IMAGINARY QUANTITIES. A VERY ingenious and useful work on Algebra has just been put into our hands, written by J. R. Young, Esq., late Professor of Mathematics in the Royal Academical Institution, Belfast. In order to enable our more advanced readers to form some opinion of its merit, as an Elementary work, we give the following extract: ab "In the instance just adduced, namely = a, an operation as p parently performed on pure symbols irrespective of all interprs tation; yet if we really look at what has actually been done, shall see that it amounts to nothing: when b is written by the m of a a certain operation, called multiplication by b, is directes ta be performed on a; except b be a number, we cannot obey direction; bat by writing 6 underneath, the direction is re-caled, so that a, which would be the result of the operations of mutse cation and division in arithmetic, is here written down free of ther operations, because they neutralise one another: their combina effect being to leave a untouched. It is not necessary that w should be able to assign the effect of the combination as and the the effect upon this of the combination; it is enough that w know, from the general laws of these combinations, that de second destroys the first and sets a free. ab GLOSSARY. Most of our writers have aimed at plainness and clearness of expression. A few words may need explanation. Let it be membered, however, that we do not wish to save our readers te trouble of thinking; and also that many technical terms can be better explained by their connexion with the subject than by any brief definition. Several words which occur la is part are es plained in the Glossary in No. 5, page 78. "Imaginary or impossible quantities, are those expressions "It is more especially this recognition of the neutralising infec which indicate an even root of a negative quantity; the arithmetical of certain algebraic combinations on one another, apart from extraction of such a root being almost an impossibility, because no mere arithmetical considerations, that readers what are here cases even power of any number, whether positive or negative, can ever impossible or imaginary quantities so available in algebra, be negative. Imaginary quantities thus differ essentially from instruments of investigation, though not admissible into aritamen other surd expressions; the root indicated in each of these latter ab cannot be accurately exhibited, solely because the quantity undera, whether & be real or imaginary." the radical sign differs from a complete power; yet a complete power may always be assigned which shall differ from the incomplete one by a quantity less than any that can be proposed, so that the defect mentioned is never of any practical consequence. But an imaginary quantity admits of no arithmetical representation either accurately or approximately: the bare idea of arithmetical value is altogether excluded from it; the symbol -4 implies an operation upon the -4 of impossible performance; so that if such a symbol were to occur in the answer to any question, we should at once conclude that the solution to that question, in real numbers, is an impossibility; and, consequently, that the conditions to be satisfied are incompatible or contradictory. Imaginary quantities thus subserve a very important purpose: whenever they present themselves as here supposed, they effectually apprise us of concealed absurdities among the conditions upon which our reasoning has been based, or which we are aiming to satisfy, and which might otherwise involve us in bewilderment or error. They are thus necessary to give completeness and certainty to our algebraic results, and on these grounds alone are valuable items in our system of symbols. But independently of this office of imaginary quantities, by which they inform us of the fact when the solution of a question is impossible, algebraists turn them to important account as direct instruments of investigation; frequently introducing them with great advantage into inquiries having reference only to real quantities, and terminating only in real results. s., substantive; spl., substantive plural; .a., verb active; ABSORPTION, . the act of swallowing up, or imbibing. ARBITRATION, S. the settlement of any dispute by peracza mutually chosen by the parties. APPALLING, a. frightful, terrifying. AUTOMATON, s. a machine which has apparently the power of moving itself. BRACK'ISH, a. saltish, like sea-water. CARDINAL, a. principal, chief, eminent. CATASTROPHE, s. a final event, generally of an unhappy character. CONCUSSION, s. the act of shaking; a shock. COROLLARY, 8. an inference, a deduction, surplus. DISCRIMINATION, s. a distinction; act of distinguishing thing from another; a mark. DOCILITY, s. aptness to be taught; teachableness. the world, dividing the globe into equal parts, north and south. FRIVO'LITY, 8. unimportance. FRIVOLOUS, a., slight, trifling. of no moment. GERMINATION, s. the act of sprouting; growth. "In his first steps in the study of algebra, the learner naturally looks upon the new symbols of quantity to which he is introduced as nothing more than the familiar figures of arithmetic in disguise. It is not easy, nor would it be prudent to correct this too limited notion at the outset; the more comprehensive scope of the symbolic language of algebra gradually unfolds itself to him as he proceeds, till he at length comes to combine his characters and contract his expressions without any thought towards the numerical processes bearing the same names as those which enter into his symbolical combination. In fact, the important truth discovers itself by degrees, that the thing called algebra is a science in which symbols of any interpretation whatever are subjected to certain prescribed laws of combination, in obedience to which various operations may be performed and various results obtained without any reference to the particular characters of arithmetic. This latter science is no doubt suggestive of the symbolical science of algebra; and the learner sufficiently sees that its laws of combination actually become those of arithmetic, when the particular symbols of the latter re-supernatural ideas. place the more general symbols of the former. In fact, he further sees that, till these general symbols are so replaced by those of arithmetic, many of the so-called operations of algebra are but operations indicated, not operations executed. If we have to multiply a by b, we write ab or axb, and say that the thing is done; although, in truth, nothing is done, although something, by the sign of operation, is inarcated; we have no idea of the actual performance except each symbol, or the multiplier at least, be interpreted by a number; yet if the so-called product ab is to be divided by b, there is no doubt that the result is a, whatever the multiplier b may have been: whether a number or something having no arithmetical meaning. It is true that in the latter case the term 'multiplier' might be objected to as not sufficiently significant, but a similar objection might be made to nearly every term introduced from arithmetic into algebra: the terms have a more comprehensive meaning as well as the symbols INSPIRATION, s. a drawing in of the breath; an infusing of INUNDATION, s an overflow of water; a deluge. JUNGLE, 8. land overgrown with trees, brushwood, and rask vegetation. MAGNAN'IMOUs, a. great minded, brave. MAM'ALUKE, or MAM'ELUC, s. an Egyptian horse-soldier. PHENOMENON, s. a natural appearance; also any extraordinary appearance in the works of nature. PH is sounded as Fin such words as Phenicia, Phrygia, PROBLEM, s. a question proposed for solution or explanation PSAMMETICUS, PTOL'EMY:-in all words beginning with Ps or plants called fungi. "During their growth," he says, "they so entirely RESPIRATION, s. the act of breathing; relief by breathing. STADIUM, s. a race-course; a space for combatants; also, the eighth part of a Roman mile. TAL'ENT, s. a certain weight or sum; the Jewish talent was 125 pounds in weight; a talent of gold was worth £5,475; a talent of silver, £375 6s. TEME'RITY, s. rashness, unreasonable contempt of danger. THEOREM, s. a position laid down as an established truth; a given principle. TRANSMIGRATION, s. a passage from one state, place, or body, into another. The philosopher Pythagoras, and his followers, believed that when a man died his soul passed into other bodies, including those of brute beasts. He pretended that his soul had lived in the bodies of several persons of preceding ages, whom he specified by name. TROUBADOUR, s. a poet, or travelling minstrel. CORRESPONDENCE. LEEDS CO-INSTRUCTION SOCIETY. MR. S. VESLEY, of Kirkgate, Leeds, on behalf of Call-lane Mutual Improvement and Phonetic Society, most of whose members are subscribers to this work, writes to inform us, that as soon as our periodical was announced, they all determined to profit by its lessons, and to study them as we should see fit to give them out. He states that they have not been disappointed, but on the contrary highly gratified with our attempt to place at so reasonable a price, such valuable information within the reach of all. They have now a room adjoining Call-lane Chapel, Leeds, capable of accommodating about 100 persons, and by paying one penny per week, they are able to meet all expenses, and purchase the periodicals which are published at this office, and about a dozen others. They meet every Monday, Tuesday, Wednesday, and Friday evenings, at eight o'clock, and close at half-past nine; on each evening they have writing, arithmetic, &c.; they have also a grammar class, taught by Mr. Elisha Waite, on the plan and from the pages of the EDUCATOR; and a phonographic class on Wednesday evenings, under the care of our correspondent; while the other branches are under the care of Mr. Daniel Rider, cloth merchant, of the same town; and the Rev. Jabez Tunnicliffe is their president.. We are requested to give these statements in the POPULAR EDUCATOR, as it is believed that there are a number of our subscribers in the town who would be glad to join the society if they knew of its existence; and thus to increase its efficiency, by enabling it to employ able teachers for the different departments, which may appear in this work. The increase in the number of its members, would also enable the society to form themselves into classes for the study of those branches which would be most useful to them in their different employments, as they tre fully aware of the advantages to be derived from union and co-operation. The society has not mustered a library of books yet, but this is in progress. To the Editor. DEAR SIR,-I am much pleased to observe the success which is attending your labours in connexion with the POPULAR EDUCATOR, and am further gratified to observe that you propose to make arrangements for the delivery of Penny Lectures to the working classes, on the various subjects which are treated upon in the EDUCATOR. I think this suggestion a very valuable one, and likely to be greatly conducive to the elevation of the working classes. I am much accustomed to lecture to working men on various topics, such, for example, as phonography, temperance, electricity, astronomy, physiology, &c., and will be very glad to do as much as I possibly can to forward your scheme in this locality. By the way, will you oblige by giving in your answers to correspondents some explanation of the phenomena frequently observable in meadow-fields,-viz., well defined rings of various sizes, from 1 foot to 6 feet in diameter, formed sometimes of beautifully-coloured long grass. and at other times of discoloured or short yellow grass; these rings are sometimes called fairy rings, which appellation is, perhaps, not very philosophical, and yet it is, nevertheless, about as much as is generally known respecting these remarkable circles.-I am, yours respectfully, 26, Granger-street, Newcastle-on-Tyne, May 16, 1852. T. P. BARKAS [FAIRY RINGS have been ascribed to various causes, the most satisfactory one appears to be that of Dr. Wollaston, who traces them to the absorb all nutriment from the soil beneath, that the herbage is for a while destroyed, and a ring appears, bare of grass, surrounding the dark ring. In the course of a few weeks, after the fungi have ceased to appear, the soil where they stood grows darker, and the grass soon vegetates again with peculiar vigour, so that I have seen the surface covered with dark grass, although the darkened soil has not exceeded half an inch in thickness, while that beneath has continued white with spawn, for about two inches in depth. The extent occupied by the spawn varies considerably, according to the season of the year, being greatest after the fungi have come to perfection, and is reduced to its smallest dimensions, and, in some instances, may not be discernible before the next year's crop begins to make its appearance.] DEAN-STREET CO-INSTRUCTION SOCIETY. SIR, I have the pleasure of informing you that there is a co-instruction society of young men, called the Soho Mutual Instruction Society, held at Little Dean-street, Soho. It is managed by a president vice-president, secretary, librarian, and eight committee-men. The members meet every quarter to appoint fresh officers and examine the books. Your valuable work, the POPULAR EDUCATOR, is much admired; a great number the members take it weekly.-I am, Sir, yours, &c., May 16, 1852. D. V. J. [We observe, from a bill enclosed, that the subscription to this society is 4d. per month; and that the classes are for reading, writing, grammar, spelling, arithmetic, mathematics, and French, with the use of a library.] EDUCATIONAL NOTICES. A correspondent at Chatham states his willingness to devote one or two evenings a week to explain the English and the French languages, and arithmetic. He has been for twenty-seven years a national schoolmaster, and has had about 2,500 children under his charge He finds that fully five out of every six of that number have left school under fourteen years of age to go to work, and that their arithmetic and other mental acquirements are entirely forgotten, so that at the age of twenty years they can barely read and write. He offers his services to the new scheme with no other desire or expectation than the pleasure of succeeding in his undertaking. Mr. Strachan, of Aberdeen, the author of an Introduction to Arithmetic; that is, to the four simple and compound rules, has sent us a copy, in which we find the proof of the simple rules by casting out the nines. The proof of subtraction is in principle the same as Mair's. Mr. E. P. Hill, of Islington, states that from the appearance of our first number he has had an evening class for teaching French on the plan laid down in this work, and he hopes to be useful in promoting our scheme of education. He intends to teach the Latin and the German (as soon as it appears) on the same principle. Mr. Simpson, of Low Torrie, proposes the simplest method of proving subtraction by casting out the nines; namely, cast them first out of the minuend, and note the result; then cast them out of the subtrahend and remainder, as if they were two numbers in addition, and note the result; the two results should be the same, if the operation of subtraction be right. LITERARY NOTICES. FINE EDITION OF THE POPULAR EDUCATOR.-EDUCATION OF FAMILIES.-No publication has ever been welcomed with such tokens of approval from heads of families as this last of JOHN CASSELL'S works. An EXTRA EDITION, at 14d. per number, or in Monthly Parts, in a neat wrapper, at 7d., or when Five Numbers, 84d., is now published, which is issued without the weekly headings. Persons wishing for this edition must be careful to order the "Extra Edition." The whole of the Numbers may now be obtained, or the first Twc Parts.-l'art I., 7d.; Part II., 8. THE ILLUSTRATED EXHIBITOR AND MAGAZINE OF ART.-The First Volume of this splendidly embellished work, handsomely bound, price 68. 6d., or extra cloth gilt edges, 78. 6d., will be ready July 1, and will contain upwards of Two Hundred Principal engravings, and an equal number of Minor Engravings, Diagrams, &c. COMPLETION OF JOHN CASSELL'S LIBRARY.-This invaluable Work double is now complete in 26 Volumes, 7d. each in paper covers; The entire Series Volumes, cloth, 1s. 6d., or when 3 Vols. in 1, 2s. 3d. may be had, bound in cloth, 198. 6d., or arranged in a Library Box, 253. The EMIGRANT'S HANDBOOK, a Guide to the Various Fields of Emigration in all parts of the Globe, is now ready, price 6d. THE PATHWAY, a Monthly Religious Magazine, is published on the 1st of every month, price twopence-32 pages enclosed in a neat wrapper. Vols. I. and II., neatly hound in cloth and lettered, price 28. 3d. each, are now ready. PORTFOLIOS for enclosing 26 numbers of THE POPULAR EDUCATOR, price 1s. 6d., may be procured at our office. These Portfolios are so constructed as to form, upon the completion of each volume, a neat Case for binding the same, which will be done at a trifling expense by any bookbinder. ANSWERS TO CORRESPONDENTS. MR. GALT (Glasgow) is right; thanks for his communication.-P. C.: It can; for the wisdom of Solomon or Solomon's wisdom, means the same thing-MUNGO: Order required; French, Italian, German. J. B. We are of opinion, that Y-grec is so called not for its sound but its form, which is that of speilon in Greek. Suggestions, among which are some of great value, have been received from the following readers and subscribers:-William Tucker, Hoxton; A Subscriber, Birmingham; A. A. Fryer, Inner Temple; Schwarz, Liverpool; Charles Currie, Glasgow; Amicus; F. G., Sunderland; W., Edinburgh; Benjamin Williams, Norwich. Caux (Snainton) will find his query answered at page 59, col. 1, No. 4.—JAMES JAMIESON, Aberdeen, will find his difficulties removed in the answers to C. L., p. 112, and J. S. R., p. 128-M. J. Perthshire: Quite right.-T. E. VIBERT, St. John's-wood: Correct, but the 3rd prop. of Book I. is used.-J. ORD: Right.-Mr. ARCHER (Brighton), must address his inquiries to us.-S. WOOD, Macclesfield: Right, but rather short.-M. J. H.: The plan on the first page of No. 7 will probably meet his views -J. ASHWORTH, Crawshawbooth: Correct.A LEARNER; C.: Yes.-J. S. K. is right on all points but the last, for which let him consult Latham-A. B C.: Riddle's.-W. E. H.: The e is silent at the end of words except when accented acutely, thus & JOSEPH WEBSTER: Under consideration. J. K. S. B. (Belfast).-His solutions are all right, and do him credit. One of the subjects he mentions is begun; the other will follow in due time.-A SUBSCRIBER wants lessons in drawing; they will be given.— JOSEPH CORK, Belfast, shall be gratified soon by the history of Persia.— ALFRED B. is anticipated; the Lessons on Geography are begun B. W. M.: Conchology must take its turn; but it shall have it.-A YOUNG STUDENT is informed that they are always sounded in the middle of words; but not at the end, except they be marked with the acute accent, thus été (aytay) summer.-DUNCE: We very much regret that some misprints have annoyed many readers; and among others a painstaking subscriber who assumes this signature. It is not his fault, but the printer's and ours. Saepe means often.-D. N., Ayrshire, is very correct in his solution.-PALLIO: Yes. GEORGE DARNELL (Birmingham) has forwarded the first subscription to the POPULAR EDUCATION FUND, and suggests that the first lectures should be on English Grammar. D. R. (Glasgow): Yes.-GRATULATOR is right; the corrections Chemistry; but what can we do? let him only look at what either have been or will be made.-A SUBSCRIBER earnestly requests we have to do to please, interest, and instruct so many.-P. R. B. is the man for us: we shall do what we can for him; we shall keep Lessons on Carpentry, Joinery, &c., in our eye, until we get an oppor tunity of giving him some hints on the subject. THOMAS PATTISOs (Newcastle-on-Tyne). His solution is very excellent.-J. H. O. The only correct expression is, "thou wentest," or thou didst go."—R. E. Try both the Latin and the Mathematics; they are very good companions, especially as you have a liking for them; this is the first and great point in all studies; it will carry you on in spite of yourself; and if you feel inclined to flag at any time, remember the adage, fortuna faret fortibus, fortune favours the brave;" or, likening the studies to two ladies to be won (a species of bigamy perfectly law. ful), keep in mind the poet's words, "None but the brave deserve the fair." fear that there are some persons who take a delight in science and With T. R. (a subscriber) we certainly agree in the general; yet we learning, who would still think it no harm to tease their fellow-crea tures, and have a little fun with them if they could; it is but human nature. Now, we wish if possible to raise them above even this part of their nature. But our correspondent need not be alarmed, as the lady's friend said to her in a country church, we are not going to sing," that is, we are not going to reprint Chesterield, as new. P. P. HAYES (Chorley).—If the flags have no dimensions in common, the LAW of nature. If they have all the same length, but different they MUST be calculated separately: there is no help for it. Such is breadths; add the breadths together; multiply the sum by the common length, and you have the superficial area of all the flags. If they have all the same breadth, but different lengths, add the lengths together; multiply the sum by the common breadth; and you have the superficial ares of all the flags. On this subject, we speak positively and definitively. The lessons in geometry will be carried as far as he wishes and farther too. As to former questions, he must have overlooked the answer. P. T. S.—The statement about which he inquires is a misprint; it should have been Loch Greenock. LATIN.-Non omnia nimirum omnibus dii dedere, in English is, the been received from MATTHEW SPEARS, Glasgow we shall take an Solutions of all the geometrical problems recently proposed have gods have certainly not given all things to all men; that is, to these they early opportunity of noticing them more particularly. The solution have given some things; to those, others.-R. M. B. will in time be of J. J. N-N, Bridgewater, is barely within the prescribed limits. instructed how to "put the day of the month;" all things cannot be The solution of STUDENS, Dalry, is very good.-G. W., Dundee, taught at once. Domine is the equivalent of Sir.-Let J. H. E. learn is right. John Mahoney, Dublin, right. R. A., Dublin, will to believe, if he wishes to become a scholar-C. A. S. will learn by-and-find answers to the rest of his questions among the notices to corre by that the verb est has the same case after it that it has before it; spondents in preceding numbers.-We advise G. R. H-L to confine consequently praedam is wrong; he translates the sentence correctly. himself to one language at present; say French, for the reason he has -Let 8. M. study carefully what we have said respecting the inversion stated.-J. F-D, Poland-street, has proposed a plan for squaring the and collocation of words, and his difficulties will be removed.-J. L. circle, which is far inferior to the methods now known to mathemaDERMER'S inference is unwarranted; if he will have a little patience he ticians. It can be demonstrated that the diameter of a circle is incomwill be taught the exact force of the interrogatory particle.-P. P. is mensurable with the side of a square equal to it in area; but the ratio wrong in saying that "ornemini is given," &c. Orno has 1 after it, of these two straight lines can be given, by approximation, to any signifying that it follows the form of the first conjugation. Conjugation degree of accuracy required.-A LEARNER, Warrington, should now has to do not with meaning, but certain variations of form. Should study geology, the first lesson being given in this number - Us we go on to treat of synonyms, P. P. will be instructed in the difference FRANÇAIS: Yes. - A Subscriber, Guernsey: Yes.-W. G-Y, Yeovil: between amo and diligo. It is not well to anticipate. By so doing we His plan is not practicable; but the index of the volume will answer should teach nothing well, and our students would learn nothing well. all the purpose required.-J. H E-D, Middleton: Right.-R W. and -Let G. C. pronounce Latin words as he would pronounce correspond- w. S, Audenshaw: The e is not sounded in the last three words, and ing English words, with such limitations as are mentioned in the very slightly heard in the first two-W. L- N, Newark; GREEK: Yes. Lessons. To follow his suggestion would be to fill our pages with gro--J. R, Glasgow: The old names show the continental mode of protesque combinations of letters.- A MECHANIC's exercise is correct. The nunciation; the new names, the English mode. "art" as in "art taught," is included in the one Latin word doceris. Unus ex tuis discipulis (which should be unus e discipulis tuis), is partly wrong, partly right. Funestum, i, n. is correct, being the neuter gender of the adjective funestus. The e of the stem in the fifth declension is e long. Merces as a collective noun or a noun of multitude, may have a verb in the plural number. ERRATA IN SOME COPIES, col. 1, p. 5, for ta cemus read tacemus. Line 36 from top, 1, p. 36, for nor read non. 1, p. 70, for after read often. We have received a great number of solutions of the problems and queries proposed in the preceding numbers of this work. Most of these solutions are excellent and do great credit to their authors, and a few are defective. We have endeavoured to notice a great many in our answers to correspondents; but we find that these notices are not always consulted as they ought to be; we would therefore recommend all our readers to peruse them, as they will often find in them a solution of difficulties which may occur, as well as the correction of important errata. Some will also be saved the trouble of writing for an explanation of things already explained to others, and sometimes even to themselves. We have not yet noticed the numerous methods of proving arithmetical rules by casting out the nines, which we have received; and for this reason, that we have not quite finished the explanation of the four common rules; when this has been done, we shall then take up this subject in good earnest. Printed and Published by JOHN CASSELL, 335, Strand, and Ludgate-hill, THE object of the author of the following German Lessors, is | 3. 3, ii, as in pique, pin. Ex. mir, to me; mit, with; ihn to unite theory and practice; to introduce, one by one, the him; wider, against; bitter, bitter. easier forms and usages of the language; and to direct the 4. D, oo, as in no, door. Ex. Ofen, stove; Moos, moss; Kohle, coal; Port, port; Post, post-office. hyssop; Styr, Styx; Opern, Ypres. Ex. Ysop, student's attention to the more obvious differences between the German and the English. He will be supplied, through- 5. u, u oo or o, as in poor, do. Ex. Blut, blood; Du, thou; out the various exercises, with the materials necessary for Uhr, watch; Hut, hat; gut, good. their due performance. Every section is headed with the 6. V, i, (mostly in words from the Greek). statement and illustration of all new principles involved, with an explanation of words and phrases, and a vocabulary alphabetically arranged. To render these Lessons complete, there will be given at the end a series of reading lessons, and a full Vocabulary. The whole is specially intended for those who aim at the acquisition of the German language without a teacher, The sound of a vowel when doubled is thereby lengthened; as, Aal, Meer, Moos; followed by a double consonant, the vowels are usually shortened; as, Blatt, Brett, Sinn, Gott, &c. See, however, 18. H. Dissyllables (See Vocabulary), unless otherwise noted, are accented on the first; as, leben, Ehre, &c. Sounds of the Diphthongs. 7. Ai, ai (sometimes aj or a)ay nearly, as in aye. Ex. Raiser, emperor; Bairn, Bavaria; Mai, May. 8. Au, au ou, as in our. Ex. Haus, house; Maus, mouse; laut, loud; Faust, fist; Braut, bride. 9. Ei, chi or ei, as in fine, eider. Ex. Stein, stone; dein, thy (ie ie, as in pier; never as in pie. Ex. viel, &c. . 16. Eu, cu nearly to oi or oy, as in boil, boy. Ex. Beute, booty; Leute, people; Heuen, to hay. Umlaut signifies changed or modified sound. The Umlauts are produced by a union of e with a, o, u (also at respectively. Except when they are capitals, the e is expressed by two dots; thus, à, ō, й (and äu). 12. Ae, à somewhat (though shorter) like c. Ex. Merger, vexation; Fähre, ferry. 13. De, è, as in Del, oil; Pöbel, populace; tödten, to kill; Röhre, pipe; Köhler, collier. 14. Ule, i, as in Uebung, practice; müde, weary; führen, to guide; Müller, miller. De and Ule have no corresponding sound in English. Del and müte, for example, might, perhaps, be generally understood, if pronounced, ale, meede, but this is by no means the correct pronunciation. De is pretty accurately given by the French eu in peur, and ũ, by the French u in vu. Sounds of the Consonants. 15. B, b; D, d; F, f; K, k; 2, 1; M, m; N, n; P, p; Q, q; 17. g, sounds like our g in gild, foggy, &c., but never as in 18. 5,, in the midst and at the end of a syllable is silent, but serves to lengthen the preceding vowel. Ex. lehren, to teach; ohne, without; Thee, tea. 11 19. 3, i, sounds like y consonant. Ex. Jahr, year; Januar, January; jung, young. 20. R, r, is uttered with a trill or vibration of the tongue, and G. with greater stress than our r. Ex. Rohr, reed; Rath, council; reif, ripe. R. 21., at the beginning of a syllable followed by a vowel, has. 24. W, w, has a sound between that of our w and v. Ex. Welt, 25. 3, sounds like ts. Ex. Sal, salt; Zahn, tooth; 3unge, tongue; zehn, ten. Sounds of the Compound Consonants. S. lesson; Gallcuta, Calcutta; Gontract, contract; Gur, cure Jüngling, youth; Jute, Jew; ja, yes; Joseph, Joseph; Juli, Reif, ripe; reich, rich; Reft, rest; rar, rare; Rücksicht, regard; Sattel, saddle; Segel, sail; Speer, spear; Spros, sprout; start, strong; @trumpf, stocking; ut, south; Reid, rice; Straße, street; wijen, to know. T., table; Tarif, tariff; Temvel, temple; Truppe, troopi V. Vampyr, vampire; Vase, vase; Bers, verse; Bioline, violin; B. Wort, word; Wurm, worm; Wunter, wonder; Wille, will; 3. 3int, zinc; Zuhl, number; zahm, tame; Zeit, time; Zentne hundred-weight; Holy, wood. Ch Flachs, flax; svrechen, to speak; wachsam, watchful; Cher, choir Schaft, shaft; Schatten, shadow; Schnee, snow; frisch, fresh; ss. Bleis, diligence; ließ, fleece; lassen, to let; bassen, to hate; 26. Ch, ch, in primitive words when followed by f, has the 27. Ech, ich, sounds like sh. Ex. Schuh, shoe; Schiff, ship; schon, 28 (though compounded of j and 3) sounds like f, and is used only at the end of a syllable. Ex. Mas, measure; Fluß, river, &c. 29. (though compounded of t and 3) sounds like ¿ but like is only employed at the end of a syllable. Ex. Stug, Play, &c. Note, that this letter being a double consonant, the preceding vowel is thereby shortened. To aid in producing the sound of c, take for experiment the above word bech pronounce bo precisely like our word ho; observing to give as full and distinct a breathing of the h at the close, as at the beginning; thus, h-o-h=hech. Except when preceded by a, o, or u, as will be perceived by experiment, a slight hissing sound of, or ich naturally attaches to the ; as, in recht, reich, ich, Grieche, &c. EXERCISE 1. (a) Altar, altar; Paar, pair; Ahle, awl; Balsam, balsam; baten, to bathe; Pfalm, psalm. (e) Heer, host; mehr, more; etel, noble; Ente, end; Setter, letter; Herbft, autumn. (i) Trinken, to drink; finten, to find; Biber, beaver; hier, here; Kind, child. (0) Boot, boat; hohl, hollow; oft, often; Hobel, plane; Koller, collar; Roffer, trunk. (u) Fus, foot; gut, good; unten, below; Putel, poodle; kudul, cuckoo; Muth, courage. (4) Nymphe, nymph; Rhythmus, rhythm; Sylbe, syllable; fynonym, synonym; Syrup, syrup. (ai, ei) Main, Maine; mein, my; Laib, loaf; Leib, body; Rain, Cain; fein, no. (au) Bauen, to build; Mauer, wall; grau, gray; Raum, room; rauh, rough. (3). Sige, heat; tcs, log; figeln, to tickle; schwagen, to prattle; schwißen, to perspire; fur, short; schwarz, black. LESSONS IN MUSIC.-No. V. THE PROPER MANAGEMENT OF THE VOICE in singing is of great To produce a good note, the singer should be in an easy posture, with his head upright and his shoulders back, so nato allow the muscles of the chest and the larynx (that little box in the throat which we can feel with our fingers) to have free movement. His mouth should be moderately open. H tongue should lie down, just touching the roots of the lower teeth; and his lips should have the position most easily or plained by referring, to that of a gentle smile, but really expressing no smile and giving no emotional expression. Some teachers require a small cork of the thickness of a little finger, or the little finger itself to be placed between the back teeth during the earlier exercises. We have a friend who to improve his voice for speaking, used to read aloud for half an his front teeth. Of course this did not cultivate his enuncia hour before breakfast every morning with a large cork between the larynx and lungs, and prevented his over-exertion of the tion-his words were curiously pronounced-but it strengthened throat, so that he could speak in public with the greatest ease and without the slightest fatigue of voice, as we have had laffe, class; Greatur, creature; Criminal, criminal; Section, ample proof, nearly a whole day long. (au, eu) Raumig, roomy; reuen, to rue; Haute, skins; heute, to- (a, e) Aebre, ear (of corn); Männer, men; leben, to live; Krahe, reddish. röthlich, (ü) Uebel, evil; fünf, five; Rüffel, proboscis; Krüppel, cripple; Jünger, disciple. EXERCISE 2. |