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ACOSTA. translation, London, 1740; Latin and German edition, H. Jellinek, Leipzig, 1847. He is the hero of an effective tragedy by Gutzkow.

ACOSTA, .ToA(jriN- (?-18")2). A South Aniori- caii geofiiaiilier. He was born at Giiadiias, C'oloniliia. In!8:i4 he made a lour with the botanist tVspt'des through the valley of the Soeor- ro as far as the Maf;(hUeiia, ami seven years afterward traveh'd from . lioi|uia to Anserma for the ]nirpose of studying the history and ens- toms of the native tribes. Besides an e.eellent 7nap of New Oranaihi, Acosta |)ublished the fol- lowing interesting and valuable works: Coiii- pciidio historico del (Icscubriiiiiciito y coloniza- cidn (le la Xiirra (Inmnda en cl siglo d^ciino sexto (Paris, 1848); tSemeiwrio de la Xucva (Irnnadd, M iscrllihua de eioieia.^, Uteratura, arlex e iiiduslriii. with portraits and map, pub- lished in eonjunetion with Laserre under the di- reetion of Franeiseo .Jos^i de Caldas (Paris, 184!)).

ACOSTA, Jose DE. (1530-lGOO). A Spanish Je-<uil. He was born at Medina del C'ampo, Spain. He entered the Society of Jesus and went as niissionarj' to Peru, where he labored for many years. I'pon his return home he be- came sujierior of the Jesuit Seminary of Valla- ilolid, and afterward rector of the University of Salamanca, where he died. His fame rests upon his work on the natural history of the New World and the cll'orts put forth for its evangel- ization, published in Latin at Salamanca in ]r)8<.), and in Spanish (Seville, 1590). The last- nan'ed publication was under the caption His- toria natural y moral de lafi Iitdins. and was several times reprinted and translated into Krench, Butch, and English {The aturalc and Morale Historic of the East and West Indies, London. lt)04).

ACOUCHY, a-k<7n'slu or ACUCHI. See Acori 1.

ACOUMETER, a-kou'nie-ter or a-kCC-, or ACOUSIM'ETER {C.k. OKitt'eiv, akoiiein, to hear -f fihimv, metron. measure). An in- strument used to determine the aeuteness of hearing. It is a small steel bar which, when strick by a hammer, gives a uniform sound.

ACOUSTICS, a-kou'stiks or a-koo'- (Gk. qkou. o-iKof, akdiislitus, relating to hearing, from dxoe- ttv, aliouein, to hear). The name applied to the science of the phenomena of souml. The name "sound" is given to the sensation perceived by the auditory nerves, and it is a matter of every- day e.perience that the innnediate cause of the sensation is some vibrating body, e.g., a violin string, a drum head, a hammer when striking a nail. This was early recognized, and, so far as acoustics is considered as a science dealing with the vibrations of matter and with the waves pro- ihu'cd in the air by this motion, the history of its development is identical with the progress of mathematics and dynamics from the time of Galileo and Newton to the present. Few dates can be assigned to definite discoveries. The laws of vibrations of a stretched string were first deduced mathematically by ISrook Taylor in 1715 and by Daniel HcrnouUi in 1755. althotigh they had been discovered experimentally by Mersenne in KiiUi. Longitudinal and torsional vibrations of bars were first investigated by Chladni (1750-1827). Daniel Bernoulli was the first to attack the problem of the lateral vibra- tions of bars; but the mathematical treatment of the question is still of interest. Poisson (1829) was the first to give a correct mathematical so- lution of the free vibrations of a membrane, and good experimental work on the subject has been done by Savart, Bourget, and Elsas. The vibra- tions of plates have been studied mathematically by Poisson. KirchhofI", and more recent writers, and experimentally by Chladni, Savart, and Wheatstone. A full account of the history of the mathematical side of acoustics will be found in Rayleigh's gieat work on the Theory of Hound.

The history of that portion of acoustics which considers the plienoniena of the sense of hear- ing, harmony, discord, pitch, etc., begins un- doubtedly with the earliest days of civilization. It was known to Pythagoras (sixth century B.C.) — and to whon before him no one can tell — that sounds were in harmony when produced by two stretched strings of the same material, cross-sec- lion and tension, provided their lengths were in the ratio of 1: 2, 2: 3, or 3: 4. Mersenne discov- ered in 1030 that the frequencies of such vibrat- ing strings varied inversely as their lengths, and so proved that for two notes to be in harmony it was necessary for their frequencies to bear sim- ple numerical relations to each other. No ex- planation of this fact was given until the great research of Helmholtz, begun in 1854, the results of which were published in 1802 in his classical work on the >Seiisalio>is of Tone. Helmholtz was the first to discover the existence of summa- tional times, although the dilTerential tones were discovered probably by Koniieu in 1743, and cer- tainly by Sorge, the court organist at Loben- stein, in 1745. Helmholtz's theory of vowel sounds is still under discussion. Most interest- ing work on audition has been done in recent years by Rudolf Kc'inig of Paris and Professor Mayer of Hoboken.

Many of the physical properties of sound are matters of common experience and can readily be appreciated. In the first place, it is well known that an interval of time elapses between the vibration of the body and the perception of the resulting sound if the vibrating body is at a considerable distance; thus the flash of a gun is seen before the sound is heard. It was shown by Otto von (Juerickc that if a bell is set ringing in a glass jar from which the air has been exhausted no sound is heard; so that the presence of some material medium between the vibrating body and the ear is essential for the production of sound. This medium need not be air, but may be water, or, in fact, any gas, liquid, or solid which can carry waves. The whole mechanism is, then, as follows: The vibrations of the body, e.g., a drum-head, luoduce waves in the medium in contact with it, e.g., the air: these waves spread out through the medium and. after a certain interval of time, reach the ear; in the ear the waves produce motions of the eardrum and corresponding efl'ects in the internal ear where the auditory nerves have their endings. It should be noted that not every vibration will produce waves in a fiuid medium; because if the number of vibrations per second is too small, the lluid will simply flow around the body as it vibrates, and so w'll not be compressed; consequently, in order to produce waves in a fluid, the frequency of the vibrations of the body must exceed a certain number, which depends upon the viscosity and density of the fluid. Further, it is evident that, since lluids can carry only com-