Dr Wallis about the same time discovered the fact, that if a string be made to sound near another which corresponds to it in thickness and tension, but of which the length is any multiple of it, the latter will divide itself into several vibrating portions, each equal in length to the former string, and sounding the same note with it. He also discovered, that, when a string is divided by any slight pressure into two portions, commensura ble with each other, the vibrations excited in one of these portions will communicate itself to the other. The grave harmonics produced by the union of two sounds, were observed about the year 1753, by both Tartini and Ramjet'.
Ic we rub our moistened finger along the edge of a drinking glass, or draw a bow across the strings of a violin, we can in both cases procure sounds which re main undiminished in intensity, as long as the operation by which they are excited is continued. A similar fact takes place with respect to any other sonorous body, whose structure is not destroyed by the mode of excita tion employed. When therefore the sound of a body becomes by any means extinguished, we are not to at tribute this extinction to the capability of the body for producing sound being exhausted, but rather to the dis continuance of that mode of action by which the excited body had formerly produced sound.
Though all bodies may, by some mode of excitation, be made to sound, there is a great difference among them in the intensity of the sounds which they produce during the operation, and in the permanence of these sounds after the excitation has ceased. Thus, if we strike two bells, one of lead, and the other of brass, the sound of the former is feeble and momentary, compared with that of the latter. In the former, therefore, ac cording to the remark which we have made above, that action, by which the body produces sound, is excited only in a small degree, and ceases with the excitement ; in the latter there is some power, by which, when this mode of action is once begun, it perseveres in it for some time afterwards. By examining the characteristic difference between these two classes of bodies, we may be enabled to discover what are the physical properties on which the production of sound depends, and what is their mode of action. This difference is found to depend on the substance and the form of the sounding bodies, and also upon the various external circumstances in which they are placed.
In comparing the properties of these substances, we shall find them distinguished from each other by the de gree of vibration which they are capable of having ex cited in them, and by the length of time during which they can preserve a vibratory motion ; those substances which are most capable of vibration being most sonorous, and those which can longest maintain a state of vibra tion also persevering longest in emitting sound. In stances of this law will readily suggest themselves to the reader. Bodies, though of the same substance,
differ in these respects according as their form varies ; those forms which are most favourable to the produc tion and continuance of a vibratory motion, being also most propitious to the production and permanence of sound.
A similar analogy prevails with respect to the exter nal circumstances which affect sounding bodies ; and gives us sufficient ground to believe, that there is some connexion between the production of sound and the vi bration of bodies. Accordingly, when a body sounds powerfully, such as a large bell, or the lowest string of a harpsichord, we can, by the naked eye, perceive that it actually vibrates ; and even in those cases where this is not so perceptible, we may detect it by the microscope, or some other artifice. Thus, if we put some water into'a glass, and make it sound, as in the experiment first mentioned, the water will be agitated. If we hold the open hand over the pipe of an organ, we shall feel a tremulous motion in the air passing throtIgh it. Such experiments may be extended to all solid bodies, by strewing them with fine sand, or placing upon them small pieces of paper.
These observations, showing that the intensity and permanence of the sounds which can be produced from sonorous bodies, are uniformly proportional to the de gree and permanence of the vibration which can be ex cited in them, and that the production of sound is al ways accompanied by such a vibration, prove, that sound and vibration are necessarily connected, either as cause and effect, or as simultaneous effects of the same cause. But as we are already acquainted with the causes on which vibration depends, and which sufficiently account for it, there remains for us either to consider sound as produced by vibration, or to believe that those physical properties by which bodies vibrate, are capable of be ing at the same time excited to some other mode of ac tion, by which they produce sound : Thus, when we strike a hell with a hammer, and produce a sound, we may either suppose, that the vibration which is thus excited is the cause of the sound, or we may imagine, that those physical properties which render the bell ca pable of vibration are excited to some other mode of action which produces sound ; and that the hammer not only acts by its impulse in producing vibration, but also exerts some other influence which excites sound. This latter opinion will appear inadmissible, if we consider, that a tendency to produce motion in the sounding body is the only thing common to the several modes of excit ing sound ; and that the physical properties by which bo dies vibrate are not in all cases the same ; some vibrating in consequence of their cohesion, some by means of a strong repulsion between their particles, which opposes their being compressed, and others from either of these causes separately, or from both of them combined.