequency of a Note by the Siren. A siren is essentially an instrument for producing a musical note by a rapid succession of puffs of air. The simplest form of siren is a large circular cardboard disc, provided with perforations arranged in circles concentric with the disc. The puffs of air may be produced by blowing through a fine nozzle on to the circle of holes while the disc is maintained in rapid rotation. In order that the disturbances produced by the puffs of air passing through the holes may be periodic (see p. 218), the holes must be punched at equal distances from each other, and the disc must be driven at a uniform rate. If the pressure of the water-supply of the laboratory is sufficiently high, a small water-motor is a convenient engine for driving the disc, which must be mounted on an axle with a driving pulley. If the diameter of the disc is considerable, so that a large number of holes can be arranged in the circle, a rotation of the disc giving four revolutions per second is quite sufficient to produce a note of easily recognisable pitch. The revolutions in a given interval, say, one minute, can be counted, if a pointer be attached to the rim of the disc, and arranged so that it touches a tongue of paper fixed to the table once in every revolution. The number of taps on this paper in a given time is the number of revolutions of the disc. Suppose the number of taps in one minute is N, and the number of holes in the circle which is being blown is n, then the number of puffs of air produced per minute is Nn, and hence the number per second is N n/60. The disc is generally provided with a series of concentric rings of holes differing in the number of perforations in the circle, so that a variety of notes can be blown for the same rate of rotation of the disc. In the more elaborate forms of the instrument a metal |