area of the contracted section of the vein is considerably smaller than that of the orifice, as in discharges which issue from orifices in a thin wall; or, that the velocity at this section is less than the theoretical velocity, in consequence of the friction of the liquid particles issuing from orifices pierced in a thick wall. Thus, in either case, the effective discharge is less than the theoretical discharge; and in order to reduce the latter to the former, it is necessary to multiply it by a certain fraction which is called the co-efficient of correction. From numerous experiments, it has been found that the effective discharge is, in general and at a mean, only two-thirds of the theoretical discharge. Constant Efflux. In a great number of hydraulic experiments, it is necessary that the velocity of efflux should be constant, that is always the same, and this requires that the height of the liquid level above the orifice should be invariable. This result may be obtained in several ways. 1st, by means of a sluice, which is so regulated that it opens whenever the water in the reservoir tends to rise above the level, and permits it to run off by another channel; 2nd, by means of a siphon or Marriotte's bottle, instruments which will be described in the sequel; 3rd, by means of the float of M. de Prony. The latter apparatus, shown at fig. 45, is composed of a reservoir or vessel PQ full of water, in which are placed two floats FF, connected with each other by an iron rod, which stretches over the reservoir and is bent at both of its lower extremities in order to support a moveable reservoir B, placed under the former. A plate A, making part of the wall of the reservoir PQ, is pierced with orifices of different forms and sizes. A funnel placed under these orifices conveys the water which flows from them into the reservoir B. According to this arrangement, if one of the orifices of the plate be opened, and if three pounds of water be discharged from it, the weight of the floats is increased by three pounds; therefore, according to the conditions of equilibrium in floating bodies, laid down in a former lesson, these floats will sink and occupy the space of a quantity of water equal in volume to the water discharged, so that the level in the reservoir PQ remains constant, and therefore the velocity of efflux remains the same. Efflux by Ajutages.-A short pipe or tube, see fig. 46, applied to or inserted in the orifice of a reservoir in order to increase the discharge is called an ajutage (French, from Lat. adjutare, to assist). The form of an ajutage is generally that of a hollow cylinder, or a truncated hollow cone. When ajutages are applied to an orifice, results of two kinds present themselves; either the liquid vein passes through the ajutage without adhering to its sides, and the discharge remains the same as before; or the liquid vein adheres, in consequence of the molecular attraction existing between the sides of the tube and the particles of the liquid, and the contracted portion of the vein being increased by expansion, the discharge is likewise increased. The best form of a cylindrical ajutage for increasing the discharge, is that which has its length from two to three times its diameter, The liquid then issues with a full flow, and the discharge is increased by about one-third part. Conical ajutages converging outwardly from the reservoir increase the discharge still more than the preceding. They produce very regular jets, and throw them to a greater distance or to a greater height than the cylindrical. Their effects, as to discharge and velocity of projection change with the angle of convergence, that is, with the angle formed by the production of two opposite sides of the truncated cone which forms Of all ajutages, those which 'give the greatest the sintage. discharge are those now described. Venturi concluded from his experiments that these ajutages gave an effective discharge 2.4 times greater than that delivered by an orifice in a thin wall having the same diameter as the smaller base, and 1:46 times greater than the theoretical discharge. The ancient Romans were acquainted with the value of these ajutages. The citizens of Rome, who enjoyed the privilege of drawing a certain quantity of water from the public reservoirs, found that by the use of these ajutages, the quantity permitted by their privilege might be greatly increased; and the fraud thus practised became so notorions, that a law was passed to pre vent their use. Efflux through Long and Wide Pipes-When a liquid flows through a pipe of great length, the efflux takes place either in consequence of the inclination of the pipe, as on an inclined plane, or in consequence of a pressure which acts on the liquid at the orifice of the pipe. In both these cases, the force being constant, the motion ought to be accelerated. Yet at a very short distance from the orifice, it is observed that the motion is uniform, which indicates the existence of a force tending to destroy or counteract the accelerated velocity which the liquid would naturally acquire by the force in question. This force is the resistance arising from the cohesion of the liquid particles to each other, and their adhesion to the sides of the pipe. Besides these resisting forces, there are others which arise from turns and contractions in the pipes themselves; but the former are always by far the most considerable. In consequence of these various resistances, the velocity of efflux, and therefore the discharge through pipes, becomes much leз3 than the velocity and discharge through orifices in a thin wall. Eflux through Capillary Tubes.-The efflux of liquids through tubes called capillary (from Lat. capillus, hair) because their bore or diameter is very small and fine, is of considerable importance in a physiological point of view. Dr. Poiseuille has made numerous experiments on this subject, varying the lengths of the tubes, their diameters or degrees of capillarity, and the pressures which produce the efflux of the liquids through them. In his experiments on capillary glass tubes, he discovered the three following laws: 1st, in the same tube, the discharge is proportional to the pressure; 2nd, in tubes of equal lengths and under equal pressures, the discharge is proportional to the fourth powers of their diameters; 3rd, in tubes of the same diameter and under the same pressure, the discharge is in the inverse ratio of the lengths. Dr. Poiseuille has observed besides these laws that the velocity of efflux is modified by the nature of the liquid. The nitrate of potassa dissolved in water, causes a more rapid efflux of that liquid. Alcohol, on the contrary, has a retarding effect. The efflux of serum is only half as rapid as that of water; and when alcohol is added to serum, the velocity of efflux is diminished still more; but if to the mixture we add the nitrate of potassa, the serum resumes its original velocity. These different experiments were made with glass tubes; and it became important to know whether the results would be the same in the capillary vessels of organised bodies. Now, in experimenting on dead animals, which were cooled down to the temperature of the surrounding atmosphere, it was found by injecting serum into the principal artery of an organ, that the nitrate of potassa increased the efflux in the capillary organs of dead bodies, in the same manner as in glass tubes; and that alcohol, on the contrary, retarded it. These facts tend, therefore, to prove that the circulation of the blood in the arteries and the veins follows the same laws as the efflux of liquids in capillary tubes. Jets d'Eau, or Spouts of Water.-Streams of water which spout up with force from an orifice in consequence of the pressure of a liquid column more or less elevated above that orifice, are called jets d'eau, If the orifice be made in the upper surface of a horizontal wall or tube below the level in the reservoir, the jet is vertical and upwards; if the wall or tube be inclined to the horizon the jet is inclined, and describes a curve, which, abstracting the resistance of the air, would be a paralola. According to a principle formerly mentioned, a jet of water tends to rise to a height equal to that of the level of the water in the reservoir; but this is never exactly the case, as it meets with three resistances: 1st, the friction of the water in the tubes or pipes, which destroys a part of the velocity; 2nd, the resistance of the air; 3rd, the resistance which those liquid particles, falling from the highest part of the jet, present to those which are ascending. In order to obtain the maximum height of a jet, the diameters of the tubes must increase with their length; the tubes must be free from all inequalities and all sudden windings; and, the orifice of efflux must be made in a thin wall, and have a slight inclination in order to avoid the third resistance just mentioned. Such orifices are those which raise the jet to the greatest height, and impart to it the greatest regularity and transparency, Conical ajutages also produce jets uniform and transparent, but the height is only about eight or nine-tenths of that produced by orifices in a thin wall. Lastly, cylindrical ajutages produce confused jets, of which the height is only about of that which is produced by orifices in a thin wall. In order that a jet may take the greatest range horizontally, it is found by analysis, that when the resistance of the air is abstracted from the calculation, the angle which it makes with the horizon must be 45°, or half a right angle; that is, mid-way between the horizontal and the vertical directions. Fig. No. 1. of sulphuric acid. Now nine is the precise chemical equiva lent of water, and forty the precise chemical equivalent of sulphuric acid. A few remarks concerning equivalents have already been offered; I do not expect you, however, to understand this rather abstruse subject perfectly just yet. I must, nevertheless, have you to remember, even though you do not understand it, the following fact: When I say that our strongest English oil of vitriol is a compound of one equivalent of water and one of real sulphuric acid, I do not mean equal weights, but equal equivalents; the equivalent of the one being forty and the other nine, as we have seen. The same remark applies to all similar expressions. Well, then, in order to indicate the kind of hydrate which oil of vitriol is, chemists term it the protohydrate of sulphuric acid, or protohydrated sulphuric acid. The Greek word proc means first; that is to say, this is the first in the ascending scale of many hydrates. From this digression (a necessary one, however) let us now return to the materials in our flask-or rather let us investigate, by means of a diagram, the changes which have ensued. The case stands thus : Hydrochloric acid (Hydrogen Hydrosulphuric acid Chloride of antimony mony If the resulting liquid be thrown into water, in certain proportions, which may be ascertained on trial, a powder (oxide of antimony) deposits. This powder is, however, readily dissolved by the addition of more hydrochloric, or a sufficient quantity of tartaric acid. LESSONS IN CHEMISTRY.-No. XII. RESUMING the consideration of antimony, I now want the student to take a little of the orange or black sulphuret of the latter: powder it; and having thrown it into a Florence flask, pour upon it some hydrochloric or muriatic acid, known in commerce under the name of spirit of salt; applying now to the The precipitate which occurs on throwing the chloride into flask either the naked flame of a spirit-lamp, or, what is pre-water is the type of an important feature in the demeanour of ferable, the heat of a sand-bath, sulphuretted hydrogen gas antimony solutions, most of which are liable to become decomposed from the operation of very slight causes. Tartar emetic is not so prone to be unstable as the others are; it may be mixed with mere water, in any proportions, without throwing down a precipitate; but tea-infusion of galls, or indeed almost any vegetable or animal infusion, throws down, even with it, a copious precipitate. Try these experiments; the results will be found to have an important bearing upon circumstances to be mentioned hereafter. Assume, for example, that a person has taken an injurious dose of tartar emetic, and that the emetic action does not supervene; this is the case sometimes. What would you do? In the first place, propose to yourself the object you would desire to accomplish. There is a general rule to follow in all these cases-a rule which I have already mentioned. It is this:-Convert the poisonous irritating fluid into a solid. Give then-if tartar emetic be the poison under consideration-give copious draughts of tea; a fluid which, as we have seen, renders tartar emetic insoluble-more insoluble, at any rate, than it was originally. will be evolved, as you will readily discover by its disagreeable odour; and if a sufficient amount of hydrosulphuric acid have been added, the whole of the sulphuret will be dissolved. The result of this solution is termed the chloride of antimony, procurable in commerce under the name of butter of antimony. Let us see what decomposition must have ensued in order to furnish us with these results. Sulphuret of antimony is, as its name indicates, and as we demonstrated in our preceding lesson, a compound of sulphur and antimony. Separation of Antimony from Zinc, Manganese, Cadmium, and Arsenic.-I trust that the student has sufficiently reflected upon the properties of these four metals to recognise an indication of a process by which this might be accomplished. We have not yet demonstrated the composition of hydroFirstly, It is evident that arsenic and antimony admit of chloric acid gas; but its name, if analyzed, evidently points to separation from the other metals by the operation of hydrogen, a compound of chlorine and hydrogen, just as the term hydro- which would remove them in the condition of arseniuretted sulphuric points to something which is a compound of sulphur and antimoniuretted hydrogen gases; and the latter, on comand hydrogen. Remember, therefore, the following general bustion, would deposit the two metals in a mixed crust. Fifact:-Whenever you see the syllabic prefix hydro (before a nally, these metals would be separable from each other by the vowel hydr'), the prefix always means hydrogen-never water, prolonged action of boiling nitric acid, which, as we have seen, the presence of which is expressed, not by the syllabic prefix reduces the antimony to the condition of an insoluble white hydro or hydr', but by the full word, hydrated, or hydrate. powder, and changes the arsenic to soluble arsenic acid. The Thus, for instance, hydro-sulphuric acid is synonymous with latter proposition has not been demonstrated. Nitrate of potsulphuretted hydrogen, indicating the compound of sulphur ash produces this result, as I have explained (p. 42). Nitric and hydrogen; but hydrated sulphuric acid, or hydrate of sul-acid has the same effect; indeed, nitre acts by virtue of its conphuric acid, is a compound of sulphuric acid with water. tained nitric acid. Several other analytical processes suggest Practically we call oil of vitriol sulphuric acid; really it is hy- themselves from combinations of agencies already discussed; the drated sulphuric acid-or a compound of true sulphuric acid most evident process, however, is that which I have given; and (which is a solid) with water. But you will say-If I take oil my object not being to write a systematic course of analysis, I of vitriol and add more water to it, I get a liquid which is no need not detail the others. onger oil of vitriol, but it is still hydrated sulphuric acid. Truly-the remark is just; hence has arisen the necessity for certain precise terms. The strongest oil of vitriol which we in England obtain by our process of manufacture is composed of nine parts by weight of water united with forty parts by weight Before concluding my remarks on this interesting metal, I will mention a curious fact. Two sulpnurets of antimony have been spoken of: there exist others; one an orange-coloured sulphuret, generated artificially; the other a black substance, usually sold as antimony by druggists. Now, different thoug the two are in general appearance, their chemical composition is precisely the same. Chemistry furnishes us with many similar examples, all of which are comprehended under the general term allotropism, from the two Greek words alλoç, another, and rperw, I turn. Thus the diamond, coke, charcoal, and plumbago (the latterly commonly known as black-lead), have all a composition which is exactly similar. Chemists, indeed, have succeeded in changing the diamond to coke; but the other change, far more interesting than the last, remains to be accomplished. The substance phosphorus, again, the inflammable nature of which, in its ordinary state, is so remarkable, may be converted into a second state, in which it is no longer combustible, andi n which it is totally devoid of smell; nay, what is still more extraordinary, this allotropic phosphorus is totally devoid of all poisonous agency, although common phosphorus is a violent poison; its mere vapours rapidly destroying the jaw-bones of the workmen exposed to their influence, and causing a frightful death. Perhaps the question will occur to you of this sort-What can be the use of this allotropic phosphorus, a substance which, you tell us, is not inflammable? True, allotropic phosphorus is not inflammable; but, if heated beyond a certain temperature, this curious substance changes into the ordinary form. Now the mere friction of a phosphorus match is sufficient to generate this amount of heat; so, practically, allotropic phosphorus may be employed for the purpose of making matches. In England these matches of allotropic phosphorus have not as yet come much into use; but on the continent, especially in Prussia, they are common enough. Whilst on the subject of allotropism, I will furnish you with another example as afforded by sulphur. Take some common sulphur (brimstone), put it into a Florence flask, and apply heat either by means of a spirit-lamp, or, what is preferable in this case, by a flowerpot charcoal furnace already described in a previous lesson, and here represented, No. 2. The sulphur fuses, giving rise to a limpid fluid, which retains this character Fig. No. 2. and hard, the new substance, allotropic sulphur, is black, ductile, soft; a substance capable of receiving the most exquisite impressions; indeed it is used in practice very advantageously for the purpose of copying the impressions of medals, coins, &c. Judging from the appearance of this body, one might at first imagine it to be something else than sulphur; chemical analysis, however, proves them to be the same. In making the latter assertion, I am aware it must be taken with some qualifications. The truth is, the contemplation of allotropism leads us into the metaphysics of chemistry; the very term allotropism meaning another state is expressive of a change; a change in appearance you have had pointed out to you, but this is not all, there is a change of medical properties, a change as to solubility in certain fluids: yet when we come to combine this allotropic sulphur with other bodies, we obtain exactly the same results that we should have obtained with sulphur in the ordinary state. until every portion of the sulphur becomes melted. Keeping your eye on the flask, observe the period at which this perfect fusion of the sulphur takes place: being accomplished, remove the flask, and pour a little of the fused contents into water. The melted sulphur solidifies as a matter of course, and you get a result identical in every respect with the sulphur before it was fused; that is to say, the result is brittle-is yellow; physically and chemically similar in point of fact. Replace now the sulphur over the source of heat, and remark the changes which ensue. You will first observe a change of colour: the fluid becomes dark, almost black. You will next observe a change of aggregation, the material becomes thick, thicker still, and in a few instants a solid. By dexterous management it is possible to remove the flask whilst its contents are thus solid. Try to do so. Replace the flask once more, and observe the result; the dark solid liquifies once more, and the liquid still remains black; pour some of this liquid into water, and a curious result will be obtained. Instead of ordinary sulphur, yellow, brittle, The most elegant way of demonstrating the characteristics of allotropic sulphur, consists in pouring it in a small continuous stream into a basin of water, which contains a funnel, and around the latter in this way a thread of the substance may be obtained, in appearance very much ike a thread of india-rubber, No. 3. The various phenomena of allotropism are directly at variance with the chemical doctrine long accepted, that identity of composition must necessarily accompany identity of chemical effects; and, curiously enough, these same phenomena are favourable to the idea of metallic transmutation, that longcherished hope of the alchemists. LESSONS IN ITALIAN GRAMMAR.-No. XI. By CHARLES TAUSENAU, M.D., Of the University of Pavia, and Professor of the German and Italian Languages at the Kensington Proprietary Grammar School. THE proper use of the words di, a, da, in, con, per, su, só-pra, shall devote this section to an elementary explanation of some fra, and tra, is of such primary importance in Italian, that I of their peculiarities. Di. The use of this word very frequently coincides with the use of the case-sign, or preposition of, in English grammar:I. When the questions of whom? of which? of what? whose? what kind or sort of? require the genitive also in English; e. g. L'a-mó-re del pá-dre, the love of the father; paé-si del prin-ci-pe, the countries of the prince: la cle-mênza di Di-o, the clemency of God; la gran-déz-za del-la cit-tà, the greatness of the town; il li-bro di Giá-co-mo, the book of James. i II. When geographical or other proper names indicating possession, domain, authorship, &c., or merely for the purpose of defining them, are joined to other nouns; e. g. la cit-tà di Ve-nê-zia, the city of Venice; il ré-gno di Spá-gna, the kingdom of Spain; il mé-se di Lu-glio, the month of July; il nó-me di Fran-cé-sco, the name of Francis; l'i-so la di Cor-fù, the Adverbs of place or time before, nouns or even adjectives island of Corfu; la re-gi-na d' In-ghil-ter-ra, the Queen of England; il Re di Prús-sia, the king of Prussia; 'im-pe-ra-tó-re of this class, frequently, also, are translated by the genitive d'Au-stria, the emperor of Austria; l'as-sê-dio di Mán-to-va, case; e. g. the back door or room, la pôr-ta la, stán-za di dié-tro the siege of Mantua; lo strét-to di Gi-bil-têr-ra, the straits of (the door or room of behind); the hind-feet, i pie-di di diê-tro Gibraltar; l'im-pê-ro di Rús-sia, the empire of Russia; le tra- (the feet of behind); the following day, il giorno di do-má-ni gê-die di Al-fiê-ri, the tragedies of Alfieri; le com-mê-die di Gol-(the day of to-morrow); the present age, il món-do d' og-gi-di (the world of now-a-days); after the present fashion or style, dó-ni, the comedies of Goldoni. III. When words expressing quantity, weight, or any kind of al mô-do d' og-gi-di (after the fashion of now-a-days); the whole measure are joined to other nouns; e. g. ú-na quan-ti-tà di pê-last night, la not-ta-ta di jê-ri (the whole night of yesterday); co-re, a quantity of sheep; ú-na lib-bra di cár-ne, a pound of yesterday, il giór-no di jê-ri (the day of yesterday). Whenever the infinitive mood of any verb explains and demeat; un cen-ti-ná-jo di fiê-no, a hundred-weight of hay; ú-na doz-zi.na di cuc-chid-ji, di guán-ti, d'uô-ra, a dozen of spoons, fines another word, the preposition di must be placed before gloves, eggs; un brác-cio di pán-no, a yard of cloth; ú-na bot-it (just as the preposition of with the present participle of ti-glia di ví-no, a bottle of wine; ú-na ca-ráf-fa d'á-cqua, a English grammar in such cases); e. g. Ha ú-na gran vô-glia di decanter of water; un' ón-cia di caf-fè (kahf-fe), an ounce or viag-giá-re, he has a great desire to travel or of travelling; è têm-po di an-dá-re, it is time to go or of going; ra-gió-ne di coffee; vi-no di diê-ci án-ni, wine of ten years. la-men-tár-si, right to complain or of complaining; l'o-nó-re di ve-der-vi, the honour to see you or of seeing you; li-cên-za di par-tir-si, permission to go away or of going away. For the sake of elegance, the preposition di is, however, sometimes omitted after the words ca-sa, house; pa-láz-zo, palace; piáz-za, place, square; vil-la, villa; gal-le-rí-a, galDi is also placed after the words quan-to, how much, or great, lery; fa-mi-glia, family; pôr-ta, gate, entry, and some others, when they are followed by the name of the owner or of the or long; al-quan-to, something, a little, some; tan-to, so much, or great, or long; al-tret-tán-to, just as much, equal; pô-co, person after which they are called; e. g. in cá-sa Al-tiê-ri, at little, few; mól-to, much, a great deal; niên-te, nothing; più, the Altieri-house; vi-ci-no al pa-láz-zo Bor-ghé-se, near the Borghese-palace; súl-la piaz-za Bar-be-ri-ni, on the Barberini-more; mé-no, less; trôp-po, too much, &c.; e. g. quán-to di square; per la vil-la Pan-fi-li, for the villa Panfili; nel-la gal-no-ja sa-rêb-be per me, how a great a nuisance would it be for Is-ri-a Do-ria, in the Doria-gallery; dél-la fa-mi-glia Co-lon-na, me; dó-po al-quan-to di têm-po, after some time; tán-to di ví-no of the Colonna family; la pôr-ta di San Gio-ván-ni, St. John. ed al-tret-tán-to d' á-cqua, so much wine and just as much gate or entry; a cá-sa'i zi-o (instead of a cá-sa del zi-o), at the water; pô-co di ú-ti-le ne ri-ca-ve-ré-te, you will derive from house of the uncle; ó-ra a cá-sa qué-sto, ó-ra a cá-sa quell' al- this little advantage; mól-to di má-le ne po-trêb-be se-guí-re, a tro (instead of di qué-sto, di quell' al-tro), now at the house of great deal of evil might be the consequence of it. In these two phrases, la Di-o mer-ce! thank God! and la this one, then at the house of the other. Di-o grá-zia, the grace of God, the word di is understood, and in full they run thus: la di Di-o mer-cè, and la di Di-o grázia. When, however, Di-o is placed after the words mer-ce and grá-zia, the case-sign di cannot be omitted; e. g. la mer-cè di Di-o, and la grá-zia di Di-o.† The word di is sometimes a mere expletive; e. g. é-gli di-ce di sì, ed i-o di-co di no, he says yes, and I say no; qué-sto diávo-lo di qué-sta fém-mi-na, that devil of a woman; quel po-ve-rino di mi-o fra- têl-lo, that poor brother of mine. English compound nouns, or combinations of nouns, for the greatest part must be decomposed by the genitive case with the case-sign di, especially when one of the nouns merely defines and qualifies the other, which is the principal word conveying the principal idea; e. g. garden-door, pôr-ta di giardi-no (door of the garden); stone-quarry, cá-va di pie-tra (quarry of stone); autumn fruits, frút-ti d'au-tún-no (fruits of autumn); a music amateur, un di-let-tán-te di mú-si-ca (an amateur of music); Leipzig fair, fiê-ra di Li-psia (fair of Leipzig); ox-tongue, lin-gua di bô-ve (tongue of an ox); horse's-present, I shall state that this word, among all the prepositions head, tê-sta di ca-vál-lo (head of a horse); felt-hat, cap-pêl-lo di fél-tro (hat of felt); sugar-box, cás-sa di zuc-che-ro (box of sugar). Whenever it is necessary with greater precision to define the noun in the genitive case so as to distinguish it from other objects of the same class, the article, according to its peculiar function of particularising that which is general, must be joined to the case-sign di. As a last remark on the use of the case-sign di for the of the Italian language, is of by far the most extensive use. The reason of this is, that di, properly and philosophically speaking, merely expresses the mental separation of ideas or notions, while da indicates a real separation of objects, which distinction constitutes the principal and fundamental difference between these two important words di and da. The mere mental separation of ideas or notions may, however, serve any connexion and relation between words, ever so loose and general, and no reader, bearing this truth in mind, henceforth need be surprised at meeting, in Italian books and conversations, with frequent substitutions of the case-sign di for many other di Nd-po-li, Ischia is an island close to Naples; for da: u-scire del-la pri-gió-ne, to go out of or from prison; é-gli di pri-gióne il trás-se, he took him from prison; for con: di gran-dis-sima for-za si com-bat-té-a da cia-scú-na pár-te, they fought with the greatest energy on each side; for in: i-o l' uc-cí-si di led-le bat-ta-glia, I killed him in fair fight; for per: é-gli pia-gné-a e di gran pie-tà non po-té-a môt-to fá-re, he wept, and on account of his great emotion he could not utter a word. The disregard of this rule will not unfrequently cause ambiguity; e. g. il pa-dró-ne dél-la cá-sa dó-ve a-bi-tid-mo, the master of the house where we live (il pa-dró-ne di cá-sa, is the master of the house in general); un boc-cd-le del vi-no che bév-prepositions; e. g. for a: I'-schia è ú-na i-so-la as-sá-i vi-ci-na vil' ál-tra sé-ra, a measure (about two pints) of the wine which I drank the other evening (un boc-cá-le di vi-no, is a measure of wine in general); il mer-cd-to dei ca-vál-li, the horsemarket (il mer-cá-to di ca-vál-li, is merely a place where horses are sold); il mer-cá-to dél-la sel-vag-gi-na, the game-market; il ma-gaz-zi-no dél-la pá-glia, the straw-magazine (ma-gaz-zi-no di pá-glia, is merely a magazine full of straw); il ma-gaz-zí-no dél-le le-gna, the wood-magazine. It is evident that the variable nature of di will admit of many translations into English; e. g. by with: só-no con-ten-to di te, I am satisfied with thee; by at: mi rí-do di lui, I laugh at him; by of: mo-rír di fá-me, to die of hunger; by as: ser-vir di rê-go-la, to serve as a rule; by for: pre-gá-re ú-no di ú-na cô-sa, to request one for something; by than: più di du-e-mi-la scu-di, more than two thousand crowns. English adjectives, indicating the material or stuff from which anything is manufactured, or denoting qualities attributed or derived from proper names of countries, nations, or towns, for the greatest part will be best translated into Italian by means of nouns in the genitive case; e. g. a gold watch, un o-ro-lô-gio d' ô-ro (a watch of gold); a marble statue, ú-na stá-tua di már-mo (a statue of marble); a wooden table, ú-na tá-vo-la di lé-gno (a table of wood); an iron gate, ú-na pôr-ta di fer-ro (a gate of iron); a silver spoon, un cuc-chia-jo d' ar-gênto (a spoon of silver); a meritorious soldier, un sol-dá-to di mêri-to (a soldier of merit); a spirited or talented youth, un gióva-ne di spi-rito, di ta-lên-to (a youth of spirit, of talent); Italian silk, sé-ta d' I-tá-lia (silk of Italy); Viennese citizens, cit-ta-dini di Viên-na (citizens of Vienna). It is, however, quite allow-merely general rule will be, I think, sufficient. able to say: stá-tua mar-mô-rea, sol-dá-to me-ri-té-vo-le, gió-vane spi-ri-tó-so, cit-ta-di-ni Vien-né-si. In some instances, the peculiarities in the use of di may, without difficulty or twisting, be explained by ellipsis, par * Which special class of verbs, nouns, and adjectives, requires the preposition di before the infinitive mood governed by them, will be explained hereafter. For the present, the above-stated + Some other important omissions of the case-sign di will be explained hereafter. ticularly when it denotes descent or children; e. g. Gian-nuôl đi Se-ve-ri-no, Céc-co di Mes-sé-re An-giu-liê-ri, in Boccaccio, where fi-gliuô-lo, child or son, is understood. EXERCISES.-ENGLISH-ITALIAN.* EXERCISES.-ITALIAN-ENGLISH. La me-mô-ria. Dél-la ciê-ra. Al-la col-lí-na. Dál-la spia-na-ta. Le bec-che-rí-e. Dél-le lo-cán-de. Al-le pôrte. Dal-le strá-de. In fac-cia. Nél-la ví-gna. Nél-le fo-rêThe rising of the sun. The dawn of the day. The return ste. Con pá-glia. Cól-la ví-te. Cól-le pén-ne Per disof spring. The warmth of the air. The beauty of the flower. grá-zia. Per la vál-le. Per le scioc-chéz-ze. Súl-la car-rôzThe darkness of the night. The abyss of error. The fertility za. Súl-le rú-pi. L'au-rô-ra. Dell' al-le-gréz-za. All' oof the fields. The colours of the rainbow. The senses of man. pi-nió-ne. Dall' o-ste-ri-a. Le i-dê-e. Dell' êr-be. Al-le The faults of young men. Money is the soul of commerce. ar-ti. Dál-le cit-tà. In i-slit-te. Nell' im-ma-gi-na-zió-ne. Usage is the legislator of languages. The master of the garden Nél-le a-ni-me. Con á-cqua. Coll' ún-ghia. Cól-le in-séis not here. The palace belongs to the prince. Here are the gne. Per a-mi-cí-zia. Per l'as-si-cu-ra-zió-ne. Per le arooms of the uncle. The dresses belong to the cousin and not zió-ni. Sull' in-sa-la-ta. Súl-le in-fer-riá-te. Un fan-ciúlto the aunt. The brother tells the sister the will of the lo. U-no stól-to. Un a-ni-má-le. U-na set-ti-má-na. D'un father. The children must always obey the parents. The fiú-me. Ad ú-no schiop-pet-tiê-re. Da ú-na bal-le-rí-na. physicians say the disorder shortens life. Exercise is useful In ú-na chiê-sa. Con un ba-stó-ne. Per ú-no sco-la-re. Su to the body and to the mind. The countenance is the mirror d' un sas-so, só-pra un sás-so. of the soul. Tranquillity of mind is the highest degree of happiness. Temperance is the treasure of the wise man. The true ornament of the soldier is courage. The practice leads to perfection. Interest, pleasure, and glory, are the three motives of the actions and of the behaviour of men. Dawn, spun-tár, m. Day, giór-no, m. Return, ri-tór-no, ni. Beauty, bel-léz-za (ts), f. Error, er-ró-re, m. Fertility, fer-ti-li-tà, f. Colour, co-ló-re, m. VOCABULARY. Rainbow, ar-co-ba-lé-no, m. Sense, sên-so, m. Man, uô-mo, ma Fault, er-ró-re, m. Young man, gió-va-ne, m. Money, da-ná-ro, m. Soul, d-ni-ma, f. Commerce, com-mêr-cio, m. Is, è Legislator, le-gi-sla-tó-re, m. Room, cá-me-ra, f. Uncle, xi-o (ts), m. Dress, á-bi-to, m. Belong, ap-par-tên-go-no Cousin, cu-gi-na, f. And not, è non Aunt, zi-a (ts), f., Bister, so-rêl-la, f. Memoria, memory. VOCABULARY. Osteria, public-house, tavern. face. Collina, hill. Spianata, plain, esplanade. Beccheria, slaughter-house, Locanda, inn, hotel. Faccia, face (di-re in fác-cia, to tell one to one's face). Vigna, vineyard. Foresta, forest. Con, with. Paglia, straw. Vite, vine. Penna, pen. Per, for, through, on account Countenance, fi-so-no-mi-a, f. Disgrazia, misfortune, dis Soul, d-ni-ma, f. Tranquillity, quiê-te, f. Highest degree, cól-mo, m. Is, é grace (per dis-gra-zia, unfor- Valle, valley. Carrozza (ts), carriage, coach. Aurora, aurora, dawn. Allegrezza (ts), joy. Opinione, opinion. Arte, art. Città, town, city (no change in the pl.) Slitta, sledge. Immaginazione, imagination, Anima; mind, soul. Acqua, water. Insegna, sign, arms, colours. Assicurazione (ts), security, in surance. Azione, action. Insalata, salad. Inferriata, iron-grate. Fanciullo, child. Stolto, fool. Animale, animal. Schioppettiere, arquebusier, Ballerina (f.), dancer. Chiesa, church. Bastone, stick. Scolare, pupil. Su, sopra, upon. LESSONS IN GEOMETRY.-No. XXIV. LECTURES ON EUCLID. (Contiuued from page 50). BOOK I.-PROPOSITION XIX.-THEOREM. The greater angle of every triangle is subtended by the greater ride (that is, has the greater side opposite to it). In fig. 19, let ABC be a triangle hav- Three motives, tre mo-ti-vi, pl. opposite the angle в CA. Fig. 19. A Man, uô-mo, m.; pl. gli uô- AC is not equal to the side A B; for, if so, the angle A B C is mi-ni. equal to the angle A C B, by Prop. V., which is contrary to the hypothesis; therefore, the side A c is not equal to the side A B. Second, the side a c is not less than the side A B; for, if so, the angle ABC is less than the angle ACE, by Prop. XVIII., which is also contrary to the hypothesis; therefore, the side The pupil himself must examine whether he is to use before any noun or adjective the article or not, the prepositions di, a, and da, only being occasionally employed to denote the genitive, dative, and ablative. It is, moreover, to be noted, that the words are placed in the order in which they are to be translated into Italian. A c is not less than the side AB; and it has been proved that I have thought it useful, in some cases, to denote the pronuncia- the side A c is not equal to the side A B. Therefore, the side tion of the 2 or zz. I have done so by placing after such words in AC is greater than the side AB. Wherefore, the greater angle parenthesis ts, thus (ts), when the pronunciation of the zor zz is to of every triangle, &c. Q. E. D. be the sharp, hissing one; and ds, thus (ds), when the pronunciation of the ≈ or az is to be the soft one. Corollary 1.-One side of a triangle is greater than, equal to, or less than another, according as the angle opposite to the |