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radical of acetic compounds, acetic aldehyde being, according to his view, hydrated oxide of acetyl (C,H,O, HO), whilst acetic acid was regarded as the hydrated teroxide of acetyl (C,H,O, HO). Secondly, the name has more recently been applied by Gerhardt to the group (C,H,O,) which is regarded by the latter chemist as the true radical of acetic compounds, acetic aldehyde being the hydride of this radical (CH,O,, H), and acetic acid its hydrated oxide (C,H,0,0, HO). Wil-ness, are considered as acids because they agree with them in some liamson proposes the name othyl for the group (CHO). [NEGATIVE RADICALS.]

ACETYLAMINE (Acetylia). An organic base first obtained by M. Cloëz, and, subsequently, by M. Natanson, in acting upon bibromide of ethylene and bichloride of ethylene with ammonia, and regarded by these chemists as having the formula C,H,N. The recent researches of Hofmann prove this body to belong to the family of diamines; according to this chemist it is diethylene-diamine, and its formula is N2 (C ̧H ̧"),H,. [DIAMINES.]

ACHROMATIC (from a without, and xpwua colour), a term applied to those combinations of lenses used in the best telescopes and microscopes, for preventing the formation of coloured fringes which surround the edges of objects when viewed by means of common instruments. [LIGHT.] ACIDIMETRY, the process of determining the quantity of real acid contained in a given sample of any acid, and thereby ascertaining its actual or intrinsic value. There are various methods of accomplishing this: the simplest is by determining the specific gravity of the acid in question. As in most cases the specific gravity of an acid diminishes in regular proportion to the amount of water it contains; the amount of real acid is easily calculated from its density. To facilitate this, tables have been constructed by Dr. Ure and others, in which the specific gravity and the amount of real acid corresponding to it, are placed in parallel columns. These tables will be given in describing the various acids.

The above method however is not always absolutely accurate, and some acids do not admit of its use at all. Advantage has therefore been taken of the fact, that the blue colour of litmus is reddened by acids, while alkalies restore the original colour, to construct a method of estimation which is highly accurate and expeditious. An alkaline solution is prepared of a known strength, and is poured from a graduated tube-an alkalimeter-into an accurately weighed quantity of the acid to be examined (which must be tinged red with litmus) till the point of neutralisation, known by the change from red to blue, is reached. From the number of measures of the test liquid so used it is easy to calculate the quantity of real acid in the sample tested.

It

A convenient method of preparing the test liquid is to dissolve 530 grains (10 equivalents) of pure dry carbonate of soda-made by fusing the pure bicarbonate-in 10,000 grains of distilled water. The lkalimeter should be made to hold 1000 grain measures, and would thus contain 53 grains, or an equivalent of carbonate of soda. should be divided into 100 parts, each of which will then contain 53 of the carbonate. An equivalent of carbonate of soda will exactly neutralise an equivalent of acid, so that 100 grain measures or divisions of the test liquid will represent

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Supposing, then, that 100 grains of the sample of acid to be tested are weighed, and they require 70 measures of the test liquid, if the acid be sulphuric, then 100: 40: 70: 28, the amount of real acid in the quantity taken; if hydrochloric, 100: 365:: 70: 25'55, and so on. A solution of ammonia may be substituted for that of carbonate of soda, and may be so adjusted that 1000 grain measures shall contain 17 grains of ammonia, which is the case when its specific gravity reaches 992. It is not easy however to adjust it exactly to such a density; it is better, therefore, when near the convenient strength to estimate the ammonia in a given number of measures of the alkalimeter, by evaporating them to dryness on a water-bath, with an excess of bichloride of platinum. The resulting platinum salt, after being washed on a filter, with a mixture of 2 parts of alcohol with 1 of ether, and carefully dried at 212°, and weighed, contains in 100 parts, 7 624 of ammonia (NH).

The strength of the test ammonia may in this way be made to suit the convenience of the operator, and the amount of ammonia in each division being known, the calculation is perfectly simple. Supposing that each measure contains 20 grains of ammonia, and that 100 weighed grains of the sample of sulphuric acid require 50 measures, the eq. of ammonia, 17: 40: 50 × 20: 23·53 grains of sulphuric acid in the quantity taken.

There are other processes for accomplishing the same object. Those used in Alkalimetry, which will be fully described, may, in many cases, be used in a reverse way in Acidimetry, the one process being the reverse of the other. Some acids require special methods of analysis, which will be described under their particular titles.

ACIDS. The acids are a numerous and important class of chemical bodies. As the word acid is, in common language, almost synonymous with sour, it might be supposed that the taste of a substance would determine whether it was included among the acids. The term has, however, been so much extended by chemists beyond its original meaning, that some bodies, which are nearly or quite devoid of sourother qualities. The acids are generally sour; usually, but not universally, they have great affinity for water, and are readily soluble in it: they redden most vegetable blue colours, and combine readily with alkalies and earths, and generally act upon and unite with most metals or their oxides, with great facility, forming compounds which are termed salts. Such are the properties of the greater number of acids; but the last only, namely the power of combining with bases, belongs to them all. Many acids are entirely natural products, some both natural and artificial, while others are altogether the result of chemical agency. They are derived from various sources, and, except in the few particulars above-named, vary greatly in their properties. Thus, under common circumstances of temperature and pressure, some are gaseous in form, as the carbonic acid; others are fluid, as the nitrous, or solid, as the boracic acid; some require water or a base to retain their elements in combination, which is the case with the oxalic acid, while others, as the sulphuric and nitric may exist independently of either. Most acids are colourless, but the chromic is red; some are inodorous, as the sulphuric; others pungent, as the hydrochloric acid; there are acids which are comparatively fixed in the fire, the phosphoric for example; others are volatilised by a more moderate heat, which is the case with the sulphuric acid; whilst those which are pungent to the smell are, to a certain extent, volatile at all temperatures.

Acids occur in all the kingdoms of nature: the margaric acid is of animal origin; the citric and the oxalic acid are products of vegetation; while the chromic and the arsenic acid enter into the composition of certain minerals. In many instances however acids are not exclusively derived from one source, but are sometimes produced by them all, and may be also artificially formed. This is the case with the phosphoric acid, which occurs in animals, plants, and minerals, and is formed whenever phosphorus is burnt in excess of oxygen. The citric acid is produced only by the process of vegetation; but the oxalic acid, also found in plants, may be obtained by chemical agency. The carbonic and the sulphuric acid are very common in mineral bodies, and may also be artificially produced; the former is also one of the results of respiration, combustion, and of animal and vegetable decomposition; and both the carbonic and sulphuric acids may be obtained by combining carbon and sulphur respectively with oxygen. The chromic and the arsenic acid are found only in mineral bodies, but they may be formed by chemical agency; and indeed, except many of the vegetable acids, there are but few which cannot be so prepared. Soon after Dr. Priestley's celebrated and important discovery of what he called dephlogisticated air, in 1774, it was found that several substances, such as sulphur and phosphorus, were converted into acids by combining with this elementary gas. On this account it was assumed, hastily and incorrectly, that all acids contained dephlogisticated air, and derived their acidity from it; on this account the name oxygen was given to it, signifying acid-making, and it was regarded as the universal acidifying principle; not indeed that it always formed an acid when combined with a body, but that no acid existed without it. It has however since been found that there are acids, the hydrochloric acid for example, which contain no oxygen; and further, it has also been proved, by the brilliant discoveries of Sir H. Davy, that oxygen, by combining with certain elementary bodies, converts them into alkalies; a class of substances possessing properties diametrically opposite to those of the acids.

It was therefore considered necessary to divide the acids into oxyacids -in which oxygen was supposed to form the acidifying principle; and hydracids-in which that principle was due to hydrogen. Hydrated sulphuric acid, HO, SO, may be considered as a type of the former class; hydrochloric acid, HCl, of the latter class of acids. When sulphuric or any oxyacid is united to a metallic oxide, the result is a salt in which the water of the acid is replaced by the oxide, forming a so-called oxysalt. Thus HO,SO,+ NaO=NaO,SO, + HO. When hydrochloric acid or any hydracid is so combined, the hydrogen is replaced, not by the oxide, but by the metal itself. Thus, HCl + NaO NaCl + HO, or chloride of sodium, a salt containing neither oxygen nor hydrogen, and called a haloid salt (from äλs, the sea), sea-salt being the type of such a compound. Thus the two classes of acids produce in their combinations apparently anomalous results. To obviate this, it was suggested by Sir H. Davy, and has since been supported by Graham, Liebig, and others, that all acids are hydracids, and all salts haloid salts. By this theory, an oxyacid is in all cases a combination of hydrogen with a compound salt-radical. Thus sulphuric acid, instead of being HO, SO, is H+ the salt radical SO,, or HSO.. Nitric acid, not HO,NO,, but H,NO,, and so on. In the formation of salts, therefore, the hydrogen of the acid is simply replaced by a metal, as in common saltNaO+ HCl NaCl + HO. NaO+HSO, = NaSO, + HO. NaO + HNO。 = NaNÓ ̧ + HO.

This theory is equally applicable to the organic acids. The formula of acetic acid, HOC,H,O,, becomes H,CH,O,; and so with others. Further elucidation of the theories of salts will be found in the article SALTS.

It may be here proper to notice the method adopted by the framers of the French nomenclature, in giving names to different acids. It has been already mentioned, that oxygen was supposed to be the acidifying principle, and it was found that, by combining in different proportions with the same substance, it formed acids of very different properties; but it was not then known that oxygen combined with any one body to form more than two acids. It was, however, proved to unite with sulphur in two different proportions; and in this, and similar cases, the name of the acid which contained least oxygen was made to end in ous, and that which contained more in ic; thus sulphurous acid contains less oxygen than sulphuric acid. Cases have, however, occurred during the progress of chemical science, requiring an extension of this principle: an acid has been formed which contains less oxygen combined with sulphur than in the sulphurous, and this is called hyposulphurous acid; another containing more oxygen than the sulphurous, but less than the sulphuric, and this is termed hyposulphuric acid. An acid has also been formed which contains more oxygen than the chloric-this has been called perchloric acid.

Acids which form neutral salts by combining with one equivalent of a base are said to be monobasic, as the acetic and nitric acids; those which combine with two equivalents of base are said to be bibasic, as tartaric and pyrophosphoric acids, whilst those which require three equivalents of base to form a neutral salt are termed tribasic acids. [CHEMICAL NOMENCLATURE.]

The means adopted for preparing the acids, whether from the natural compounds which contain them, or by the direct combination of their component parts, are almost as various as the acids themselves. For an account of the processes employed in obtaining them, and of the numerous and important purposes to which the acids are applied in medicine, science, and the arts, or for domestic uses, we refer the reader to each particular acid. Although in the course of the present work some acids of minor importance will occasionally be mentioned, 'the following are those which, as being used either in scientific researches, in medicine, or the arts, will be more particularly treated of in their respective places :

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ACONITIC ACID, зHO, C12H2O, (EQUISETIC ACID ; CITRIDIC ACID), exists naturally in Aconitum napellus, Delphinium consolida, and Equisetum fluviatile, but is most easily obtained by the action of heat on citric acid. Crystallised citric acid is submitted to distillation until oily streaks appear in the receiver. The residue contains aconitic acid, which is dissolved out by absolute alcohol, etherified by hydrochloric acid, and then obtained as a potash salt by the action of caustic potash upon the aconitic ether. Aconitic acid is tribasic; it crystallises indistinctly. At a temperature of about 320° it is decomposed into a

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crystalline substance called itaconic acid, and an oily liquid called citraconic acid, both having the formula 2HO,CHO.. ACONITINE (CH, NO14). An alkaloid existing in Aconitum napellus, and other varieties of the aconite. It crystallises from a solution in dilute alcohol in white grains; it is also often obtained in the state of a vitreous, transparent, compact mass. It is inodorous, but intensely bitter and acrid. It is extremely poisonous; one 50th of a grain is sufficient to kill a sparrow in a few minutes, and a tenth of a grain instantly. It is very slightly soluble in cold water, unalterable in the air, very fusible, and not volatile; its alkaline re-action is very distinctly marked; it requires 50 parts of boiling water to dissolve it, and the solution does not become turbid on cooling; it is very soluble in alcohol, and to a less extent in ether. Aconitine forms perfectly neutral salts. Those which have been examined crystallise with great difficulty, and dry in the state of a bitter gummy mass, which is acrid and very poisonous. Fuming nitric acid dissolves them without colour; moistened with concentrated sulphuric acid, they assume a colour, at first yellow and then reddish violet. Infusion of galls produces in their solution an abundant precipitate of white flocculi, and solution of iodine a kermes-coloured precipitate. Aconitine is said by Geiger and Hesse to dilate the pupil, but that obtained by Dr. Turnbull contracts it; and Dr. Pereira mentions the power of contracting the pupil as one of the distinctive properties of the alkaloid. When applied to the skin in very minute quantity, it produces a sensation of intense heat and numbness. It is used medicinally in the form of ointment, and is of great use in severe neuralgia, and rheumatic affections. ACONITUM (Monkshood or Wolfsbane), Medical Properties of.The botanical characters of this genus of Ranunculaceous plants have been already given. [NAT. HIST. DIV., vol. i. p. 58.] Which species merits the preference as a medicinal agent is a greatly controverted point. The London and Dublin Pharmacopoeias, following the notions of Decandolle as to the identity of his Aconitum paniculatum, var. y Storkianum, with the A. napellus officinalis, figured by Störk in his Libellus de Stramonio, Hyoscyamio, Aconito,' Vindobon. 1762, have given that as the officinal one, while the Edinburgh College has retained the common A. napellus. The preponderance of evidence and good sense is in favour of the latter, as, besides the almost impossibility of procuring the plant indicated by the two former, since it is only a rare inmate of botanic gardens, it is substituting a confessedly less potent for a more potent plant. The London Pharmacopoeia' has restored in the edition of 1851, the A. napellus, as the officinal plant. But besides this, two other species are grown at the physicgardens at Mitcham, whence the London market is chiefly supplied. One, a party-coloured sort, having white flowers with a little blue in them: perhaps intended for the A. paniculatum (Decandolle); another A. exaltatum (Bernhardi), synonymous with A. decorum (Reichenbach). This, if found equally potent as the common A. napellus, has much advantage. Its tall size supplies more leaves, and as it does not flower till much later in the year (September) its leaves retain their virtues till the flowers begin to fade-and can yield a supply of fresh leaves, when these are wanted, long after the common species have become inert. A. ferox is now largely imported from India, in a dry state, to yield aconitine, of which it contains three times as much as the European species. The aconite of Störk, whatever species he used, was a plant possessed of great acrimony, while A. paniculatum has scarcely a perceptibly acrid taste. The officinal parts are the root and leaves. But the seeds might be added with propriety. Every part of the plant has a narcotico-acrid property. The live plant has little of the virose repulsive odour common to poisonous vegetables; neverthe less very sensitive individuals, by merely smelling the flowers, have fainted, and had dimness of vision for some days, and handling the fresh plant has occasioned tremblings and faintness. Honey collected from these flowers has caused severe suffering and even death. In making the essential extract, and in procuring the alkaloid aconitine, the vapours have powerfully affected the operators; hence much care is required on their part. A small piece of the leaf, root, or a single seed, if chewed, causes a feeling of tingling, followed by numbness of the lips and tongue, which lasts for hours. A greater portion causes these sensations in the palate and throat, where in larger or poisonous doses a choking sensation is felt. The resemblance of many aconites, especially before flowering, to several umbelliferous plants in common use, such as celery, lovage, masterwort, &c., proves a frequent source of poisoning by them; a calamity further augmented by the inconsiderate practice of giving ignorant persons portions of the leaves to chew, or as a kind of parsley. (See a melancholy case of poisoning by Aconitum neomontanum, in Johnson's Medico-Chirurg. Review,' vol. lxi. p. 264.) Such unprincipled practices cannot be too severely reprobated. No complete analysis of the root or leaves of the A. napellus has hitherto been published, though Pallas analysed the root of A. lycoctonum and Bucholz the leaves of A. medium, Schrad. It is probable that all the species contain similar constituents, differing only in degree, the most powerful being the A. ferox (Wallich, 'PI. Asiat. Rariores,' i. t. 41) or Bisk of Northern India. The most important are the alkaloid aconitine, aconitic acid, a fatty oil, and perhaps a volatile acrid principle. The latter probably results from the decomposition of aconitine by the action of heat. Almost all ranunculaceous plants have an acrid principle, which is very easily driven off by heat. Much care is therefore requisite in drying the root or leaves

of aconite not to apply too high a temperature. The same precaution is required in forming the extract or inspissating the juice. A knowledge of this fact leads to the most convenient and effectual antidote in cases of poisoning by these plants, viz., causing the patient to drink very warm water till vomiting is excited. Linnæus saw aconite, disarmed of its virulence, so that it could be used as a pot-herb, by merely boiling it, and adding a little fat or butter. (Linnæus, Flora Lapponica,' p. 187, ed. Lond. 1792.)

The fatty oil is destructive of the sensibility of any part to which it is applied, but whether from inherent powers or from having aconitina dissolved in it is yet unknown. The alkaloid is regarded as the efficient principle when aconite is used medicinally. The forms of administration are various. Powder is objectionable from the variable degree of power. This further varies with the period when the leaves are collected. The best time to gather them is immediately before the flowers wither, as when the seeds advance to maturity the acrimony of the leaves rapidly diminishes. (Christison.) When the seeds are intended to be collected, this should be done just before they are perfectly ripe. The root should be taken up before the flowers expand; it must be carefully, yet speedily dried, at a very low temperature, otherwise it soon becomes mouldy and its activity is impaired, while a high temperature quite dissipates its valuable properties. The watery extract is a worthless preparation; and the inspissated juice of the London Pharmacopoeia, improperly termed an extract, is also objectionable. All these anomalies, and the diversity of strength of the different preparations enjoined by the different pharmacopoeias of London, Edinburgh, and Dublin, from the existence of which, serious consequences often result, will in future be avoided, by the publication of the National Pharmacopoeia,' ordered to be prepared under the new Medical Bill. Besides the officinal preparations, various popular ones exist. Of the scientific ones, Dr. Fleming's tincture is the best. It requires great care in its use. An excise officer lost his life, from merely tasting it (Journal of Pharmaceutical Society,' vol. xi. p. 237). A spurious aconitine is prepared in France, and imported into this country. It is devoid of the valuable properties of the genuine, the high price of which offers too great a temptation to fraud. The best forms are either an alcoholic extract of the leaves, or an alcoholic tincture of the root made by displacement. The inactivity of the watery extract and inspissated juice has led to statements in some popular treatises that it may be given in the dose of twenty grains, a quantity which would prove fatal when the extract is prepared with alcohol. Of this latter it is rare that two grains can be given with safety: a quarter of a grain is sufficient to begin with. Possessing narcotico-acrid properties, the action of aconite on the human frame is different according to the quantity used. In small medicinal doses its most obvious action is purely local; in larger, its action is both local and remote. Thus a small portion chewed produces an immediate action, tingling, followed by numbness of the lips and tongue; increased secretion of saliva also occurs. Minute doses taken into the stomach cause augmented secretion both of the mucous membrane and of the glands in the vicinity, the secretion of the liver is often markedly increased; while tingling of the extremities, with heat, is often felt, and either perspiration or increased action of the kidneys. The effect on the pupil is variously stated. Geiger affirms that aconitine produces dilatation of the pupil, Dr. Pereira most positively asserts, in his Materia Medica, that the external application of it produces contraction; while in his experiments with the extract of the Aconitum ferox (recorded in Edinb. Journ. of Natural and Geograph. Science, July 1830, p. 235) he distinctly states that while the animal continued alive the pupils were much dilated,' contraction taking place only after the animal was apparently dead. Large doses cause redness and inflammation of the parts brought in contact with it; but the intellectual powers do not seem impaired by it, even when a fatal result occurs. Sir B. Brodie thinks that it occasions death by destroying the functions of the brain. ('Phil. Trans.' 1818, p. 186.) For this effect he does not consider absorption necessary; while Dr. Pereira concludes from his experiments, that the intensity of its remote action on the nervous system is in proportion to the absorbing powers of the part to which it is applied (Edinb. Jour.' p. 242). The susceptibility of the heart to galvanic agents is greatly impaired by it. When first introduced into medical practice it was recommended in many diseases; but it is now almost entirely restricted to painful affections of the nerves, and to rheumatic complaints, particularly when they are complicated with syphilis. For nervous affections it is more used externally than internally, but this last mode is to be commended at the same time. An ointment is formed with one or two grains of the aconitine to one drachm of axunge. A small portion of this is to be applied frequently to the part affected. An eruption sometimes appears, especially if the ointment be strong. The internal use of aconitine is scarcely to be advised, one-fiftieth of a grain having endangered the life of an adult. The very high price of this article is an obstacle to its extensive employment; but ingenious chemists are endeavouring to simplify the process of extracting it. To obtain it perfectly pure it is almost essential to use sulphuric ether in the preparation of it, which necessarily increases the expense. The alcoholic tincture or extract is of great service in chronic rheumatism, and even in some cases of acute rheumatism

Should poisoning occur, no time is to be lost, as it has proved fatal in one hour after being eaten instead of horseradish, at Bristol (Jour. of Pharmaceutical Society,' vol. xiii. p. 294). Animal charcoal has been recommended as an antidote. But even if really useful, it is only serviceable when quite freshly prepared, in which state it is rarely to be had promptly. The best mode of proceeding is as soon as it has been ascertained that Monkshood has been taken if the root or leaves have been eaten-to endeavour to empty the stomach as quickly as possible. Warm water alone, or with flour of mustard in it, will generally effect this; or a stomach pump, if at hand, may be used. Perhaps magnesia diffused through the water may be useful. But abundance of very warm water' is good alone. Afterwards hartshorn, properly diluted, tincture of cardamoms or brandy may be given. The patient should be kept walking, if possible. Should inflammation ensue, venesection may be needed.

ACOUSTICS is sometimes divided into the science of hearing (from akoúw, to hear), and that of sounding or PHONICS (from pwrn, sound). It is not necessary to attempt to define what sound is, or to dwell on the fact that some sounds differ only in intensity or loudness, as the reports of a cannon and a musket; others in musical pitch, as two notes of the same instrument; others again in character or tone, or, as the French call it, timbre, such as the same note sounded on a flute and a trumpet. These differences being understood, we proceed to inquire by what agency these different sounds are conveyed to the ear; in what manner the ear is acted upon by sounds of different loudness, tone, and character; and how far we can explain the remarkable fact that we can hear and distinguish, at the same time, almost any number of different sounds. Unfortunately, our knowledge is limited by the nature of the question, which requires the improvement of one of the most difficult branches of mathematical analysis; and by our very imperfect knowledge of the constitution of matter, and the effect which the putting in motion of some particles of a body has upon the other particles. Strictly speaking, we ought to say, that sound has no existence except in the mind of the hearer; but, in accordance with common phraseology, we shall speak of a body as sounding when it is in that state in which it would produce the impression of sound, if the proper medium were placed between it and the ear.

No body can produce a sound, as we know from observation, unless its parts be put into rapid motion. We have evidence of this in a tuning fork, the string of a musical instrument, the parchment-head of a drum, &c. Neither will any sound be perceived unless there is a continual supply of solid or fluid matter, possessed of a moderate degree of elasticity, between it and the ear. Thus, a bell, when rung in the exhausted receiver of an air-pump, yields hardly any sound; and the small portion which it does give may be destroyed or materially diminished by lining the receiver with cotton or wool; or still better, by exhausting the receiver as much as the air-pump will allow, then filling it up with pure hydrogen gas and again exhausting. The air is generally the medium through which sound is conveyed; but only because this is most commonly the one with which the membrana tympani or membrane of the drum of the ear is in direct communication. A bell rung under water has been distinctly heard by M. Colladon across the whole breadth of the lake of Geneva, a distance of 9 miles, the sound being observed to pass through the water with a velocity of 4708 feet per second; those who work in one shaft of a mine can often distinctly hear the sound of the pickaxe in another shaft through the solid rock; and persons wholly deaf, who therefore are not at all affected through the ear, have received pleasure from music, by placing their hands upon a shutter or other solid body near the instruments. Biot's experiments, too, have shown some very curious results of the varying velocity of sound for different media. He fixed a bell at the end of an iron tube of about 3120 feet in length, and he found that the sound of the bell was double as heard at the other end, the first sound being transmitted through the metal, and the second through the column of air in its interior. He also found that the slightest whisper at one end was distinctly communicated to the other. To this fact he added the observation, that the well-known double report of a musket is owing to the same cause, the sound being unequally carried through the air and the vapour floating in it. In the following remarks we will confine our attention to what takes place in air during the production of

sound.

The body of air which surrounds us produces no sound if it be all moved together, that is, if the velocity of all its particles be the same : the highest wind makes no noise except when it is forced against some obstacle; but the sound of a cannon is heard in whatever direction the wind may blow: it may also be remarked, that the strongest band of music does not produce any sensible wind in any direction. It is therefore to some other kind of motion that we must look for the agent of sound, and the manner in which sonorous bodies move immediately points it out. If a tuning-fork or string be struck, a rapid succession of vibrations is the consequence, which, as we shall see, causes the particles of air to vibrate in a similar manner. We find, moreover, that in order to produce a note, there must be not only a succession, but a rapid succession, of vibrations. Now, experiments show that the ear is not capable of receiving the impression which we call sound, unless the particles of air in contact with it vibrate at least 30 times in a second. The vibration produced in the particles of air by a sonorous body may be distinctly proved by the following experi

ment. Let a tuning-fork be sounded, and while yet in vibration, let it be stopped by the finger. A sensation will be felt for an instant, for which we have no name in our language, arising from the prong of the fork rapidly, but gently, striking the finger, and very different from that which is produced by merely touching the fork when at rest. Now, blow into a common flute, and at the same time stop gently two or three of the higher holes. The same sort of sensation, though in a much smaller degree, will be felt on that part of the fingers' ends which is in communication with the interior air. For this purpose the fingers should be warm, but if the observer be not used to the instrument, the effect is made more certain by tuning the string of a violoncello to the note which is to be fingered on the flute, and then sounding the former strongly, while the latter is held over it, with the fingers placed as before. The column of air in the flute will be made to vibrate by the motions of the string, forming a case of what is called sympathetic vibration. That any very violent and sudden noise produces a concussion in the air even farther than the sound can be heard, is proved by the fact, that the explosion of a large powder-mill will shake the windows in their frames for nearly twenty miles around.

We now proceed to describe, as far as can be simply done, the motion which takes place in the air when the impression of sound is communicated; and here we stop to explain a method which may be adopted in many cases, of making the eye assist the reason. Suppose we wish to register what takes place in the vibration of a spring, of which the position of rest is A B (fig. 1), but which, having been set in motion, passes through all the positions between AC and AD. The Fig. 1. Fig. 2.

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put in motion, yet that those particles which are nearer the disturbing piston receive their first impression sooner than those which are more Fig. 3.

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distant; and we find that this successive propagation, as it is called, of the disturbance, goes on uniformly at the rate of about 1125 feet in a second, the temperature being 62° of Fahrenheit; for example, a second must elapse before those particles, which are 1125 feet distant from A, will have their first news, so to speak, of what is going on at A, and in the same proportion for other distances. It is also shown that the velocity of communication is not affected by the greater or less degree of violence with which the air is struck, but remains the same for every sort of disturbance. With such a velocity, we may see that the column of air made up of all the particles which feel, or have felt, the effects of the disturbance, must be very long when compared with a C, the extent of an almost insensible vibration; so that it will lead to no sensible error if we suppose that the effect of the piston at every point of its course is propagated instantaneously to c, and thence only, with the velocity of 1125 feet per second. We will now consider what this effect is. Divide the whole length ▲ c, fig. 4, into a large number of very small parts, described in equal times, and instead of the piston moving continuously, and with imperceptible changes of velocity, along A C, let it move by starts from each point to the next, with the proper increase or decrease of velocity. In the figure we have divided a c into ten parts, but the same reasoning applies to any greater number. We have much enlarged ▲ ¤ (fig. 4), to give room for the figure: the reader Fig. 4.

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spring being drawn aside by the finger or other disturbing cause to a C, and then released, the elasticity of the metal makes continued efforts to restore it to its first position A B, by which it is made to move, and with continual accession to its velocity, until it actually does arrive at A B, where, if the velocity were suddenly destroyed, it would remain at rest. But the velocity still continuing, the spring continues to move towards a D, with a change of circumstances, inasmuch as the elasticity, now opposing its motion, gradually destroys the velocity by the same steps as it was before gradually created; so that when the spring comes to a D, it will be again at rest, but will not continue so, since the elasticity will cause the same phenomena to be repeated, and the spring will move back again towards a c. But for friction and the resistance of the air it would again reach Ac; it does not, however, get so far, owing to these causes, which always diminish, and never increase, velocity. This alternation will go on until the spring is reduced to a state of rest. Similar phenomena occur in the motion of a pendulum, of the string of a harpsichord, and gene: ally, wherever small vibrations are excited in a body, which remove it, but not much, from its position of rest. We might, perhaps, conclude, that each successive oscillation is performed in a shorter time than the preceding, seeing that a less space is described by the spring. But this is not the fact; it can be observed, as well as demonstrated, that the oscillations which take place before a body recovers the effects of a small disturbance and resumes the state of rest, are severally performed, if not in the same time, yet so nearly in the same time, that the difference may be entirely neglected in most practical applications. Such being the case, we may omit the effects of friction and resistance, so far as the time of vibration is concerned, and consider the spring as describing exactly the same path in each successive vibration. Let D C (fig. 2) be the line described by the top of the spring, which we may call a straight line, since it is very nearly so, and while the spring roves from D to c, imagine a curve Dy c to be drawn, in such a way that, the spring being the perpendicular xy is the rate per second at which the top of the spring is then moving. A little attention will show that the curve which we have drawn represents the various changes of motion just alluded to: thus TB, the greatest perpendicular, is over the point B, where the spring moves fastest; and at D and c there is no perpen. dicular, because the spring comes to rest when it reaches those points. During the return from c to D, in which the motion is the same, but in a contrary direction, let a similar branch ctD be drawn, on the other side of C D. We will call the whole curve DTCtD the type of the double vibration of the spring, the two branches being the types of its two halves. Now, suppose a column of air inclosed in a thin tube A B (fig. 3), which is indefinitely extended towards B, but closed at a by a piston which can be moved backwards and forwards from a to c, and from c to A, after the manner of a spring, the type of its motion being represented by the curves on a C. And first let the piston be pushed forward from a to c. If the air were solid, we should say that a column of air AC in length would be pushed out of the end B of the tube in the time in which the piston is driven in, but we certainly can have no notion that such an effect would be produced upon a column of elastic fluid like the air. Experiment, as well as mathematical demonstration, show us that though every particle of the fluid will finally be

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may help his ideas by supposing that a c is viewed through a powerful microscope, and the rest of the tube by the naked eye. Whatever may be the common time of moving through each of the parts a 1, 12, &c., the portions of the column affected by the starts of the piston will be of the same length, and each will be as much of 1125 feet as the time of each start is of one second. Set off the lengths c P, PQ, QR, &c., each equal to this length, and for the present let us agree to call the common time in which the piston starts through a 1, 12, &c., an instant. The reader must bear in mind throughout that we intend to carry the supposition of dividing a c into parts to its utmost limit, by which we shall have to suppose CP, PQ, &c., to be very small, though still great when compared with A1, 12, &c. We also think it right to repeat, that all the figure on the left of c is immensely magnified, and that the propagation is supposed to be instantaneous from 1, 2, &c., to c. In the first instant, the piston moves through a 1, with the velocity p 1 per second, and forces the column of air a 1 into CP, which therefore has its density increased, or is compressed, the air which was held in CP and ▲ 1 together being now confined in CP. As the propagation has not travelled farther than P, the effect is just the same as if there had been a solid obstacle at P during the first instant. The portion CP is then compressed, strictly speaking, unequally; that is, the parts near to c are more compressed than those near to P; but on account of the small length of c P, and the rapidity of the transmission, we may suppose all the parts to be equally compressed. Again, the particles near c begin to move towards P, and for a similar reason we may suppose the velocities of all the particles to be the same; this velocity being that of a during the first instant. The reader must not confound the absolute velocity of the several particles, which is always small, with the rate at which they transmit their velocities and compressions, which is very great. We will use the phrase that the portion C P has received its first compression. If the piston were stopped at the end of the first instant, the whole effect upon CP would be transferred to P Q in the second instant, both as to compression and velocity, and the particles of CP would return to their first state, and receive no further modification. But in the second instant, the portion C P receives its second compression, which is greater than the first, since a column 1 2 longer than a 1 is forced into it. Similarly, the velocity is increased, being 2 q per second instead of 1 p. If the spring were then stopped, the third instant would see the portion P Q transmit its velocity and compression to Q R, CP to PQ, and CP would resume its natural state. But in this instant, CP receives its third compression, which is greater than the former two, and the same process goes on, each portion transmitting its velocity and compression to the succeeding one, receiving in its turn more than it parted with, from the preceding. This continues until the piston has reached the middle point of a c, after which the compression of C P still continues, but becomes less and less in successive instants, because 56, 67, &c., down to 9 c, decrease in length, in the same way as a 1, 12, &c., increased. When the piston begins to return through c 9, in the eleventh instant, the portion C P receives its first rarefaction; for the air in CP now occupies C P and c 9; the particles in o P therefore move towards c instead of from it, and the preceding modifications are suc

cessively repeated in quantity, but changed into their contraries; that is, each portion undergoes successive rarefactions, equal in amount to the former condensations, and the particles move towards c with the same velocities which they formerly had from 0. This continues until the piston reaches A again, after which the same phenomena recommence in the same order. Thus it appears that the absolute velocity of each particle is in the direction of the propagation so long as it is compressed; but in the contrary direction, when it is rarefied, and that each particle, during the progress of a double series of compressions and rarefactions, moves forward in the direction of propagation, and back again to its former place, where it rests, unless a third vibration follow the first two. When we talk of the compression of a particle, we mean that it is nearer the succeeding particle than it would have been in its natural state; and vice versa for rarefaction. We may represent these phenomena in the following table, which, to save room, is made on the supposition that a c was divided into four parts, and might be equally well constructed if the number of parts into which a C was divided had been greater. The numbers in the top horizontal line are the successive portions of the tube, those in the left vertical column the successive instants of time, and under any portion of the tube, opposite to any instant of time, will be found the state in which that portion of the tube is at that instant of time,-1 denoting its first compression, l' its first rarefaction; these latter numbers recommencing when a complete cycle of changes is finished. The blanks denote that the effect has not yet reached the corresponding particles.

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dicular, through something more than a quarter of a vibration: the first disturbance has reached D, and the curve D K is the type of the state of each particle as to velocity; that is, the perpendicular FG is the rate per second at which the particle F is moving from c, and the same for every other perpendicular.

If the piston be performing its third complete vibration, or its second vibration forwards, there will have been a preceding series of compressions and rarefactions propagated onwards, as in fig. 5 (1). In fig. 5 (2), a vibration forwards has been completed; the curve on CD now represents a complete undulation, as far as the compressions are concerned. In fig. 5 (3), the return of the piston has commenced, and the particles between C and D are rarefied, and moving towards c; this we explain by placing the type beneath the tube, and dotting the curve; FG expressing the velocity per second of the particle F towards c. The length of the whole wave CD is easily calculated. If, for example, the single vibrations of the piston are made in of a second, the first impulse will have travelled through one hundredth part of 1125 feet, or 11 feet. This is the length of CD, in fig. 5 (2). The complete series of compressions is called a wave of compression; and that of rarefactions a wave of rarefaction. And the same type which represents to the eye the velocities of the various particles, will also serve to represent the degrees of compression or rarefaction. For those particles which are moving quickest from c are most compressed, and those which move quickest towards c are most rarefied. In returning to fig. 4, we see that ▲ 1, 12, 23, &c., are spaces described in equal times, and are therefore in the same proportions as the velocities, that is, as 1p, 2q, 3 r, &c. But these spaces, in the preceding explanation, are proportional to the degrees of condensation; these latter then are proportional to the velocities. If, then, we suppose the series of compressions and rarefactions to have gone on for some time, and an unfinished wave of compression to have been formed at the instant we are considering, we may represent the whole state of the particles in the tube at that instant by the following figure (fig. 6):-R G N is a line parallel to the tube, and therefore GF is of the same length for all positions of F. It is to be made 1125 feet in length. Its use depends upon the following proposition :-That in the simple undulation which we are now considering, so long as the disturbance is small, the velocity of any particle bears to the velocity of propagation (two very distinct things, as we have before observed) the same proportion as the change in the density bears to the density of undisturbed air. This follows from the investigation attached to fig. 4. for, in the fourth instant for example, the column 3 4 of air is forced into o P, and 3 4 and C P being spaces described in equal

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On casting the eye down any vertical column, we see the state of the same portion in successive instants of time: on looking along a horizontal column, we see the state of all the portions of the tube at the same instant, as far as the effect has reached them. In the latter case, we see that all the successive states are continually repeated, in such a way, that whatever states two portions may be in, the intermediate portions have all the intermediate states. There is also at the beginning an unfinished series in process of formation. If we look down a column, we see that any one particle successively undergoes the different states, from the moment when the effect first reaches it. We shall now sup pose the division of AC to go on without end, and examine the final result. The different states of compression or rarefaction will then become more and more numerous, but the difference of quantity between each and its preceding will become less and less, so that when we at last give to the piston a continuous or gradually increasing and decreasing velocity, we must also suppose a continuous or gradually increasing and decreasing compression or rarefaction of the air in the tube. This being premised, we return to the figure, and construct the type of the motion of the piston, both backwards and forwards, and also the type of the state in which the particles of air actually are for two or three several positions of the spring; as in the figure below, which we proceed to explain. (Fig. 5.)

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times with velocities 4 and 1125 feet per second, are spaces propor
tional to these velocities. And the compression will be the same if we
increase C P in any proportion, provided we increase the quantity of air
forced into it in the same proportion. A similar proposition holds for
rarefactions. Or, in other words, F K being the velocity with which
the particle at F is moving towards c, the rarefaction of the particles at
F is that which would be obtained by allowing the air naturally con-
tained in a tube G F, 1125 feet long, to expand into the length G K.
Similarly, the compression at L is that which would be obtained by
compressing the air in a tube N L into the shorter tube N M.
wish to see the state of these particles at any succeeding instant, let
of 1125 feet per second, new curves being continually formed and
the curvilinear part of the figure travel uniformly forward at the rate
finished at c: we shall thus have the state of the whole tube at any
the phenomena of sound, we must see what will take place if the tube
succeeding moment. Before proceeding to apply this explanation to
be agitated by several different undulations at once.

If we

All readers, however little acquainted with Mechanics, are aware, that if a body be impressed by two forces in the same direction, it will proceed with the sum of the velocities produced by the two forces; and with the difference of the velocities, if the forces act in contrary direc tions, the motion in the latter case being in the direction of the greater of the forces. Hence, if there be different undulations excited in the same column of air, the velocities of each particle will be made up of the sum or difference of those, which it would have received from each undulation, had each acted alone; the sum when it would have been compressed by both, or rarefied by both, and the difference when it would have been compressed by one and rarefied by the other. And the compressions or rarefactions being proportional to the velocities, a similar proposition will hold of them. We have represented in fig. 7,

In fig. 5 (1) the piston has tavelled from A to the small perpen- the state in which a column of air would be at a given instant from

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