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S 141. RULE.
(6) The Subjunctive appears, also, in asking indirect ques
tions; as, ich fragte ihn, ob er mir das Gelb geben könne, I asked him, The first Future tense is employed merely to express what whether he could give me the money. When the question is shall or will take place hereafter; while the second Future is made directly, of course the Indicative is used. used to denote what shall have occurred at some future period.
(7) The Subjunctive is sometimes employed as a sort of
softened Imperative, to express a wish or permission; as, gebe es OBSERVATIONS.
ber Himmel, may heaven grant it! dieser Baum trage nie wieder Fruct, (I) The Future tenses, both first and second, have their let this (or may this) tree never again bear fruit ! et thue wað er precise , equivalents in the corresponding English tenses, and will, let him do what he will ! should be used accordingly. (2) When a future action is represented, or is mentioned, as
$ 144. RULE. 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 The Conditional mood is used where a condition is supposed verb expressive of obligation or necessity; as, ich soll es Haben, I which may or may not be conceived to be possible ; as, am (shall be obliged) to have it. Er soll sprechen, &c.
Wäre ich reich, fo würde ich ihm feine Bitte nicht abgeschlagen haben,
were I rich, I would not have refused his request. $ 142. RULE.
Wenn er noch lebte, so würde er 50 Jahre alt fein, if he yet lived, he The Indicative mood is used in affirming or denying that would be fifty years old. which is conceived to be certain or undoubted; as,
OBSERVATIONS. Er wirb morgen zurüdfommen, he will return to-morrow.
(1) Besides the two tenses ranged in the paradigms under OBSERVATIONS.
the head of the Conditional, it must be observed that the Im(1) Since the proper office of the Indicative is to express perfect and the Pluperfect of the Subjunctive are equally often reality, it is employed in all absolute or independent sentences, employed in expressing conditional propositions. In point of Even in conditional sentences, moreover, it is used, if the con- time, indeed, there is no difference between the Imperfect of dition is assumed as a fact; as, bist du reich, so gib viel, art thou the Subjunctive and the first Conditional, and between the Plurich (i. e. if thou art rich), give much.
perfect of the Subjunctive and the second Conditional. Ordi(2) Sometimes the Indicative is employed instead of the Im- marily, where both forms are employed in the same sentence, perative, where that which is enjoined is treated as something the Subjunctive will be found in the clause expressing the conalready in progress; as, du trittst vor, thou steppest forward, i. e. dition, while the form peculiar to the Conditional appears in the step (thou) forward. This is regarded as the strongest form of other; as, ich würde es thun, wenn es möglich wäre, I would to it, if command.
it were possible; wenn er hier wire, würde er dich besucht haben, if he
were here, he would have visited you. § 143. RULE.
(2) When the condition is assumed and treated as a fact, it The Subjunctive mood is used when that which is expressed by is expressed, not by the Conditional, but by the Indicative ; as, the verb is conceived to be uncertain, though possible; as,
much. Ich habe gehört, daß er die gewünschte Stelle erhalten habe, I have
(3) Sometimes the verb expressing the condition is merely heard, that he has obtained the desired situation.
understood; as, ich hatte dic Sache anders gemacht, I should have Id wünsche, daß er glücklich werde, I wish that he may become done it otherwise (if it had been committed to me); in seiner happy.
Lage hätte ich es nicht gethan, (if I had been), in his situation, I OBSERVATIONS.
would not have done it. (1) The Subjunctive, from its very nature, stands chiefly in
(4) Sometimes, in the way of exclamation, the condition is dependent clauses; and in these appears under various cir- expressed, while that which depends upon it is omitted: in
which case the whole expression being of the nature of a wish cumstances. Thus, it is employed : (2) When the design of the speaker is merely to repeat or that," and the like: as, Hätte ich doch diesen Mann nie gesehen ! as,
or petition, is often introduced in translation) by“ 0," "I wish quote a statement, without vouching for its accuracy; as, er fugt
; O, that I had never seen this man ! literally, had I never seen fer Brum blühe
, he says, that the tree blossoms; er meldete mir, daß this man (how happy I should be)! märe er dochy am leben! 0, cr fich verheirathet ħabe, he told me, that he had been married. When, on the contrary, the design of the speaker is to set forth that he were yet alive!
(5) The Conditional is frequently employed in questions dethe thing repeated or quoted, as something real and undoubted, the Indicative must be used; as, cr will es nicht glauben, daß sein signed to elicit a negative answer; as, märe es denn maýr? could
er du ? Pruter gestorben ist, he will not believe that his brother is dead.
(3) In like manner, the Subjunctive is used in subordinate would you have been so faithless ? (you would not.) clauses, after such verbs as hoffent , to hope ; fürchten, to fear; dürfen, follen, können and wollen, is employed to render an espres
(6) Not unfrequently the Conditional of the auxiliaries mögen, wünschento ; wollen, desire; bitten, to ask; rathen, to advise; verbieten, to'forbid; ermaincu, to exhort; since the event, Sie begleiteten miờ, I could wish (instead of, I wish) you would
sion less positive, or to give it an air of diffidence; as, id) wollte, in such cases, may be supposed to be always more or less uncertain ; as, cr füriptet, tag er Strafe erhalte, he is afraid that he i accompany me; ich möchte schwer zu überreden sein, I should be
hard to be persuaded, or, it would be difficult to persuade me; may be punished. (4) So; also, the Subjunctive is employed in clauses which dürfte ich Sie um bas Meffer bitten? might I (be permitted to
| ask you for the knife ? indicate an end, object, wish, or result; and which are introduced by tai, ani tuš, damit, or by a relative; as, sprich Inut, damit
§ 145. RULE. er sich verstehe, speak loud, that he may understand you; er fucht arbeit, welde ihm Brod gebe, he seeks work, which may give him The Imperative mood is used in expressing a command, enbread,
treaty, or exhortation; as, (5) In cases such as those explained in the observations
Fürdyte Gott und ehre den König, fear God and honour the king. above, the student must note that that tense of the Subjunctive is employed which corresponds with the one used by the sub.
OBSERVATIONS. ect of the dependent clause, of the time when he said or did that which is affirmed of him : as, cr sagte, er Habe diesnial feine (1) The Imperative is sometimes employed to indicate a conZvit, he said, that he had (literally has) no time at present; er dition on which something is declared to depend; as, sei stolz, !cate mnie geagt, derß er s8 getsan jabe, he had told me, that he had und du wirst wenig Achtung finden, be haughty (i. e. if you be
haughty) and you will find regard.
(2) In order to make a request in a manner modest and po- opinionis, 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, du wollteft feiner nie vergessen, pray, understand. Partly this arises from an omission in printing, part!y 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.
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 (sulphu
rous acid) and 16 (oxygen). Let A. J. then attend to the following remarks. (3) Sometimes, by a peculiar ellipsis, the past participle is
ellipsis, the past Participle is Throughout this diagram the figures have reference to parts by weight, not employed in place of the Imperative; as, nur nicht lange gefragt! espression immediately following, i.e. * In this diagram I have avoided all do not ask long! where the full phrase would be, es werde nur fractional numbers for the sake of greater clearness.” Now there can be no nicht lang gefragt, let it not long be asked! An die Arbeit gegangen, fractions of an atom, and had we been treating of atoms we should have had let them go to their work!
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 composi
tion is immediately deducible from our numbers thus, ANSWERS TO CORRESPONDENTS.
1.20 : 0.96 :: 1.00 : 4 (Nitrogen)
1.20 : 0.24 :: 1.00 : 3 (Oxygen)
strictly He should write to Mr. R. Griffiths, 4, Cullum-street, Fenchurch-street.
true, viz. that the sp. grs, of oxygen and of nitrogen are equal. Our dia THE FOUR BALL QUESTION.-We have received numerous solutions of gram, in point of fact, is not atomic, but approximate. Nevertheless it is this question, but with one or two exceptions, they are all erroneous. The a near approximation. We have no right to make the atmosphere amenable chief cause of error is the supposition that the centres of the four balls must to the laws of the atomic theory, inasmuch as it is not even proved to be a lie all in one plane. Now this cannot be the case; for if so, then the four compound, much less an atomic mixture. 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 con
A. JOHNSON: Hydrosulphite of lime may be made by boiling together tact with each other, and the fourth ball be placed above them so as to lime, sulphur, and water, filtering, exposing the filtered liquid to the air, touch each of the three, then the four balls will be in contact with each breaking the scum on the surface of the liquid as often as formed, and
Now the ball which is to touch each of the four must be placed in filtering again. Hyposulphite of soda is made by adding a solution of the interior space among the four balls, and must be of considerably less carbonate of soda to hyposulphite of lime, Altering, and evaporating. Hydiameter than theirs. We have received a correct and ingenious solution posulphurous acid can barely be obtained. Herschell thought he had
profrom QUINTIN PRINGLE (Glasgow), in which the 47th of Euclid's Ist cured it, by adding sulphuric acid to hyposulphite of baryta; but the evolved Book is the only element in the calculation, a matter of some importance to acid was almost immediately decomposed. Our correspondent will purchase a learner, and we would at ouce insert it; but, like the lion's cub, it wants hyposulphite of soda much cheaper than he can make it. 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 beep expected from some of our old correspondents, such as PETER SIMPLE, X PLUS Y, JOHN BATES, etc.?
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such as the walls of a building, woods, and rocks; but also ON PHYSICS OR NATURAL PHILOSOPHY. from the clouds, at their meeting with a stratum of air having
a different density from that through which they have been No. XXV.
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 (Continued from page 351.)
themselves through the air with immense rapidity. At night,
when the air is clear, calm, and of uniform density, sounds are Rcroes and Ringing Sounds.-The repetition of a sound in the heard at by far the greatest distance. air by reflection from any obstacle, is called an echo. In order The Speaking and the Hearing Trumpets. — The speakingthat the phenomenon of an echo may take plaee, the sound trumpet and the hearing-trumpet are two small instruments must be reflected in the direction of the observer, and the constructed on the principles of the reflection of sound, and on , reflecting obstacle must be at the distance of at least 56 feet; its conductibility in cylindrical tubes. The former, as its for it is scarcely possible to distinguish one sound from another, name indicates, is intended to carry the sound of the voice to unless about one-tenth of a second elapses between the two great distances. It consists of a tube made of tin-plate or sounds. Now, the velocity of sound being about 1,120 feet brass, fig. 128, which is slightly conical throughout its length, 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
Fig. 128. Ieflecting 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 refiectors 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 but funnel or bell-shaped at the one end, and which is held to eight or ten notes of a tune played with a trumpet, but a third the mouth at the other end in order to convey the sound of lower; after a short interval, another repetition is heard in a the voice to a distance. The principle of the instrument is still lower tone; and after a similar interval, a third repetition explained by the successive reflections of the waves of sound in a tone a third lower still.
Among the ancients, the echo at Capo-di-Bove was reckoned from the sides of the tube ; reflections which, in consequence famous ; so also was that at the tomb of the
, at Rome, of its form, tend to render the waves more and more diverwhich is seid to have distinctly repeated
eight times the first gent. In the theory of this instrument, it is shown that to the Ferse of the Æneid of Virgil, which contains fifteen syllables. increase of the amplitude of the oscillations which the particles There is an echo on the Villa Simonetta, near Milan, which of the air undergo near the funnel, must be assigned the prinrepeats a shout thirty times; and
another in Pavia repeats
the cipal cause of the effects which it produces in practice. last syllable of a question the same number of times.
The hearing-trumpet is employed by persons who are very The laws of the reflection of sound being the same as those hard of hearing. It is also a conical metal tube, one of the of the reflection of light and heat, the curve surfaces on which extremities of which terminates in a funnel or bell, by which it falls give rise to acoustic foci analogous to the luminous and close against the ear. The funnel or bell, in this case, is the calorific foci which are produced by concave reflectors. For ex- mouth-piece, that
is, it receives the sounds which come from if turned to one of the piers, the words will be reproduced
with reflections in the interior of the instrument, so that the waves
the speaker. These sounds are transmitted by a series of so much intensity at the opposite pier, that a conversation can which had taken a wide development are concentrated in the be carried on in a low voice without being heard by persons auditory portion of the instrument, and there produce a much situated in the intermediate space. In the ground floor of the Conservatoire des Arts et Metiers," at Paris, there is a
more sensible effect than if they had proceeded from divergent
waves of sound. square hall with an arched ceiling which exhibits this phenomenon in a remarkable manner, when two persons place
VIBRATIONS OF CORDS, THEIR NUMBER AND themselves at two opposite corners. The Whispering Galleries
INTENSITY both of ancient and modern times have their origin in the similar architecture of their roofs and ceilings; as in the Ear Two kinds of Vibration in Cords.-In acoustics, cords are or grotto of Dionysius of Syracuse, and in the whispering thread-shaped bodies rendered elastic by tension. In tense gallery of St. Paul's Cathedral, London.
cords two kinds of vibration are observed, the one transversal, Sound is reflected not only from the surface of solid bodies, or in a direction perpendicular to the cords; the other longitus
Sinai, or in the direction of their length. The transversall the vibrations attain their maximum of altitude, is called a vibrations are produced by a bow, as on the violin, or by swell. pulling them quickly in the direction perpendicular to their In order to prove the existence of nodes and swells in the length, as on the harp and the guitar. The longitudinal vibra- vibrations of cords, one is fixed at both ends, and under it a tions are produced by rubbing the cords in the direction of their small bridge is successively placed at a third, a fourth, and a length with a piece of silk sprinkled with rosin. As the fifth part of the cord. If the bridge be placed at one-third of transversal vibrations are those only which are concerned in the cord, as represented in fig. 129, No. 1, and the part B D be the theory of music, we shall confine our inquiries to this kind made to vibrate with a bow, the other part A B will then of vibrations in cords.
divide itself into two parts, Ac and C B, which will vibrate The Sonometer or Monochord.--The sonometer is an apparatus separately, the point c remaining sensibly fixed. This will be which is employed in the investigation of the transversal clearly seen by placing small pieces of paper on the cord, one vibrations of cords. It is also called the monochord, because it at C, one between B and c, and one between c and A. As is constructed only with a single chord. This apparatus is soon as the cord is put into vibration, the piece of paper at c composed of a case or box of thin wood, which is intended to will only be slightly disturbed, while the other pieces will be increase the sound; on this case are fixed two bridges, A and thrown to a distance. There is, therefore, a node at the first D, fig. 129. No. 1, over which a metallic cord passes, fixed at one point, and there are swells at the other two points. If the
end, and stretched at the other by a series of weights which bridge be placed at a fourth part of the cord, it will produce can be increased at pleasure. A third bridge, B, is made between A and B two nodes and three swells; if at a fifth moveable along the case, in order to vary the length of the part, it will form between the same points three nodes and four cord which is put into the vibratory state.
swells, and so on. Laws of the Transversal Vibrations of Cords.-It has been The following side view of a monochord, fig. 129, No. 2, found by analysis that if l be made to represent the length of the cord, that is, the part which vibrates between the two!
Fig. 129, No. 2 bridges A and B, in fig. 129; r the radius of a transverse
B. section ; d the density of the cord; f the weight which keeps it stretched; and n the number of vibrations per second ; the 1 P
D formula n =
in which denotes the ratio of the
ril circumference to the diameter of a circle, and the relation which subsists among the quantities just enumerated. Whence
b the four following laws are easily deduced :
Ist. The tension of a cord being constant, the number of may suggest a simpler construction than the preceiling to Fibrations in the same time is in the inverse ratio of the length. 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
which is deteris in the inverse ratio of the radius of a transverse section of the case, B' the place of the moveable brid the cord.
mined in any experiment by means of a graduated scale on the 3rd. The nunber of the vibrations of the same cord is box placed below the cord, P the pulley over which the cord directly proportional to the square root of the weight by passes, and 6 the weight which keeps it tense. which it is kept stretched.
The existence and the form of nodal lines in vibrating plates 4th. Other things being equal, the number of the vibrations and membranes will be proved in a subsequent lesson. of a cord is inversely proportional to the square root of its
Savart's Toothed Thecl.--The toothed wheel of M. Savart, density.
which bears the name of its inventor, is an apparatus con
structed to show the absolute number of vibrations which The first of these laws, which is the most important, may correspond to a determinate sound. It is formed of solid be verified by experiment, if we employ a cord sufficiently pieces of oak firmly fixed together on a stand, like a booklong and sufficiently tense to admit of the number of its oscil- binder's bench, having an aperture in the middle through lations being counted by the observer.
nearly its whole length. In the aperture are placed two Nodes Nodal Lines. When a body is made to vibrate, it wheels, A and B, fig. 130, No. 1, of which the first, A, .is does so not only in its whole mass, but it divides itself gene- employed to communicate a great velocity to the second, B; rally into a number of aliquot parts, of which each is animated and the second, which is toothed, is employed to produce with its own proper vibrations. Between these different parts vibrations in a card or flexible plate, E, fixed at one end of the certain points or lines exist which vibrate less than the rest, bench. This card, being struck by each tooth on its passage, and which may be considered as sensibly fixed. Such points makes, by the revolution of the toothed wheel, as many comare denominated nodes ; and such lines are denominated nodal plete vibrations as there are teeth. On a small dial, h, is lines. The vibrating parts comprised between two nodes and placed a counter, which receives its motion from the axis of two nodal lines are called a concameration, that is, an arching the toothed wheel, and which indicates the number of turns @r_vaulting. The zaiddle of a concameration, the place where per second, and consequently the number of vibrations. If a slow motion be given at first to the toothed wheel, the succes- the toothed wheel, e is the place where the card is fixed which sive strokes of the teeth upon the card are distinctly heard; catches the teeth of the wheel. but if the velocity be gradually increased, a continued sound The Siren.The siren is a small apparatus employed, like is obtained, which gradually rises higher and higher. When, the preceding, for the purpose of measuring the exact numby this means, the sound is produced whose number of vibra- ber of the vibrations of a sonorous body in a given time. M. tions are required, the same velocity is kept up during a deter- Cagniard de Latour, the inventor, gave this name to the minate number of seconds ; and by reading off on the counter instrument, because it can be made to yield sounds under the number of turns of the toothed wheel 2, we have only to water. It is made wholly of brass, and is represented in
multiply this number by that of the teeth it contains, in order | fig. 131, mounted on the box of a blowing machine or bellows, to obtain the whole number of vibrations. Then dividing this hereafter described, which is employed to send a continued product by the corresponding number of seconds, the quotient current of air into the siren. Fig. 132, No. 1, and fig. 133, will be the number of vibrations per second. The following show the interior details of the siren. The lower part of this representation of the same instrument in outlige may suggest instrument consists of a cylindrical box, o, surmounted by a
fixed plate, B. On this plate rests a vertical rod T, to which Fig. 130, No.2.
is fastened a disk A, that turns freely with the rod; several d 量
holes are made at equal distances, in a circular form, in the ъ
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 d
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 improvement or simplicity in the construction, fig. 130, No. 2. the hole m, it obliquely strikes the sides of the hole ", and aa is the oaken bench, 6 is the large wheel furnished with a imparts to the disk A, a motion of rotation in the directions winch c, d is an axle on which is placed the toothed wheel d' " A. and a pulley of small radius, x is the band which passes over the In order to simplify the explanation of the play of the siren, large wheel and the pulley, and communicates the motion to we shall first suppose that the moveable disk A is pierced with