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from the point G are drawn two straight lines G B, G. F., and prolonged to an infinite length, the distance between them will become greater than any assigned magnitude, and consequently than that which may be the distance between the parallels; when, therefore. they are distant from each other by more than this, G F will cut G D.”* Without disputing that the distance between the straight lines which make the angle will become greater than any assigned magnitude—(though the reason given appears to be founded on ignorance of the fact that a magnitude may perpetually increase and still be always less than an assigned magnitude), -the defect is in begging the question, that the distance between the parallels is constant or at all events finite. For the very point in dispute is, whether the parallels (as for instance two perpendiculars to a common straight line, both of them prolonged both ways) may not open out or grow more distant as they are prolonged, and to do this so rapidly, that a straight line making some very small angle with one of them, shall never overtake the other, but chase it unsuccessfully through infinite space, after the manner of a line and its asymptote. 4. Clavius announces that “a line every point in which is equally distant from a straight line in the same plane, is a straight line;” upon taking which for granted, he finds himself able to infer the properties of Parallel Lines. And he supports it on the ground that because the acknowledged straight line is one which lies evenly sea aoquo) between its extreme points, the other line must do the same, or it would be impossible that it should be everywhere ! equidistant from the first. Which is only settling one unknown by a reference to another unknown. 5 and 6. In a tract printed in 1604 by Dr. Thomas Oliver, of Bury, entitled, De rectarum linearum parallelismo et concursu doctrina Geometrica (Mus. Brit.), two demonstrations are proposed; both of them depending on taking for granted, that if a perpendicular of fixed length moves along a straight line, its extremity describes a straight line. Which is Clavius's axiom a little altered. 7. Wolfius, Boscovich, Thomas Simpson in the first edition of his “Elements,” and Bonnycastle, alter the definitions of parallels, and substitute in substance, “that straight lines are parallel which preserve always the same distance from one another;” by distance being understood the length of the perpendicular drawn from a point in one of the straight lines to the other. Attempts to get rid of a difficulty by throwing it into the definition, are always to be suspected of introducing a theorem in disguise; and in the É. instances, it is only the introduction of the proposition of lavius. No proof is adduced that straight lines in any assignable position, will always preserve the same distance from one another; or that if a perpendicular of fixed length travels along a straight line keeping always at right angles to it, what mathematicians call * locus of the distant extremity is necessarily a straight line at all. 8. D'Alembert proposed to define parallels as being straight lines “one of which has two of its points equally distant from the other line;” but acknowledged the difficulty of proving, that all the other points would be equally distant in consequence j. 9. Thomas Simpson, in the second edition of his “Elements,” proposed that the Axiom should be, that “If two points in a straight line are posited at unequal distances from another straight line in the same plane, those two lines being indefinitely produced on the side of the least distance will meet one another.” 10. Robert Simpson proposes that the Axiom should be, “that a straight line cannot first come nearer to another straight line, and then go further from it, before it cuts it.”.] By coming nearer or

* We omit the Greek. + “Nam si onnia puncta lineae AB,aequaliter distant à rectā D c, ex æquo sua interjacebit puncto, hoc est, mullum in ea punctum intermedium ab extremis sursum, aut deorsum, vel hue, atque illuc deflectendo subsultabit, nihilque in ea flexuosum reperietur, sed aequabiliter semper inter sua puncta extendetur, quemadmodum recta D C. Alioquin non omnia ejus puncta aequalem a reetà D D, distantiam haberent, quod est contra hypothesin. Neque verö cogitatione apprehendi potest aliam lineam praeter rectam, posse habere omnia sua puncts a rectà lineš, quae in eodem cum illā plano existat, aequaliter distantia.’—Clavii Opera. In Euclidis Lib. I. p. 50. * † ——“la vraie définition, ce me semble, et la plus nette qu'on puisse donner d’une parallèle, est de dire que c'est une ligne qui a deux de ses points €galement éloignés d'une autre ligne.—il faut ensuite démontrer (et c'est-lä, le plus dimeiej, que tous les autres points de cette seconde, seront également éloignées de la ligne droite, donnée.”—ENOLYCLOPEDIE. Art. Parallèle. | This and most of what has preceded, is in the Arabic. In a manuscript copy of Euclid in Arabic but in a Persian hand, bought at Ahmedabad in 1817, the editor on the introduction of Euclid's Axiom comments as follows. “And this is what is said in the text. I maintain that the last proposition is not of the universally-acknowledged truths, nor of anything that is demonstrated in any other part of the science of geometry. The best way therefore would be, that if it should be put among the questions instead of the rinciples; and I shall demonstrate it in a suitable place. And I lay down #. this purpose another proposition, which is, that straight lines in the same

going from it, being understood the diminution or increase of the perpendicular from one to the other. • The objection to all these is, that no information has been given on the subject of the things termed straight lines, which points to any reason why the distance's growing smaller should be fiecessarily followed by the meeting of the lines. It may be true; but the reason why, is not upon the record. On the contrary, it is well known that there exist lines (as for instance the neighbouring sides of two conjugate hyperbolas) where the distance perpetually decreases and yet the lines never meet. It is open therefore to ask, what property of the lines called straight has been promulgated, which proves they may not do the like. 11. Varignon, Bezout, and others propose to define parallels to be “straight lines which are equally inclined to a third straight line,” or in other words, make the exterior angle equal to the interior and opposite on the same side of the line. By which they either intend to take for granted the principal fact at issue, which is whether no straight lines but those that make such angles cars. fail to meet; or if their project is to admit none to be parallel lines of which it shall not be predicated that they make equal angles as above with some one straight line either expressed or understood, then they intend to take for granted that because they make equal angles with one straight line, they shall also do it with any other that shall in any way be drawn across them,--a thing utterly unestablished by any previous proof. 12. Professor Playfair proposes to employ as an Axiom, that “two straight lines, which cut one another, cannot be both parallei to the same straight line ;” in which he had been preceded by Ludlam and others, and which he says “is a proposition readily enough admitted as self-evident.” The misfortune of which is, that instead of being self-evident, a man cannot see it if he tries. What he sees is, that he does not see it. He sees that a straight line's making certain angles with one of the parallels, causes it to . meet the other; and he sees that by increasing the distance of the point of meeting, he can cause the angle with the first parallel to grow less and less. But if he feels a curiosity to know whether he can go on thus reducing the angle till he makes it less than any magnitude that shall have been assigned (or in other words whether there may not possibly be some angle so small that a straight line drawn to any point however remote in the other parallel snall fail to make so small a one), he discovers that this is the very thing nature has denied to his sight; an odd thing, certainly, to call self-evident. 13. The same objections appear to lie against Professor Leslie’s proposed demonstration in p. 44 of his “Rudiments of Plane Geometry;” which consists in supposing a straight line of unlimited iength both ways, to turn about a point situate in one of the parallels, which straight line, it is argued, will attain a certain position in which it does not meet the other straight line either way, while the slightest deviation from that precise direction woul occasion a meeting. 14. Professor Playfair, in the Notes to his “Elements of Geometry,” p.409, has proposed another demonstration, founded on a remarkable non causa pro catasa. It purports to collect the facto that (on the sides being prolonged consecutively) the intercepted or exterior angles of a rectilinear triangle are together equal to four right angles, from the circumstance that a straight line carried round the perimeter of a triangle by being applied to all the sides in succession, is brought into its old situation again ; the argument being, that because this line has made the sort of somerset it would do by being turned through four right angles about a fixed point, the exterior angles of the triangle have necessarily been equal to four right angles. The answer to which is, that there is no connexion between the things at all, and that the result will just as much take place where the exterior angles are avowedly not equal to four right angles, Take, for example, the plane triangle formed by three small arcs of the same or equal circles, as in the figure; and it is manifest that an arc of this circle may be carried round in the way described and return to its old situation, and yet there be no pretence for inferring that the exterior angles were equal to four right angles. And if it is urged that these are curved. lines and the statement made was of straight; then the answer is by demanding to know, what property of straight lines has been laid down or established, which determines that what is not true in the case of other lines is true in theirs. It has been shown that, as

plane, if they are subject to an increase of distance on one side, will not be subject to a diminution of distance on that same side, and the contrary; but will cut one another. And in the demonstration of this I shall employ another proposition, which Euclid has employed in the Tenth Book and elsewhere, which is, that of any two finite magnitudes of the same kind, the smallest by being doubled over and, over, will become greater than the greatest. And it will further require to be laid down, that one straight line cannot be in the same straight line with straight limes more than one that do not coincide with one another; and that the angle which is equal to a right angle, is a right angle.” We omit the Arabic. * I. 32. Cor. 2.

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angles have been equal to four right angles, is a mistake. . From which it is a legitimate conclusion, that if nature had contrived to make the exterior angles of a rectilinear triangle greater or less than four right angles, this would not have created the smaklest impediment to the line’s returning to its old situation after being carried round the sides; and consequently the line's returning is no proof of the angles not being greater or less than four right angles. 15. Franceschini, Professor of Mathematics in the University of Bologna, in an Essay entitled La Teoria delle parallele rigorosa2mente dimostrata, printed in his Opuscoli Matematichi at Bassano in 1787, offers * a proof which may be reduced to the statement, that if two straight lines make o, a third the interior angles on the same side one a right angle and the other an acute, perpendiculars drawn to the third line from points in the line which makes the acute angle, will cut off successively greater and greater portions of the line they fall on. From which it is inferred, that because the portions so cut off go on increasing, they must increase till they reach the other of the two first straightlines, which implies that these two straight lines will meet. Being a conclusion founded on neglect of the very early mathematical truth, that continually increasing is no evidence of ever arriving at a magnitude assigned. The remainder in our next.

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THE preposition in denotes being, continuance, or motion in the , interior of a thing. It also denotes any kind of motion or penetration into it. The idea of existence in a time or in a certain condition, particularly in a certain state or disposition of the mind, likewise requires the use of in. The preposition a, on the contrary, merely expresses presence near or about a thing , or motion, approach, and tendency to it; e.g. ē-gli è nel giar-di-no, in qué!-la cd-me-ra, in cit-tá, in pidz-za, he is in the garden, in that room, in the town, in the square; d-glian-drd in In-ghil-têr-ra, in I.spd-gna, he will go to England, to Spain; nél' din-no mil-le sét-te cén-to, in the year 1700; sog-gior-nó al-quan-to in Ró-ma, he staid a while in Rome; Ge-si, Cri-sto nd-cque in Be-te-lém-me, Jesus Christ was born in Bethlehem; e-gl: mo-ri nel mil-le tre cén-to,

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he died in 1300; im-mér-ge-re à-no nel' d-cqua, to plunge one in the water; 4-gl: é-ra qui in quest' i-stan-te, he was here (in) this moment; 8-gl: é in a-go-ni-a, he lies in the agonies of death; ás-se-re in cól-le-ra, in gió-ja, in afft-zió-ne (i. e. né!-lo std-to di cé!-le-ra, d: gió-ja, affli-zió-ne), to be angry, cheerful, sad (i. e. in a state of anger, joy, affliction); a-vér qual-checósa in béc-ca, in md-no, to have something in one's mouth, in one's hand; ás-se-re, sta-re in cam-pd-gna, to be, reside in the country; an-dd-re, en-tra-re in i-na chiê-sa, to go into, enter a church ; ca-scd-re in i-na 'fös-sa, to fall into a pit or hole; métte-re le ma-ni in tä-sca, to stick or thrust one's hands into one's pocket; one-nd-re il ca-wdl-lo on t-stail-la, to lead a horse into the stable; sa-li-re in cd-me-ra, to go up into the room; wi-weva in won sé-co-lo di bar-bd-rie, he lived in an age of barbarity. I have already remarked that the proper names of towns and similar localities are exceptions to the above-stated rule, for they have the preposition a as well as in placed before them, whenever a stay or arrival in them is expressed; e. g. 6-gl: stét-te per tre din-ni in (or a) Ró-ona, he lived for three years in Rome; la sta-te pas-sd-ta i-o stet-to dit-e mé-st a (or in) F.-rén-ze, last summer I lived two months in Florence. There is, however, a shade of difference between the employment of a and in in such cases, which will be at once understood by the following examples; e in Lón-dra, in the strictest sense of the word, means a person being or an occurrence taking place within the precincts properly called London ; while é a Lón-dra, in the more enlarged or general meaning of the word, means a person not necessarily being in, or an occurrence not necessarily taking place within, those precincts, but perhaps in the neighbourhood of London; e. g. at Kensington.

The motion to or towards a town or village, conformably to the nature of the preposition, is always expressed by a. Motion to or towards (and, naturally, being or staying in) parts of the world, cocontries, provinces, and islands, requires the preposition in. The reason of this appears to be, that in the latter instance, the idea of a penetration into the interior of these more extended localities prevails, though, strictly and logically speaking, the idea of going to or into a town amounts to the same thing; e. g. an-did-mo con lui a Pie-iro-bār-go, let us go with him to St. Petersburgh; e-glo par-ti da Mó-na-co per re-cdr-s: a Vē-én-na, he departed from Munich to go to Vienna; 3-gli por-to a Cel-sé-a, he repaired to Chelsea ; 8-glo è an-dd-to a Pa-rá-gi e páč an-drà a Cel-te-ndm, he is gone to Paris, and after that he will go to Cheltenham ; quan-do an-dré-te in Fran-cía 2 when will you go to France ja-ré-mo un vidg-gio in Mo-scó-via, a Mo-scó-via, we shall go on a journey to Russia, to Moscow ; :-0 vd-do in I-scó-zia, in I-svézia, I go to Scotland, to Sweden; il Ba-seid fu e-si-li-d-to nell’ i-so-sa di Cipri, the pasha was exiled to (the island of) Cyprus; ē-glo è in Fran-cia, né!-la Chi-na, he is in France, in China; i. hel!' 3-so-la de Lé-sbo, he was born in the island of

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Usage allows the omission of the article after in before many nouns familiarly known and constantly recurring in conversation; e. g. 6-gl; va né!-la cd-one-ra, né!-la cit-td, né!-la chié-sa, hé!-la can-tá-na, &c.; or, é-gli wa in cd-me-ra, in cit-td, in chié-sa, on can-ti-na, &c., he goes to the room, to town, to church, to the cellar, &c.

Before the words day, week, month, year, morning, evening, when time is the subject, it is customary to omit the preposition in ; e.g. 7 dro-no che mo-ri il Ga-7′-lé-o, nd-cque is Newton, in the year in which Galileo died, Newton was born ; tl mé-seven-tū-ro, (in the) next month; la set-to-ma-na scór-sa, (in the) last week; la nót-te che vié-ne, (in the) next night, &c.; instead of: mels' do-no, nel mé-se, &c.

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Stanza, f., room, chamber. Se he stamperanno, will be

In addition to these uses, in has some indefinite meanings, which will admit of several prepositions or adverbial expres. sions for the purpose of translating them into English ; e. g. in : 70-mi-nd-re, di-re qual-che có-sa in la-ti-roo, to name, say something in Latin ; spe-rd-re in Dí-o, to hope in God; in ma-nié?"a ta-le, in such a manner;—on or woon : por-ta-re qual-che có-sa in dés-so, in té-sta, in cór-po, to carry something on one's back or shoulders, or about one’s self, on the head, on the body; por-td-re scar-pe in pié-di, to wear shoes on one’s feat; Ža pai-squa e sém-pre in so-na Do-mé-ni-ca, Easter is always on a Sunday; 6 gli má-se who a-nél-lo in di-to, he put or placed a ring on his finger; ab-êdt-ter-s: in to-no, to light on one, meet him By chance; di-stén-de-re qual-che có-sa in car-ta, to pen or note something on paper;-round: gli git-tó is bric-cio in cól-lo (for in-tór-no il cół-lö), he clasped him with the arm round his neck; ones-so-s: it-ma ca-tá-na in g6-la (for in-tor-no la gé-la), after having put a chain round his neck;-to: le cac-ció di cól-le in cól-le, he chased them from hill to hill; di tém-po in tém-po, from time to time; con-fic-ca-re in i-na, cró-ce, to fasten or nail Something to a cross;–towards: in Żne mo-vén-do de' bé-gli 6c-ch; ? ra-i, turning towards me the rays of her beautiful eyes; —of against : vá-de in se ri-völ-to il pá-po-lo, he saw the people rebelling against him;-at: 'guar-dd-re in to-no, to look at one ; in place of: a-dot-tá-re à-no in fi-gliwá-lo, to take one in place of a son, to adopt one;—as : da-re qual-che có-sa in d62.0 ad &-no, to give one something as a present; di-re gud!-che có-sa in sis-a sci-sa, to plead something as one's apology or excuse ; o Dí-0, non m'im-pu-tar-lo in pee-cd-to, O Lord, do not impute it to me as a sin; e-lès-se-ro in Pā-pa il Cardo-nd! Ma-std-i-Fer-rét-ti nel oni!-le 6t-to-cén-to qua-rdn-ta-sé-i, They elected Cardinal Mastai-Ferretti as pope in 1846;

adverbial expressions : in av-ve-ni-re, in future, for the future, e

henceforth ; in fit-ti, indeed, in fact, in reality; in frét-ta, in a hurry, hastily; in 6-gn: cón-to, at any rate, at all events; in fic-cia, to one's face.

ExERCISES.—ITALIAN-ENGLISH.

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Vicino, m., vicina, f., neighbouring, contiguous, adjoin

Ing. Sono, I am. Quast, almost, nearly, well

nigh. Porto, port, harbour. Campagna, country. Villegiattora, summer season, for pleasure or recreation spent in the country; country amusement, rural diversion or sport (essere in villegiatura, to spend the summer season in the country, to enjoy the pleasures of the country). Egli va, he goes. Camera, chamber, room. Scozia, Scotland. Turchia, Turkey. Morirono amendue, both died. Ora, hour. Tu eri, thou wast. C’é nissano, is nobody. Cortile, court-yard. Cucina, kitchen. Cantina, cellar. F andato, he is gone. Piazza, market-place, square. Osteria, public-house, tavern,

illLl,

Teatro, play-house, theatre.

Abitata, he lived.

Lo troval, I found him.

Letto, bed.

Antonio, Anthony.

Collera, anger.

Me, me.

Sene parla, they talk of it.

E’ partito, he has departed.

Fretta, haste, hurry, precipitation.

V: é andato, he is gone there.

Carrozza, coach, carriage.

Potremo andar, we shall be able to go.

Slitta, sledge.

Essi sono sorto, they have gone Out.

Punto, point, point of time, moment.

Adesso, now.

Siete, you are:

Mano, f., hand.

Lo prevennt, I came before

Punta, point (of anything). Piede, foot, leg (punta del piede, end or point of the foot, i. e. toe). E qui '' aspetto, and here I wait till he comes. Io nt riposo, I repose myself, sit down; I rely. Capacità, ability, talent, skill. Alquanto, m., alquanta, f, some, several. Copia, f, abundance, plenty ; occasion ; copy.

printed. Carta, f, paper (carta welina, vellum-paper). Vof stete, you are, Fiore, flower, bloom, prime. 4nno, year (il for degli anni or dell'età, the bloom of youth, * of life, prime of one's age). 4vete avuto, you have had. Tempo, time, weather. Viaggio, journey. Scritto, writing (in iscritto, in writing, written, under one's own hand). Stato, state, condition (in istato, having it in one's power, able). Primo, first. Luogo, space, spot, place (in primo Mogo, for the first, in the first place, firstly). Foodo, bottom, ground (in fondo, at the bottom, in the main, after all). Paragone, compa' son, parallel (in paragone do, in comparison with, when compared to). Noi, we, us. 4ncora, again, still, even, yet. Felice, happy. Mezzo, middle, midst (in mezzo, in the middle or midst of). Paese, land, region, country. Meno, less. Di, than. Segozito, suite, train, attendance, retinue ; sequel, consequence, issue, result, effect. Dopo, after. s Fatto, deed, fact, action. Poi, afterwards, after that (in séguito; depo fatto ; poi) thereupon, afterwards, after that, thereafter, hereafter, in time to come). Caso, case. Bisogno, need, want, the necessary (in caso di Özsogno or al bisogno, in case of need or necessity, at the worst). Principio, beginning. Avvenire, future. Stésso, m., stessa, f, myself, thyself, &c.; the same, selfSanté, Forza, force, power, strength. Virtu, virtue (in forza, di, in virtù di, by or in virtue of, by, in conformity with, according to, in consequence

of). Trattato, treaty. Nisstoo, on., nissuna, f, not any, none. Mančera, manner (in nissuia onantera or in kession modo, in no manner, by no means,

upon no account, not at all).

Cuore, heart, centre, middle, midst, summit. Inverno, winter. State, summer. Verità, truth. Te lo dice, he tells it you. Faccia, face (te lo dice on faccia, he tells you to your face). Weee, place, stead (in vece or a vece, instead of, in lieu of ; in the name of, by the authority of; for, in vece onia, swa or ??? moa, Sosa 2)60é, lnstead of me, of him, or in my, his stead or place). Modo, mode, way, manner. Tale, such. Traße, draught, pull, throw, touch, stroke; tıme (twit’ in wn traito, in or ad won tratto, on a sudden, all at once, in one pull, wrench, jerk, effort). Corconstanza, circumstance. Vista, sight, appearance (in vista di, in or with respect to, with regard to, in consideration of). Ció, that. Ordine, order (in ordine a, in consideration or regard of, with respect to, as for, touch

ing). Che vi detto, what I have

told you. Favore, favour, grace, aid (in

favore, in behalf of, in favour

of, for). Accusato, accused, defendant. Incisore, engraver. JRame, copper. Perito, skilled, learned. Arte, art.

Castello, castle. Aria, air. Dottore, doctor. Ambe, pl. f., both. (i.e. civil and canonical). Legge, f, law. Guerra, f., war. Ultimo, m., ultima, f, last. Vi stava, he stood there. Braccio, m. (pl. le braccia, f.), à l'Isl. Croce, cross (braccia in oroce, folded arms). Torto, curved. Arco, arc, arch. Onore, honour. Come si dice questo, how is that called P Inglese, English. Vuotö, he emptied. Iłicchiere, glass. Tre, three. Volta, time. Avere, property. Consiste, consists. Parte, partly. Danaro, money. Bene stabile, immoveable, real eState. I" venuto, he has come. Persona, person. Doveva stare, he was obliged to stand. JEgli si mise, he fell. Ginocchioni or ginocchiome, kneeling (inginocchion? or inginocchione, on the knees). Essere, to be. Salute, health. Andare, to go. . Barca, boat. Nome, name.

Dio, God.

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We have received the following notice, which we have much pleasure in submitting to our readers. “At a meeting of friends of the Tonic Sol-sa Association held on Tuesday Evening, Dec. 20th, 1853, at 4, Grocer’s Hall Court, Poultry, Rev. J. To Evitt, M.A., Incumbent of St. Philip, Friar's Mount, in the chair, it was unanimously resolved :— “That the generous and disinterested labours of the Rev. Jogin CURWEN for the diffusion of a knowledge of Vocal Music, call for a Testimonial of regard and esteem from the members and friends of the Tonie Sol-fa Association, and the classes connected with it; * A Sub-committee having been appointed for carrying out the arrangements for the above purpose, such of our readers as wisa to testify their sense of the improvements in Music introduced to public notice by Mr. Curwen, can communicate with the Secrets: of the Tonic Sol-sa Association, Robert GRIFFITHS, Milton Cottage, Plaistow, Essex. It is not considered necessary that the proposed Testimonial should be of great pecuniary worth, but it is thought that all who have derived benefit from the valuable method of teaching to sing introduced by him, will be glad to unite in this expression of their respect for him, and their earnest desire for his success in the great work he has undertaken. Post Office orders for this object, made payable at the Chief Office, St. Martin's Le Grand, to Rev. JAMES TREVITT, will be duly acknowledged.

ANSWERS TO CORRESPONDENTS.

LEHRLING has done both himself and us great credit by the progress he has made in German. We can confidently recommend him eithér of the following journals, especially the first. The Morgenblatt, Stuttgart (Wurtemberg); the Didascalia, Frankfort on the Maine; and the Dałmpf-boat, Dantzic. They may be obtained through a London agent, or by writing to i. town of publication, with the address, “The Expedition of the Morgen

tt, &c.”

R.S.T.: “Cassell’s Lessons in German Pronunciation” will answer the purpose of a German Anthology for a beginner. After that, the student could not have a better reading-book than “Cassell’s Eclectic German Reader,” which contains selections from the best authors of every class. Other works deserving of attention, are “ Wackernagel's deutsches Lesebuch,” a compendium of which may be had in one volume, and “IEmeler's, deutsches Leseuch,” which is extensively used both in France and this country.

A FATHERLess SubscribRR (Salop): We feel both for him and his sister; and we can recommend the “Lessons in Penmanship” contained in the P. E. in preference to any other, as we got them up ourselves, and know their value. It is true that we were grievously disappointed in the printing of them, for they are not so nicely printed as we expected; but they are good for all that. Next, our friend should advise his sister to study the “Lessons in English’’ in the P. E., and after that the “Lessons in French,” besides Arithmetic, Geography, &c., all contained in the P. E.-J. HALLAM (Liverpool): The difference between the words impracticable and o: seems according to usage to be this; the former means what cannot be done by reason of some let or hindranee; the latter what cannot be doese according to the nature of things.

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ON PHYSICS OR NATURAL PHILOSOPHY.
No. XXI.
(Continued from page 292.)
PNEUMATIC AND HYDRAULIC MACHINES.

Tarefaction and Compression of Gases.—The rarefaction of the air is effected in the following manner, by means of a suctionpump, fig. 93, in which F is the suction-pipe. This pipe com: municates, at its lower extremity, with the receiver or vessel in which the air is to be rarefied; and at its upper extremity, with the barrel or body of the pump D. The piston P, which moves up and down in the barrel by means of the piston-rod, is furnished with a valve in the middle, just under the semicircular piece to which the rod is fastened, and similar to the valve s (seen in the figure at the bottom of the barrel), which covers the upper extremity of the suction: pipe. Both valves open upwards, and close downwards. When the piston P is raised, "the valve s opens, the air contained in the receiver passes through the tube F into the barrel, and is there rarefied or expanded. When the piston is lowered, the valve s, closes, and the air in the barrel between this valve and the piston is condensed; it then forces open the valve in the piston and escapes through the spout B, into the atmosphere. In this manner, every stroke of the piston rarefies the air in the receiver. Thus, it appears that the common suction-pump is in its principle and construction a veritable air-pump, as will appear by the description of the latter in the following paragraph. Nevertheless, for ordinary purposes, many simple and handy air-pumps are made on the principle just described. In order to construct a pump which shall condense the air or any other gas, we have only to construct the valves so that they shall work in an opposite direction to that in which they work

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in fig. 93; but this, also, will be mole fully explained in a rapid and less laborious, the atmospheric pressure which acted

subsequent paragraph.

on both pistons tending to produce an equilibrium.

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