Acoustics. A word first applied by Mr Sauveur to the theory of sounds. By the knowledge of acoustics, we are enabled to determine the relation of tones, and the ratios of the harmonic intervals, as produced by the various vibrations of different chords, and other sonorous bodies. Acoustics, indeed, comprehend nothing Less than the whole theoretical portion of music, as discovered and laid down by Aristoxenus, Pythagoras, Lasus, Euclid, Ptolemy, and others among the great fathers of musical science. We may call acoustics the science which teaches the physical law, and phenomena of sound and hearing. Several important facts concerning sound must have been known at a very early period. The tuning of the lyre, and various other instruments, which are coeval with remotest antiquity, necessarily implies an acquaintance with the fact that, as we diminish the length of musical strings, or increase their tension, we render their tone more acute. We have, however, no reason to believe that, till 500 years before the Christian era, any attempt had been made to discover the relation which subsists between the lengths of strings producing the various notes of music. About this time, Pythagoras gave a correct determination of the ratios between different sounds. The ancients certainly seem to have understood some principles in acoustics which we have lost ; or, at least, they applied them better. They contrived to convey the voice distinctly in their huge theatres, by means of pipes, which created no echo or confusion. Our churches and theatres are yet much too large, though we do not need pipes or speaking tubes. If we rub our moistened finger along the edge of a drink-big glass, or draw a bow across the strings of a violin, we can in both cases procure sounds which remain undiminished in intensity as long as the operation by which they are excited is continued. 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 ; so we see, that, though bodies all sound, yet the sounds produced are not all alike. The circumstances which affect the sounds of bodies are, their form, their magnitude, their density, the mode by which they are excited, and the comparative force of the power by which they vibrate. Musical sounds have occupied the attention of philosophers more than any other class of sounds. The superior precision with which the ear can estimate any variation in pitch renders theme sounds more easily compared ; and the vibrations of sonorous bodies, which produce them, are, on account of their superior simplicity of form, more easily investigated. A musical string is of a uniform thickness, and is stretched between two points, by a force much greater than its weight. The stretching force which is applied is generally conceived as measured by the weight which would occasion an equal tension. The sound which a string gives, thus stretched, or in this mode of vibration, is called its fundamental sound. The tone of a string becomes more acute as we increase its tension, or diminish its length, and the weight of a given portion. On this fact depend, for the most part, the various modes of producing the several musical sounds on stringed instruments. Wind instruments constitute one of the genera of those which perform their vibrations longitudinally ; and through the air which vibrates in all of them is the same, yet they admit of such a variety in their form, and derive such different characters from this variety, that they may be regarded as a genus not less extensive and important than the class of bodies which vibrate by tension. Observations have been made to ascertain the rate at which sound travels through the air ; and the mean result is, that all sounds travel at about the velocity of 1130 feet in a second of time. A musical sound consists of a series of undulations which arrive at the ear at equal intervals of time, and the pitch of the sound depends on the length of the interval between each impression. Musical sounds can therefore he produced, not only by the isochronous vibrations of sonorous bodies, but also by any other mode in which a rapid succession of equidistant impulses can be communicated to the ear, whether those impulses originate from the same or different sources. The sounds produced by instruments are chiefly musical. Kratzeustein and Kempelen have, however, by making experiments on the effects of pipes of different forms, succeeded in constructing such as will imitate very accurately the different vowel sounds produced by the human voice. The speaking trumpet is an instrument intended for transmitting sound to considerable distances in a particular direction. The form which is usually given to the hearing trumpet corresponds to that of the speaking trumpet in being a cone, truncated near its summit ; but differs from it in being sometimes of a curved form. The summit of the cone is placed in the ear, and the wide extremity turned towards the point from which the sound comes. The effect of this instrument is to augment sound considerably. Sound may be coin-eyed to much greater distances by being confined in pipes. Such pipes are frequently used in coffee-rooms and taverns for conveying order, to the attendants. Captain Parry, during the cold experienced in Winter Harbor, was surprised at the great distance at which the human voice could be heard. "I have," he says, "often heard people distinctly conversing, in a common tone of voice, at the distance of a mile ; and to-day, I heard a man singing to himself, as he walked along the beach, at even a greater distance than this." The strong tendency of sound to ascend has also a great effect. Humboldt has remarked, that the barking of a dog has been heard when the listener was in a balloon, at an elevation of about three miles. It has also been noticed, that from the ridge of the Table Mountain, which is 3600 feet high, and the upper part of which rises perpendicularly at a distance of about a mile from Cape Town, every noise made below, even the word of command on the parade, may be distinctly heard.