S 141. Rule. The first Future tense is employed merely to express what shall or will take place hereafter; while the second Future is used to denote what shall have occurred at some future period. OBSERVATIONS. (1) The Future tenses, both first and second, have their precise equivalents in the corresponding English tenses, and should be used accordingly. (2) When a future action is represented, or is mentioned, as a thing necessary to be done, as in the English phrases, I am to go, he is to have, and the like, the German employs a distinct verb expressive of obligation or necessity; as, ich soll es haben, I am (shall be obliged) to have it. Er soll sprechen, &c. $142. RULE. The Indicative mood is used in affirming or denying that which is conceived to be certain or undoubted; as, Er wird morgen zurückkommen, he will return to-morrow. OBSERVATIONS. (1) Since the proper office of the Indicative is to express reality, it is employed in all absolute or independent sentences. Even in conditional sentences, moreover, it is used, if the condition is assumed as a fact; as, bist du reich, so gib viel, art thou rich (i. e. if thou art rich), give much. (2) Sometimes the Indicative is employed instead of the Imperative, where that which is enjoined is treated as something already in progress; as, du trittst vor, thou steppest forward, i. e. step (thou) forward. This is regarded as the strongest form of command. § 143. RULE. (6) The Subjunctive appears, also, in asking indirect questions; as, ich fragte ihn, ob er mir das Geld geben könne, I asked him, whether he could give me the money. When the question is made directly, of course the Indicative is used. (7) The Subjunctive is sometimes employed as a sort of softened Imperative, to express a wish or permission; as, gebe es der Himmel, may heaven grant it! dieser Baum trage nie wieder Frucht, let this (or may this) tree never again bear fruit! er thue was er will, let him do what he will! $ 144. RULE. The Conditional mood is used where a condition is supposed which may or may not be conceived to be possible; as, Wäre ich reich, so würde ich ihm seine Bitte nicht abgeschlagen haben, were I rich, I would not have refused his request. Wenn er noch lebte, so würde er 50 Jahre alt sein, if he yet lived, he would be fifty years old. OBSERVATIONS. (1) Besides the two tenses ranged in the paradigms under the head of the Conditional, it must be observed that the Imperfect and the Pluperfect of the Subjunctive are equally often employed in expressing conditional propositions. In point of time, indeed, there is no difference between the Imperfect of the Subjunctive and the first Conditional, and between the Pluperfect of the Subjunctive and the second Conditional. Ordinarily, where both forms are employed in the same sentence, the Subjunctive will be found in the clause expressing the condition, while the form peculiar to the Conditional appears in the other; as, ich würde es thun, wenn es möglich wäre, I would to it, if it were possible; wenn er hier wäre, würde er dich besucht haben, if he were here, he would have visited you. (2) When the condition is assumed and treated as a fact, it is expressed, not by the Conditional, but by the Indicative; as, The Subjunctive mood is used when that which is expressed by bit bu reich, so gieb riel, art thou (i. e. if thou art) rich, then give the verb is conceived to be uncertain, though possible; as, Ich habe gehört, daß er die gewünschte Stelle erhalten habe, I have heard, that he has obtained the desired situation. Ich wünsche, daß er glücklich werde, I wish that he may become happy. OBSERVATIONS. (1) The Subjunctive, from its very nature, stands chiefly in dependent clauses; and in these appears under various circumstances. Thus, it is employed : (2) When the design of the speaker is merely to repeat or quote a statement, without vouching for its accuracy; as, er fagt, quote a statement, without vouching for its accuracy; as, er fagt, ter Baum blühe, he says, that the tree blossoms; er meldete mir, daß er sich verheirathet habe, he told me, that he had been married. When, on the contrary, the design of the speaker is to set forth the thing repeated or quoted, as something real and undoubted, the Indicative must be used; as, er will es nicht glauben, daß sein Bruter gestorben ist, he will not believe that his brother is dead. (3) In like manner, the Subjunctive is used in subordinate clauses, after such verbs as hoffen, to hope; fürchten, to fear; wünschen, to wish; wollen, to desire; bitten, to ask; rathen, to advise; verbieten, to forbid; ermahnen, to exhort; since the event, in such cases, may be supposed to be always more or less uncertain; as, er fürchtet, daß er Strafe erhalte, he is afraid that he may be punished. (4) So, also, the Subjunctive is employed in clauses which indicate an end, object, wish, or result; and which are introduced by daß, auf daß, damit, or by a relative; as, sprich laut, damit er dich verstehe, speak loud, that he may understand you; er sucht Arbeit, welche ihm Brod gebe, he seeks work, which may give him bread. (5) In cases such as those explained in the observations above, the student must note that that tense of the Subjunctive is employed which corresponds with the one used by the subect of the dependent clause, of the time when he said or did that which is affirmed of him: as, er sagte, er habe diesmal keine geit, he said, that he had (literally has) no time at present; er beste mir gesagt, daß er es gethan habe, he had told me, that he had done it. much. (3) Sometimes the verb expressing the condition is merely understood; as, ich hätte die Sache anders gemacht, I should have done it otherwise (if it had been committed to me); in feiner Page hätte ich es nicht gethan, (if I had been), in his situation, I would not have done it. (4) Sometimes, in the way of exclamation, the condition is expressed, while that which depends upon it is omitted: in which case the whole expression being of the nature of a wish or petition, is often introduced (in translation) by " O," "I wish O, that I had never seen this man! literally, had I never seen that," and the like: as, hatte ich doch diesen Mann nie gesehen! as, this man (how happy I should be)! wäre er doch am Leben! O, that he were yet alive! (5) The Conditional is frequently employed in questions designed to elicit a negative answer; as, wäre es denn wahr? could it be true? (it could not be true;) du wäreft so falsch gewesen? would you have been so faithless? (you would not.) dürfen, sollen, können and wollen, is employed to render an expres(6) Not unfrequently the Conditional of the auxiliaries mögen, sion less positive, or to give it an air of diffidence; as, ich wollte, Sie begleiteten mich, I could wish (instead of, I wish) you would accompany me; ich möchte schwer zu überreden sein, I should be hard to be persuaded, or, it would be difficult to persuade me; dürfte ich Sie um das Meffer bitten? might I (be permitted to) ask you for the knife? § 145. RULE. The Imperative mood is used in expressing a command, entreaty, or exhortation; as, Fürchte Gott und ehre den König, fear God and honour the king. OBSERVATIONS. (1) The Imperative is sometimes employed to indicate a condition on which something is declared to depend; as, sei stolz, und du wirst wenig Achtung finden, be haughty (i. e. if you be haughty) and you will find regard. du (2) In order to make a request in a manner modest and po- | opiniónis, of an opinion; in like manner, veritas, átis, means that the nom lite, instead of the Imperative, the Subjunctive of mögen and native is veritas, truth, and the genitive, veritátis, of a truth. wollen is often employed; as, bu wolltest seiner nie vergeffen, pray, understand. Partly this arises from an omission in printing, partly from a A. J. calls our attention to a diagram at p. 113, Lesson VII., which he cannot never forget him; mögen Sie meiner gedenken, may you remember, misapprehension of our correspondent himself. Let A. J. begin by supplying or remember me, I pray. To express a decided command, the printer's omission, namely, two diagonal junction lines; one between the however, the Indicative is frequently used. See § 142. 2. figures 9 (water) and 8 (oxygen), the other between the figures 32 (sulphurous acid) and 16 (oxygen). Let A. J. then attend to the following remarks. Throughout this diagram the figures have reference to parts by weight, not expression immediately following, i.e. "In this diagram I have avoided all to atoms; indeed this non-reference to atoms is sufficiently indicated by the fractional numbers for the sake of greater clearness." Now there can be no fractions of an atom, and had we been treating of atoms we should have had no fractions to avoid. A. J. says our diagram represents the atmosphere as composed of 7 equivalents (atoms) nearly of nitrogen and three of oxygen, whereas he goes on to say "it is well known_that four-fifths of the almosphere consist of nitrogen and the other fifth of oxygen." Well, this composition is immediately deducible from our numbers :-thus, (3) Sometimes, by a peculiar ellipsis, the past Participle is employed in place of the Imperative; as, nur nicht lange gefragt! do not ask long! where the full phrase would be, es werde nur nicht lang gefragt, let it not long be asked! An die Arbeit gegangen, let them go to their work! ANSWERS TO CORRESPONDENTS. T. Q. Q: is informed that a class for instruction in Mr. Curwen's He should write to Mr. R. Griffiths, 4, Cullum-street, Fenchurch-street. THE FOUR BALL QUESTION.-We have received numerous solutions of this question, but with one or two exceptions, they are all erroneous. The chief cause of error is the supposition that the centres of the four balls must lie all in one plane. Now this cannot be the case; for if so, then the four balls could not by any possibility be put all in contact with each other, a thing which was required by the question. But if three balls be put in contact with each other, and the fourth ball be placed above them so as to touch each of the three, then the four balls will be in contact with each other. Now the ball which is to touch each of the four must be placed in the interior space among the four balls, and must be of considerably less diameter than theirs. We have received a correct and ingenious solution from QUINTIN PRINGLE (Glasgow), in which the 47th of Euclid's 1st Book is the only element in the calculation, a matter of some importance to a learner, and we would at once insert it; but, like the lion's cub, it wants licking into shape, so as to be fit for the public eye. Moreover, he has in his solution, assumed the principle of the centre of gravity of a pyramid, a mechanical principle which cannot be admitted into a geometrical demonstration. What has become of the solutions which might have been expected from some of our old correspondents, such as PETER SIMPLE, X PLUS Y, JOHN BATES, etc.? system of music is likely to be opened near the entrance to Waterloo-bridge. J. S. WINDOW (Monmouthshire): English Dictionaries are as plenty as blackberries in their season; therefore, Cassell's ditto won't be published for some time, if at all.--W. MERONES (Manchester) and J. WILSON (Ardwick), who seem to be the same person, are very anxious about Astronomy. We should like very much that they would study spelling and our Lessons in English in the P. E.-AMICUS (Leamington): Laplace on Astronomy.-ERASTES: The French Lessons of the P. E. may be had in a separate volume for the students you wish to instruct in that language. Mr. Cassell will shortly publish a work on Botany.-CONSTANT SUBSCRIBER (Hertford): Waud's Algebraic Geometry or Hymer's Conic Sections; Simson's Conic Sections. HENRY D. DAVIS (Maida Hill): His answer to the Four Ball Question appears to be right, but his method is a little awkward.-T. MORGAN (Llanelly) has given nearly the same answer as the preceding correspondent, but he exhibits none of the operation.-HENRY IKIN (Welshpool): The treatise of Nesbitt on Surveying is, we believe, a very good one.-J. BUCHANAN (Airdrie): All that we know of the "School of Mining " we give from a book put into our hands by Dr. Lyon Playfair. "Metropolitan School of Science applied to Mining and the Arts. Museum of Practical Geology. The following courses of lectures will be given during the Session 1853-4. 1. Chemistry, with special reference to its application in the Arts and Manufactures.-A. W. Hofmann, Ph. D., F.R.S. 2. Natural History, applied to Geology and the Arts.-Edward Forbes, F.R.S. 3. Physical Science, with its special Applications.-Robert Hunt, Keeper of Mining Records. 4. Metallurgy, with its special Applications.-John Percy, M.D., F.R.S. 5. Geology, and its practical Application. A. C. Ramsay, F.RS. 6. Mining and Mineralogy.-Warington W. Smyth, M. A., F.G.S. 7. Applied Mechanics.-Robert Willis, M.A., F.R S. fee for Matriculated students for the course of two years is one payment of £30, or two annual payments of £20. This fee includes practical instruction in the field and mechanical drawing. The fees for the chemical and metallurgical laboratories are £10 for the term of fourteen weeks. One of the "Duke of Cornwall's Exhibitions," of £30 per annum, to be held for two years, granted by H.R.H. the Prince of Wales, will be competed for at the end of the Session. Acting mining agents or managers may attend the lectures at half the usual charges. The same rule is applied to officers in the Queen's or the Hon. E. I. Company's Service, members of the College of Preceptors, and certificated schoolmasters. Tickets for separate Courses are issued at £1 each, or £15 for the whole of the lectures during the Session. For further information apply to Mr. Trenham Beeks, Curator, at the Museum, Jermyu-street, London.-H. T. DE LA BECHE, Director." The WM. R: 1. No; 2. Yes; 3. Yes; 4. See University of London, No. VI. in the P. E.-J. S. A, A. C. (Dublin): Lessons on Reading and Elocution are going on.-TRIANGLE: We do not see how Trigonometry can be practical, unless it is applied to those practical branches to which he refers.-A YOUNG BEGINNER (Machen): We can't answer, because we don't understand his question.-N.: Yes. H. ROWDEN LONG (Colnbrook): Yes.-THE BRUSH (Blisworth): Go on; we are preparing. WM. STOKER (Staffordshire Potteries): We think he is right; the Bible and the P. E. are the best books. There is a new edition of the "Working Man's Friend" being issued at a cheap rate. As to his Latin queries, 1. Yes; 2. Slow; 3. Yes; 4. No. In the vocabulary opinio, onis means, that the nominative is opinio, an opinion, and the genitive is Throughout we have assumed that which in point of fact is not strictly true, viz. that the sp. grs. of oxygen and of nitrogen are equal. Our diagram, in point of fact, is not atomic, but approximate. Nevertheless it is a near approximation. We have no right to make the atmosphere amenable to the laws of the atomic theory, inasmuch as it is not even proved to be a compound, much less an atomic mixture. A. JOHNSON: Hydrosulphite of lime may be made by boiling together lime, sulphur, and water, filtering, exposing the filtered liquid to the air, breaking the scum on the surface of the liquid as often as formed, and filtering again. Hyposulphite of soda is made by adding a solution of carbonate of soda to hyposulphite of lime, filtering, and evaporating. Hyposulphurous acid can barely be obtained. Herschell thought he had procured it, by adding sulphuric acid to hyposulphite of baryta; but the evolved acid was almost immediately decomposed. Our correspondent will purchase hyposulphite of soda much cheaper than he can make it. LITERARY NOTICES. CASSELL'S LATIN DICTIONARY, BY J. R. BEARD, D.D.-The publication of this Dictionary has commenced, and will be completed in about Twenty-six Numbers, THREEPENCE each, or in Monthly Parts, ONE SHILLING each. Part the First is now ready; Part the Second will be ready with the Magazines for April. CASSELL'S FRENCH AND ENGLISH DICTIONARY.-The FRENCH and ENGLISH portion of this important Dictionary is now completed, and may be had, price 4s., or strongly bound, 5s. The ENGLISH and FRENCH portion is in the course of publication, and will be completed in about Twelve Numbers, THREEPENCE each. The entire Dictionary, forming one handsome volume, will be ready with the Magazines for April, price 9s. 6d. CASSELL'S GERMAN PRONOUNCING DICTIONARY.-The GERMANENGLISH Portion of this Dictionary is now ready, price 5s. in stiff covers or 5s. 6d. strong cloth.-The ENGLISH-GERMAN Portion will be completed as quickly as possible, in Numbers, THREE PENCE each; and the entire Volume, strongly bound, at 9s., will shortly be issued. These Lessons have not been surpassed by any which have been published, CASSELL'S LESSONS IN FRENCH. Part I. By Professor FASQUELLE, Their aim is, by an easy method, to remove every difficulty out of the way of those who are desirous of acquiring a perfect knowledge of the French Language. Price 28. in paper covers, or 2s. 6d. cloth. Part II. Containing a complete Systematic Grammar, including Etymology and Syntax, with copious References to the Idioms in Part I., and Examples from the best French Writers, with Parallel Translations, furnishing the means of acquiring a full, accurate, and permanent knowledge of the French Language. Price 2s. in paper covers, and 2s. 6d. cloth. Parts I. and II., bound in one volume, price 4s. 6d. A KEY TO CASSELL'S LESSONS IN FRENCH. Containing Translations of all the Exercises. of all the Exercises. Price ls. in paper covers, or Is. 6d. cloth. A COMPLETE MANUAL OF THE FRENCH LANGUAGE. By Professor DE LOLME. In this Manual the Rules as to Genders, Idioms, Terminations, &c., are clear, simple, and complete; and the whole work will be found to embrace a more comprehensive and practical scheme for the acquisition of a moduga knowledge of the French Language than any hitherto published. Price 3s. neatly bound. CASSELL'S LESSONS IN ENGLISH. Containing a Practical Grammar, adapted for the use of the Self-educating Student. By J. R. BEard, D.D In paper covers, 3s.; in cloth boards, 38. 6d. ON PHYSICS OR NATURAL PHILOSOPHY. No. XXV. ACOUSTICS. (Continued from page 351.) Echoes and Ringing Sounds.-The repetition of a sound in the air by reflection from any obstacle, is called an echo. In order that the phenomenon of an echo may take place, the sound must be reflected in the direction of the observer, and the reflecting obstacle must be at the distance of at least 56 feet; for it is scarcely possible to distinguish one sound from another, unless about one-tenth of a second elapses between the two sounds. Now, the velocity of sound being about 1,120 feet per second, it is plain that in a tenth of a second, sound would pass over a space of about 56 feet; consequently, if the reflecting obstacle is at or beyond a distance of 56 feet, the sound in going to the obstacle and returning from it would have at least 112 feet to pass over. The time which elapses between the direct and the reflected sound will therefore be, at least, one-tenth of a second; thus, the two sounds will not confound each other, and the reflected sound will be distinctly heard. According to these remarks, it is evident that if we speak in a high voice before a reflecting body at the distance of 56 feet, we can only distinguish the last reflected syllable; whence the echo is monosyllabie; if the reflecting body be distant two, three, or more times the distance of 56 feet, the echo will be dissyllabic, trisyllabic, and so on. When the distance of the reflecting body is less than 56 feet, the direct and the reflected sounds have a tendency to mingle and produce confusion of sound. They cannot be heard separately, but the sound is strengthened, and this effect is called a resonance, or ringing sound. This phenomenon is observed in large rooms; empty halls are very resonant or resounding, but curtains and drapery, which are bad reflectors of sound, remove the effect of such resonances in halls and large apartments. Multiplying echoes are those which repeat the same sound several times; this takes place when two obstacles placed opposite to each other, as, for instance, two walls parallel to one another, mutually reflect the sound emitted. At Adernach, in Bohemia, there is an echo that repeats seven syllables three times; and at Lurley-Fells, on the Rhine, there is another that repeats the same sound seventeen times. There is a famous echo at Woodstock, in Oxfordshire, which is said to repeat the same sound fifty times. At Rosneath, in Dumbartonshire, there is an echo which is said faithfully to repeat eight or ten notes of a tune played with a trumpet, but a third lower; after a short interval, another repetition is heard in a still lower tone; and after a similar interval, a third repetition in a tone a third lower still. Among the ancients, the echo at Capo-di-Bove was reckoned famous; so also was that at the tomb of the Metelli, at Rome, which is said to have distinctly repeated eight times the first verse of the Æneid of Virgil, which contains fifteen syllables. There is an echo on the Villa Simonetta, near Milan, which repeats a shout thirty times; and another in Pavia repeats the last syllable of a question the same number of times. The laws of the reflection of sound being the same as those of the reflection of light and heat, the curve surfaces on which of the reflection of light and heat, the curve surfaces on which it falls give rise to acoustic foci analogous to the luminous and calorific foci which are produced by concave reflectors. For example, if we speak under the arch of a stone bridge, with the face turned to one of the piers, the words will be reproduced with so much intensity at the opposite pier, that a conversation can be carried on in a low voice without being heard by persons situated in the intermediate space. In the ground-floor of the "Conservatoire des Arts et Metiers," at Paris, there is a square hall with an arched ceiling which exhibits this phenomenon in a remarkable manner, when two persons place themselves at two opposite corners. The Whispering Galleries both of ancient and modern times have their origin in the similar architecture of their roofs and ceilings; as in the Ear or grotto of Dionysius of Syracuse, and in the whispering gallery of St. Paul's Cathedral, London. Sound is reflected not only from the surface of solid bodies, VOL. IV. such as the walls of a building, woods, and rocks; but also from the clouds, at their meeting with a stratum of air having a different density from that through which they have been passing; and even from the vesicles of which fogs are composed. Thus, when the atmosphere is foggy, sounds undergo a considerable number of partial reflections, which extend themselves through the air with immense rapidity. At night, when the air is clear, calm, and of uniform density, sounds are heard at by far the greatest distance. The Speaking and the Hearing Trumpets.-The speakingtrumpet and the hearing-trumpet are two small instruments constructed on the principles of the reflection of sound, and on its conductibility in cylindrical tubes. The former, as its name indicates, is intended to carry the sound of the voice to great distances. It consists of a tube made of tin-plate or brass, fig. 128, which is slightly conical throughout its length, but funnel or bell-shaped at the one end, and which is held to the mouth at the other end in order to convey the sound of the voice to a distance. The principle of the instrument is explained by the successive reflections of the waves of sound from the sides of the tube; reflections which, in consequence of its form, tend to render the waves more and more divergent. In the theory of this instrument, it is shown that to the of the air undergo near the funnel, must be assigned the prinincrease of the amplitude of the oscillations which the particles cipal cause of the effects which it produces in practice. The hearing-trumpet is employed by persons who are very hard of hearing. It is also a conical metal tube, one of the extremities of which terminates in a funnel or bell, by which the sound enters, and the other extremity of which is placed close against the ear. The funnel or bell, in this case, is the mouth-piece, that is, it receives the sounds which come from reflections in the interior of the instrument, so that the waves the speaker. These sounds are transmitted by a series of which had taken a wide development are concentrated in the auditory portion of the instrument, and there produce a much more sensible effect than if they had proceeded from divergent waves of sound. VIBRATIONS OF CORDS, THEIR NUMBER AND INTENSITY. Two kinds of Vibration in Cords.-In acoustics, cords are thread-shaped bodies rendered elastic by tension. In tense cords two kinds of vibration are observed, the one transversal, or in a direction perpendicular to the cords; the other longitu 103 swell. dinal, or in the direction of their length. The transversal | the vibrations attain their maximum of altitude, is called a vibrations are produced by a bow, as on the violin, or by pulling them quickly in the direction perpendicular to their length, as on the harp and the guitar. The longitudinal vibrations are produced by rubbing the cords in the direction of their length with a piece of silk sprinkled with rosin. As the transversal vibrations are those only which are concerned in the theory of music, we shall confine our inquiries to this kind of vibrations in cords. In order to prove the existence of nodes and swells in the vibrations of cords, one is fixed at both ends, and under it a small bridge is successively placed at a third, a fourth, and a fifth part of the cord. If the bridge be placed at one-third of the cord, as represented in fig. 129, No. 1, and the part в D be made to vibrate with a bow, the other part A B will then divide itself into two parts, A C and C B, which will vibrate CB, separately, the point c remaining sensibly fixed. This will be clearly seen by placing small pieces of paper on the cord, one at c, one between в and c, and one between c and A. As soon as the cord is put into vibration, the piece of paper at c will only be slightly disturbed, while the other pieces will be thrown to a distance. There is, therefore, a node at the first point, and there are swells at the other two points. If the I Fig. 129, No. 1. The Sonometer or Monochord.-The sonometer is an apparatus which is employed in the investigation of the transversal vibrations of cords. It is also called the monochord, because it is constructed only with a single chord. This apparatus is composed of a case or box of thin wood, which is intended to increase the sound; on this case are fixed two bridges, A and », fig. 129. No. 1, over which a metallic cord passes, fixed at one end, and stretched at the other by a series of weights which can be increased at pleasure. A third bridge, B, is made moveable along the case, in order to vary the length of the cord which is put into the vibratory state. Laws of the Transversal Vibrations of Cords.-It has been found by analysis that if 7 be made to represent the length of the cord, that is, the part which vibrates between the two! bridges A and B, in fig. 129; r the radius of a transverse section; d the density of the cord; r the weight which keeps it stretched; and n the number of vibrations per second; the 1 P r.l πα formula n= ป. in which denotes the ratio of the circumference to the diameter of a circle, and the relation which subsists among the quantities just enumerated. Whence the four following laws are easily deduced :— 1st. The tension of a cord being constant, the number of vibrations in the same time is in the inverse ratio of the length. 2nd. Other things being equal, the number of the vibrations is in the inverse ratio of the radius of a transverse section of the cord. 3rd. The number of the vibrations of the same cord is directly proportional to the square root of the weight by which it is kept stretched. 4th. Other things being equal, the number of the vibrations of a cord is inversely proportional to the square root of its density. The first of these laws, which is the most important, may be verified by experiment, if we employ a cord sufficiently long and sufficiently tense to admit of the number of its oscillations being counted by the observer. Nodes and Nodal Lines.-When a body is made to vibrate, it does so not only in its whole mass, but it divides itself generally into a number of aliquot parts, of which each is animated with its own proper vibrations. Between these different parts certain points or lines exist which vibrate less than the rest, and which may be considered as sensibly fixed. Such points are denominated nodes; and such lines are denominated nodal lines. The vibrating parts comprised between two nodes and two nodal lines are called a concameration, that is, an arching or_vaulting. The middle of a concameration, the place where may suggest a simpler construction than the preceding to cord is fixed, A and B the fixed bridges at the extremities of some readers; C D is the case or box, a the point where the the case, B' the place of the moveable bridge, which is deterany experiment by means of a graduated scale on the box placed below the cord, p the pulley over which the cord passes, and 6 the weight which keeps it tense. mined in 1 The existence and the form of nodal lines in vibrating plates and membranes will be proved in a subsequent lesson. Savart's Toothed Wheel.-The toothed wheel of M. Savart, which bears the name of its inventor, is an apparatus constructed to show the absolute number of vibrations which correspond to a determinate sound. It is formed of solid pieces of oak firmly fixed together on a stand, like a bookbinder's bench, having an aperture in the middle through nearly its whole length. In the aperture are placed two wheels, A and B, fig. 130, No. 1, of which the first, a, is employed to communicate a great velocity to the second, B; and the second, which is toothed, is employed to produce vibrations in a card or flexible plate, E, fixed at one end of the bench. This card, being struck by each tooth on its passage, makes, by the revolution of the toothed wheel, as many complete vibrations as there are teeth. On a small dial, H, placed a counter, which receives its motion from the axis of the toothed wheel, and which indicates the number of turns per second, and consequently the number of vibrations. If a is slow motion be given at first to the toothed wheel, the successive strokes of the teeth upon the card are distinctly heard; but if the velocity be gradually increased, a continued sound is obtained, which gradually rises higher and higher. When, by this means, the sound is produced whose number of vibrations are required, the same velocity is kept up during a determinate number of seconds; and by reading off on the counter the number of turns of the toothed wheel E, we have only to the toothed wheel, e is the place where the card is fixed which catches the teeth of the wheel. The Siren.-The siren is a small apparatus employed, like the preceding, for the purpose of measuring the exact number of the vibrations of a sonorous body in a given time. M. Cagniard de Latour, the inventor, gave this name to the instrument, because it can be made to yield sounds under water. It is made wholly of brass, and is represented in Fig. 130, No. 1. fig. 131, mounted on the box of a blowing machine or bellows, hereafter described, which is employed to send a continued current of air into the siren. Fig. 132, No. 1, and fig. 133, show the interior details of the siren. The lower part of this instrument consists of a cylindrical box, o, surmounted by a fixed plate, B. On this plate rests a vertical rod T, to which is fastened a disk A, that turns freely with the rod; several holes are made at equal distances, in a circular form, in the plate B; and in the disk a an equal number, of the same size and at the same distance from the centre as those of the plate, are perforated. These holes are not perpendicular to the planes of the plate and the disk; but they are all inclined to them at the same angle, those in the plate being inclined in one direction, and those in the disk in the contrary direction, in such a manner that when the holes in the plate and the disk face each other they are arranged as seen at mn, fig. 133. From this arrangement it follows, that when a rapid current of air comes from the bellows into the cylindrical box and into the hole m, it obliquely strikes the sides of the holen, and imparts to the disk A, a motion of rotation in the directions n A. In order to simplify the explanation of the play of the siren, we shall first suppose that the moveable disk ▲ is pierced with Fig. 133. Fig. 131, No. 1. |