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ART. V.- An Elementary Treatise on Sound, being the second volume of a Course of Natural Philosophy, designed for the use of High Schools and Colleges; compiled by BENJAMIN PEIRCE, A. M., University Professor of Mathematics and Natural Philosophy in Harvard University. Boston: 1836. James Monroe and Company. pp. 220.
THE term natural philosophy has, in the present age of discovery, a varied and extensive, if not an ambiguous meaning. Since Sir Isaac Newton's day, the domain of science has been enriched by accessions so large and unforeseen, that the ability of the mighty geometer, were he now alive, would hardly be sufficient to grasp the whole. A law, by its condition, is immutable; but principles, derived from few or imperfect observations, await, like the Stygian shapes, the bark of a Linnæus or a Cuvier to bear them into the judgment hall, and, until verified or condemned, form but imperfect bases of demonstration. They bear to facts the relation of the laws of a new colony to those who established it. When the colonists increase, and have supplied their primary wants, multiplied numbers and interests need the harmonizing influence of the lawgiver; when facts become numerous, and fresh series of phenomena spring up among those already observed, they require the co-ordination of the system-maker; and mankind gladly pour their experience into his treasury, to be dispensed for the universal good.
It is to be lamented that physics, as distinguished from metaphysics, should not have been employed by our earliest experimenters, to denote the rich field for exploration the natural world unfolds. There can be little doubt that this would have reinforced the significance of the antithetical department of philosophy. Nor can we help alluding, in limine, to the link connecting the two ends of human study the world and ourselves, nor can we even so separate physical from mental science, that the one shall not at times appear to transcend its limits, and infringe upon the other's realm. That truth, and this necessity, burst from the mystery whereby the spiritual quickens the material, and the two are linked in life and animation. Like the antique allegory of light and darkness," but for the latter, we should not need the former, nor know the one without the other"— they are
mutually dependant on each other, it is not our province to say why, or how. We have somewhere heard theoretical physics styled the metaphysics of nature, but cannot see the utility of perplexing the mind with the trammels of speculative definition.
The revolutions of thought have, then, so altered the surface of knowledge, that the buried philosopher would recognise his territory still less than did the hero of Mr. Irving's legend. In their terminology, even the ramifications of science are but little known still less, their objects immediate and remote, and less still, their harmonious ensemble. Yet may any meditative mind, unaided, divine the enigma philosophers are seeking to solve, and a fearless glance of inquiry into the aspect of nature and of science, cannot fail to detect many an unsuspected truth. We have written the word philosopher; it is a goodly, ancient term, significant of the homage paid to wisdom, of the majesty of the goddess and the humility of the votary. That of savant, if not arrogant in days of general ignorance, is at least so in the presence of modern science.
We have mentioned the divisions of science, and it would not be out of place to append a brief chart of them. The region is nature; the points laid down are the portions explored. Hence we may see how comparatively illimitable the surface and unfathomable the depths of the territory, and at the same time learn to shun the impracticable, and discern the feasible routes. We walk upon the earth, nor do we attempt to fly. Long may be our journey, the sea its barrier, and we, to surmount it, frame wooden wings with which to cross its bosom; but its profundities, the arctic ice, the inaccessible mountain peak, remind us of our finitude. We need not seek the impossible in air; it lies upon the earth also; not in the remote region or uncongenial element, only, but all around us, we tread on miracles, and breathe phe
The example of Sir Isaac Newton is, perhaps, more ardently followed in our day, than that of any great man from whom a period of years divides us, since Aristotle, and, might we add, Bacon. The application of mathematical reasoning to the illustration of truths, and the investigation of the phenomena that give them birth, is a wondrous feature in the intellectual pursuits of this age. Analysis is the locomotive of science. It does not survey the route, hew down the tree, remove the obstacle; but these once done, it appears in the cleared country, flies with lightning-celerity over the theatre of the pioneer's patient labors, transports thought in every direction, connects by an indestructible chain
result with result, and leaves a long track of light for the wonderment of the laborer, who has dug, he hardly knew why, has toiled long nor suspected his object, and to whom it becomes revealed by the powerful engine which meets his bewildered eye, as he looks up from the pickaxe or the spade.
We have been led to the foregoing remarks by the object and character of the highly valuable addition to science before us. Mr. Peirce has bestowed much care and attention on a branch of physics little understood, even by the initiated, and has rendered no trifling service to science, in establishing the laws of acoustics in so clear and masterly a manner. His selection of materials does high honor to his taste and judgment, and he handles the more complex implements of science with perfect skill and dexterity. As a book of instruction, his compilation is perfect; although it may, in some few points, lie open to criticism, yet it affords an admirable illustration of what a scientific treatise should be.
The science of acoustics, in a small space, exemplifies the history of an interesting branch of knowledge, from the earliest perception of its data, down to their present completeness of theory and proof; and much like the strange shapes that were supposed, in ancient fable, to guard the hidden treasures of an enchanter's tomb, it displays the many agents which may combine in perplexing inquiry such as various attributes of bodies, media, moisture, and temperature - all of which, in this case, modify the mechanical laws of the theory of sound. It also illustrates the mode in which the invisible tone reveals its secret to the searching interrogatory of analysis. Peirce's elegant compilation is then full of interest. The acoustical bibliography prefixed to it, displays such a catalogue of distinguished authors, who have devoted themselves to this science and its tributaries, as may well astonish him who fancied there was no sense in sound, or who had detected, in the desultory glance over the scientific shelf, no treatise, save Chladni's, upon this subject. Here are found the names of all the brightest heralds of discovery. A thousand departments of nature and of art, many a deed and passion, the scintillations of the midnight torch, and the lightnings of battle, own themselves tributary to sound. Consider its meanderings in the walks of philosophy, in the hum of the throng, from the cathedra to the forum, from the roar of Niagara to the mystic melody of Memnon's statue, from the warbling of the nightingale to the thunder-peal. See it mingling with history, arousing the echoes of
the past and accompanying the inventor whose voice is lost in faturity. Learn how it presided over Homer's song, and decoyed into discovery with its magical note the spirits of Newton and Euler, of Bernouilli and Lagrange, of D'Alembert and Laplace.
To have so thoroughly sought out these varied authorities, and to have assigned to them their respective ranks in this lucid catalogue, is in itself a merit; it is the smallest Mr. Peirce may lay claim to. We cannot but express our hope that in this he may have imitators. The gratitude of men of science towards M. Lacroix for prefixing to his great work on the calculus a similar list of treatises, after the manner of Dr. Young, in his natural philosophy, was universal.
Acoustics may be termed the study of bodies when their particles execute certain vibrations, producing what we term sounds. It involves a consideration of the gaseous fluids chiefly; and the reason is evident, if we consider that after all sound is but an action of the brain, which causes us to perceive that vibrations are somewhere occurring, and that this action is excited by the mediation of the air, which receives and transmits to the organ of hearing the vibrations of vibrating bodies.
Although still the most obscure branch of physics, acoustics is perhaps that which has been the longest studied and applied. In the preliminary catalogue are cited works of Plutarch and of Aristotle, relating to it, and different passages in ancient authors serve to show that the Greeks and Romans had learned to apply certain of its laws in a manner only partially revealed to us by the recent discoveries. We find, for instance, in Vitruvius -the very skilful architect, as he is termed by the editor of his writings various rules to be observed in the construction of theatres, many of which are pure applications of a knowledge of the propagation of sound. We quote a passage from this valuable work, which may serve to afford us a clearer idea of the state of knowledge among the Romans in that author's age. Referring to the necessity of so framing public halls, that the voice shall freely circulate, nor meet with materials that obstruct or deaden it, he says:
"The voice is a flowing spirit, audible by the percussion of the air. It moves in infinite circling rounds, like the innumerable circular waves which a stone cast into smooth water sends out from the point of immission, and which expand as far as possible unless prevented by the narrowness of the place, or by some obstacle which does not allow the outlines of the waves to attain
their limit. When an obstacle meets them, the first waves flow back upon the succeeding ones. But upon the surface of water the circles extend themselves laterally in a plane; while the voice, besides this horizontal motion, ascends. Therefore, as in the water-circles, so with the voice, when no obstruction opposes the first, nor disturbs the second or following waves, its tones all attain, without echo, the ears of the highest and of the lowest spectators."*
And he thus describes the modes of reinforcing the voice, adopted in the construction of theatres:
"From these investigations, brazen vases are made after mathematical rule, in proportion to the magnitude of the theatre, and so constructed, that when touched, they sound among themselves the diatesseron, diapente, and disdiapason. These are arranged in musical ratio, in cells constructed between the seats of the theatre, so as not to touch the sides of the cavity in which a vacant space surrounds them, and where they are placed inverted to the top of the space, having, in the part which fronts the stage, wedges not less than half a foot high, placed under them, and an aperture, two feet long and half a foot high, being left opposite to each cell in the seats of the row of benches beneath."
He goes on to give instructions as to the order of position of these rows of sounding vases, and evinces an acquaintance with the principles of sound in its minutest modifications by matter.
This perfection attained by the Romans in the construction of their theatres and amphitheatres, is indeed surprising, when we call to mind their ignorance of, and indifference to, general physics; and, it seems yet stranger, that a science so far advanced before the days of Vitruvius, should be still veiled in doubt, and stand in greater need of development than other branches of physics of far more recent origin. No one of the properties of matter may be more justly regarded as created for man's especial use, than its power of producing sound. Speech and hearing have ever ranked among the most precious of our physical endowments. Upon them society rests, and from the earliest days men seem to have sought, on the one hand, to augment the voice, and on the other, to propagate it. Barbarians would naturally strive to transmit sound to a great distance, and invent musical instruments melodious in proportion
* De Architectura, lib. v. chap. iii.
+ Three notes in the Greek scale, best adapted to the pitch of the human voice. * De Architectura, lib. v. chap. iv.