LESSONS IN ARITHMETIC. algebraic process, that a negative quantity is brought to stand alone. 42. A quantity is sometimes said to be subtracted from 0. By this is meant, that it belongs to the negative side of 0. But a quantity is said to be added to 0, when it belongs to the positive side. Thus, in speaking of the degrees of a thermometer, 0+6 means 6 degrees above 0; and 0-6, 6 degrees below 0. AXIOMS. 43. An AXIOM is a self-evident proposition. 1. If the same quantity or equal quantities be added to equal quantities, their sums will be equal. 2. If the same quantity or equal quantities be subtracted from equal_quantities, the remainders will be equal. 3. If equal quantities be multiplied into the same, or equal quantities, the products will be equal. 4. If equal quantities be divided by the same or equal quantities, the quotients will be equal. 5. If the same quantity be both added to and subtracted from another, the value of the latter will not be altered. 6. If a quantity be both multiplied and divided by another, the value of the former will not be altered. 7. Quantities which are respectively equal to any other quantity, are equal to each other. 8. The whole of a quantity is greater than a part. 9. The whole of a quantity is equal to all its parts. LESSONS IN ARITHMETIC.-No. XXIII. EXAMPLE.-Find the difference of the following fractions: * and. Here, by Problem II., p. 267, we have # Answers to the Exercises in our last Lesson follow in order :- EXERCISES TO PROB. IV. Answers, First.-24, 48, 201, 4000, and 487034 583 difference 7 6=173, the Whence is the answer required. Or, EXAMPLE. Find the difference between 20 and 2. Here, taking 1 from 20 leaves 19; and 18, by Rule 2, Prob. IV. Now, 8--18, by Rule 1 above; whence 1918 is the difference required. Numerators. RULE 4.-When a mixed number and a fraction or two mixed numbers are given to find their difference; reduce the given fractions to fractions of equal value having a common denominator, by Prob. II. Then, appending these fractions to the integers to which they belong, subtract that mixed number which has the smallest integer from the other; in subtracting the fractional part of the one from the fractional part of the other, if the numerator of the subtrahend be less than that of the minuend, apply Rule 1 above, and then the Rule of Subtraction, p. 66, vol. I.; but if the numerator of the fractional part of the subtrahend be greater than that of the minuend, apply Rule 3 above; add the difference thus obtained to the fractional part of the minuend, and then take the difference between the remaining integral parts as before. This difference, prefixed to the difference of the fractional parts thus obtained, will give the difference required. The reason of this rule is obvious from the reasons assigned for the preceding rules. EXAMPLE 1.-Find the difference between 31 and 223. Here, 28 by Prob. II.. 3 = 48 Whence, 31% = 228 Required difference 318 22 918; by the rules to which reference has been made above. EXAMPLE 2.-Find the difference between 43 and 27. Here, as before, 431 43 Now, taking 1 from 43, leaves 42; and 1= =38 by Rule 2, 36 985 3333; and 3ð + a‰ = 8; by the rule. Answers,-(1.) 54; (2.) 39; (3.) 1883; (4.) 401%; (5.) But 42-27 15, by the Rule of Subtraction, p. 66, vol. I. Therefore, 1538, is the difference required. 50; and (6.) 26891. EXAMPLE 3.-Find the difference between 7 and . Here, as before, 7% = 70 # = 48 6, Ans. Required difference EXERCISES TO PROB. V. Answers.--(1.) 1k, (2.) §; (3.) &; (4.) 1; (5.) 19; and Prob. 4; (6.) 10. 13 EXERCISES TO PROB. VI. SUBTRACTION OF FRACTIONS. In working this example, as above, we have first to take 1 from 7 PROBLEM VII. To subtract one fraction or one mixed number from another, or from a whole number. RULE 1.-When the given fractions have a common denominator, subtract the less numerator from the greater, and under it place the common denominator, for the difference or remainder required. The difference should be reduced to its lowest terms, and if it be an improper fraction, it may be reduced to a whole or mixed number, by Problem III. and. EXAMPLE. Find the difference of the two fractions, RULE. 2-If the given fractions have different denominators, reduce them by Problem II, p. 267, to fractions of equal value having a common denominator, and apply the preceding rule to these fractions, the difference will be the answer required. The reason of these rules is explained at p. 168, vol. II. EXERCISES. 1.-Between 1 and . MULTIPLICATION OF FRACTIONS. PROBLEM VIII. To multiply fractional quantities and mixed numbers by cach other. RULE 1.-When the given fractions to be multiplied are proper fractions, multiply all their numerators together for the numerator of the product, and all their denominators for the denominator of the product; the result placed in a fractional form will be the product required. The reason of this rule may be thus explained; take, for example, two proper fractions and, and let it be required to find their product. You will recollect that the fraction may be considered as of 5 (see No. 7, p. 133, vol. ii.); you will also remember that to multiply the fraction by 5, we must multiply the numerator only, and that this product will be (see No. 11, Principle 2, p. 134); now we wish to have the product of by of 5; we must therefore take of the product of this fraction by 5, that is, we must take of 15; but, by No. 8, Def. 3, p. 133, this becomes, the proper answer to the question. The process, then, is plainly this; in order to multiply one fraction by another, you first multiply the multiplicand by the numerator of the multiplier, and then divide the product by its denominator (see No. 12, Principle 3, p. 134); but this process is equivalent to that expressed in the words of the rule; for multiplying the numerator of a fraction by a whole number increases its value, and multiplying the denominator by the same diminishes its value; and the numerator and denominator of the multiplier are considered as whole numbers when taken by themselves. Another view of the reason of this rule may be taken perhaps with more simplicity and propriety as follows: When we multiply a fraction by any number we repeat or take it as many times as that number denotes; when we multiply it by unity or one we take it one time; and when we multiply it by a proper fraction we take it a part of a time; therefore, in the latter case, we must take such a part of the multiplicand as that part denotes; but to take such a part of a fraction as another fraction denotes is to take a fraction of a fraction, which, according to No. 8, Def. 3, p. 133, is to form a com o nul fraction; and this requires the operation described in the rule; see the place to which we have just referred. From the preceding observations we draw the following important observations, viz.: That whatever be the nature of the multiplicand, 1, if it be multiplied by a whole number greater than unity, it is increased; 2, if it be multiplied by unity itself it is neither increased nor diminished; 3, and, if it be multiplied by a proper fraction it is diminished, that is, the product is always less than the multiplicand. When the product of several fractions is required, the preceding rule is applicable to any two of them; it is then applicable to the product of these two, and another of them; then to the product of these three and another of them; and so on, whatever be their number; so that the rule for reducing compound fractions to simple ones, and for multiplying any number of fractions together is the same. This rule is, therefore, capable of the same abridg. ment, by the method of cancelling factors, explained at No. 15, p. 328, col. 2, where the rule for this process is given. N.B. The answer obtained by the rule above must be reduced to its lowest terms. 4 (1.) X 9 EXAMPLE. Multiply together the following (1.) § × 1; (2.) ‚† × × 78; and (3.) ! × × Here, the operations are indicated as follows: 3 8 8 X X 9 2 = 3 33 70 by the rule. 1=3 4 X 5 X 33 660 11 X 9 X 70 6930 2×2×3×3 x 11 11 × 3 × 3 × 2 × 5 × 7 1 3 4 X X X = 4 5 6 7 by the rule. = 1 י 7 (2.) (3.) (4.) (5.) Or, 1/2 × strikingly useful; for, in (1.) the factors common to both numeIn these examples, the process of cancelling the factors appears rator and denominator are 4 and 3, which being left out, gives the result, without the trouble of reducing the product to its lowest terms; in (2.) the common factors are 2, 5, 3 and 11, and the result 2; in (3.) the common factors are 2, 3, 4, 5, and 6, and the result is 3. (6.) EXERCISES. Find the products of the following fractions : 7 3 2 3 (1.) X X X 12 9 3 49 X X 70 142857 428571' 4 5 XX 32 143 6 :-* towers A M, B N, and CP by a, b, and e, respectively. Let z denote fractions :the length of the ladder, which is either M O, NO, or P o, if we sup× ×X.pose o to be the point where the ladder must be placed, in order factors. to reach the tops of the towers, at M, N, and P, respectively. It is plain that as the heights of the towers are of different lengths, it we suppose the lengths a, b, and c to be written in the order of their magnitude, a being the smallest, and e the tallest, that the by cancelling point o will be nearest to c and nearer to в than to A. From the point A, draw Ar perpendicular to BC; from the point o, draw os perpendicular to BC, and OR to AT; then ROST is a right angled parallelogram, and A Ro a right angled triangle. Since by hypothesis, the angles MA O, NB O, and PCO are right angles, we have, by the 47th of Euclid's Book I., the following equations:(1.) a o2= x2—a2, (2.) Bo2=52—¿2, and (3.) co2='r'—e, and denoting Ts by z, and os or RT by y, we have also, as2+so Bo', and cs+so2 co2, or, by substitution, from the pre 720 5010 by the rule. ceding, (4.) {+}+ y2x2-8, and (5.) { jd−z}2+y+= -c; whence, by subtracting equation (5.) from equation (4.), by cancelling the factors. 10° SOLUTIONS OF PROBLEMS AND QUERIES. 1. THE THREE TOWERS, p. 223. LET A BO be the equilateral triangle, on whose angular points the three towers AM, BN, and C P are placed; let the base or side of the triangle ABC be denoted by d, and the heights of the three 1 c2-be On se plaint de l'issue de tel événement: La fortune a trihi nos e, efforts, dit-on; c'est dire en d'autres termes: Il est arrivé un résulíat sans cause. Pourquoi ces plaintes d'enfant ? Ce qui est arrivé devait arriver. Votre maison s'est écroulée; c'est qu'elle était mal étayée. Le peuple a couvert d'acclamations ses oppresseurs : c'est parce que le peuple n'est pas assez avancé pour comprendre ses véritables intérêts. La fortune n'a rien à faire là-dedans: au lien de l'accuser, travaillez les causes, l'effet suivra. Tel est le rôle qui convient à des créatures raisonnables.-J.-B. Say. we have 2dze, and consequently (6.) = 2 2 But by the 17th of Euclid, Book I., ATA B-B T2, or by FRERE. Une coutume très-imprudente des pères et des mères, des instituteurs et des domestiques, c'est de faire naître et d'entretenir entre les frères une certaine émulation qui dégénère en discorde lorsqu'ils | sont d'un âge plus avancé, et trouble la paix des familles.—Bacon. Assuming the values as given in the question, we have a = 28, 630, 34, and d=50. By substituting these numbers in equation (6.), we find z=256e. By substituting the same numbers, with the value of e just obtained, we find y 134 9381 f; and by substituting the values of e and ƒ thus found, in equation (10.) we find ≈ 42.361 feet, which is the length of the ladder required. From this value of x, the three distances A 0, B o, and co are found, by substitution in equations (1.), (2.), and (3.), to be respectively, 31.789 feet, 29.908 feet, and 25-268 feet. This question was solved by J. SowDEN; DOUGLAS; A. SKERRITT (Holbrook); CAROLUS (Padiham); and many others. SOLUTION OF QUERY 2, P. 240, col. 2. Let x and y be the two numbers. Then, by the question xy= +y; Whence, we have, xy—x—y, by transposition; or, (y-1) y; whence, x = y y-1 Now, by assuming the value of y, we can from this expression, find the value of x which will answer the conditions of the question. This formula may be put into the words of the following rule ; From any number greater than unity, subtract unity, and divide the number by the remainder, the quotient and the number assumed will be the two numbers required. EXAMPLE.-Take any number 7 for the value of y, one of the numbers; then 7-1-6, and 7÷6=14; whence 7 and 1 are the numbers required. Proof: 7+18); and 7×14=8. FRENCH EXTRACTS. PENSEES MORALES ET MAXIMES. FAUTE. Ne dites jamais: Cette faute est légère, je puis me la permettre sans danger. Ne dites jamais: Cet acte de vertu est peu considérable, il m'est bien permis de l'omettre.-Sénèque. Il n'y a pour l'honne qu'un vrai malheur, qui est de se trouver en faute et d'avoir quelque chose à se reprocher.-La Bruyère. FIERTE. La fierté du cœur est l'attribut des honnêtes gens; la fierté des manières est celle des sots.-Duclos. FINESSE. La finesse n'a guère plus de peine à tromper l'esprit qu'à duper la bêtise.-Levis. La finesse est l'occasion prochaine de la fourberie: de l'une à l'autre le pas est glissant: le mensonge seul en fait la différence : si on l'ajoute à la finesse, c'est fourberie.-La Bruyère. Le vrai moyen d'être trompé, c'est de se croire plus fin que les autres.-La Rochefoucauld. Il y a des gens niais que se connaissent et qui emploient habilement leur niaiserie.-Idem. On peut être plus fin qu'un autre, mais non pas plus fin que tous les autres.-Idem. GLOIRE. GUERRE. Il n'y a que deux puissances dans le monde : le sabre et l'esprit; This question was solved by G. WILD (Dalton-on-Tees): PHILO j'entends par l'esprit les institutions civiles et religieuses. A la (Berwick-on-Tweed): G. W. C.; and others. longue le sabre est toujours battu par l'esprit.-Napoléon. HABITUDE. On triomphe des mauvaises habitudes plus aisément aujourd'hui que demain.-Confucius. Deux choses toutes contraires nous préviennent également, l'habitude et la nouveauté.- La Bruyère. FORTUNE. L'on voit des hommes tomber d'une haute fortune par les mêmes défauts qui les y avaient fait monter.-La Bruyère. Il faut de plus grandes vertus pour soutenir la bonne fortune que la mauvaise.-La Rochefoucauld. Ceux qui se plaignent de la fortune n'ont souvent à se plaind: e que d'eux-mêmes.- Voltaire. Le gloire des grands hommes se doit toujours mesurer aux moyens dont ils se sont servis pour l'acquérir.-La Rochefoucauld. GOUT. Il y a dans l'art un point de perfection, comme de bonté ou de maturité dans la nature: celui qui le sent et qui l'aime a le goût pafait; celui qui ne le sent pas et qui aime en deça ou au delà a le goût défectueux. Il y a donc un bon et un mauvais goût, et l'on dispute des goûts avec fondement.-La Bruyère. GRANDEUR. La fausse grandeur est farouche et inaccessible: comme elle sent son faible, elle se cache, ou du moins ne se montre pas de front, et ne se fait voir qu'autant qu'il faut pour imposer et ne paraftre point ce qu'elle est, je veux dire une vraie petitesse. La véritable grandeur est libre, douce, familière, populaire. Elle se laisse toucher et manier; elle ne perd rien à être vue de près; plus on la connaît, plus on l'admire. Elle se courbe par bonté vers ses inférieurs, et revient sans effort dans son naturel.-La Bruyère. Les grandeurs sont comme les parfums; ceux que les portent ne les sentent quasi pas.-Christine. GRAVITE. Une gravité trop étudiée devient comique; ce sont ecmme des extrémités qui se touchent, et dont le milieu est dignité: cela ne s'appelle pas être grave, mais en jouer le personnage; celui qui songe à le devenir ne le sera jamais. Ou la gravité n'est point, ou elle est naturelle, et il est moins difficile d'on descendre que d'y monter.-La Bruyère. "Vous me reprenez de bien peu de chose, disait un jeune homme à Platon.-Ce n'est pas peu de chose que l'habitude," répondit-il. Etablissez l'ordre, l'habitude l'entretiendra.-Lévis. Celui-là me semble avoir très-bien corçu la force de la coutume qui le premier forger ce conte, qu'une femme de village, ayant appris de caresser et porter entre ses bras un veau des l'heure de sa naissance, et continuant toujours à ce faire, gagna cela par l'accoutumance, que, tout grand bœuf qu'il était, elle le portait encore: car c'est, à la vérité, une violente et traitresse m-itresse d'école que la coutume. Elle établit en nous, peu à peu, à la dérobée, le pied de son autorité: mais, par ce doux et humble commencement, l'ayant rassis et planté avec l'aide du temps, elle nous découvre tantôt un furieux et tyrannique visage, contre lequel nous n'avons plus la liber é de hausser seulement les yeux.Montaigne. C'est passe temps aux mères de voir un enfant tordre le cou à un poulet, et s'ébattre à blesser un chien et un chat. Ce sont pourtant les vraies semences et racines de la cruauté, de la tyrannie: elles se germent là, et s'élèvent après gaillardement, et profitent à force entre les mains de la coutume.-Iden. HAINE. Il est indigne d'un honnête homme de se servir des débris d'une amitié qui finit, pour satisfaire une haine qui commence.-Fenelon. Il ne faut pas, sans de fortes raisons, scruter le cœur des homSe regarder scrupuleusement soi-même, ne regarder que légèrement les autres, c'est le moyen d'éviter la haine.-Confucius. mes. HAUTEUR. Tout homme qui pense assez pour n'être pas haut, n'est jamais bas.-Pascal. ANSWERS TO CORRESPONDENTS. M. Mc' GAURAN (Cavan) wishes to know the latest work on artificial memory, not too dear.-2. P. O. (Barnard Castle), will find a method of parsing laid down at p. 220, vol. 1.-A. Mc' KENNA (Cappoquin): We think that France formerly exercised the greatest influence on the literature and science of England, but that Germany now bears the palm. On this subject, however, consult Jeffrey's Contributions to the Edinburgh Review," or any volumes of the Review itself that may come in the way. We are glad that there is a "Mutual Improvement Society" in Cappoquin, Co. Waterford.-DISCIPULOS (B. Field): Right about the lean horse. Corporem is not a Latin word, neither is ingentem applied to bellum; see p. 92, col. 2, vol. I. A Latin Dictionary would certainly be of great assistance to you. Thanks for the discovery of the "round world;" the word translated round in the passages of the Psalms found in the Prayer Book, is translated habitable in the Bible; but its true meaning seems to be unknown, as Gesinius, the best Hebrew scholar of modern times, seems to be quite at fault as to this point. W. C.: His lines are capable of improvement.-A BEGINNER (Chelsea), should get Cassell's "French Manual," price 38., and continue the study of the lessons in the P. E.-F. BUXTON (Salford): Thanks for his solutions. A millwright should study mathematics in all its branches, both pure and THE AUTOGRAPHS FOR FREEDOM; containing, in addition to a New mixed.-ADOLPHUS (Hull): 12 o'clock noon, is neither A.M. nor P.M.; but Story by Mrs. STOWE, authoress of Uncle Tom's Cabin," entitled "The the minute after, it is Oh. Im. P.M.; and the minute before, it is 11h. 59m. Two Altars; or, Two Pictures in One;-The Altar of Liberty, or 1776; A.M.-XXX (Liverpool): It is highly requisite in this age of strict inquiry The Altar of, or 1850," a thrilling Narrative by FREDERICK DOUGLASS, for every clergyman to know the Scriptures in their original tongues; and it entitled "The Heroic Slave;""Passages in the Life of a Slave Woman," is equally requisite for every one who desires to confute gainsayers, by Annie Parker; "Placido, the Cuban Slave," by Professor W. G. Allen; J. RUSSELL (Kings-cavil): His new solution or rather form of the Pytha-The Heroic Slave Woman," by the Rev. J. S. May, &c.; also, Coutrigorean Theorum is ingenious; we shall endeavour to find it a place soon.butions from the leading Writers in America on the Question of Negro E. PUGH (Walsal!), will obtain such drawings as he wants at Harvey and Emancipation; and, on this side of the Atlantic, from the Earl of Carlisle, Darton's, Gracechurch-st.-AMICO (Portsmouth): We shall do what we can the Bishop of Oxford, Wilson Armistead, Joseph Sturge, &c.; with facto meet his views in relation to the European languages, &c., but Rome was similes of the Autographs of all the Contributors, Price 1s., in boards; or not built in a day.-J. L. & G. W. (Glasgow) will now be satisfied.-A bound in cloth, with Eight beautiful Engravings from designs by Gilbert SCHOOL-GIRL (Southwark): Genesis, chap. I., verse 9. If she be of suitable and Willis, price 18. 6d. age, she may get some influential friend to recommend her as a proper person for enjoying the privilege of reading in the British Museum. ATHEISM CONSIDERED THEOLOGICALLY AND POLITICALLY. This Volume, consists of thirteen Lectures, by the Rev. LYMAN BLECHER, D.D. (father of Mrs. H. B. Stowe.) These Lectures enter fully into the momentous question now at issue, or, at least, under discussion, between "Secularism" and Christianity. For close reasoning and eloquent declamation, these Lectures have rarely been surpassed. The Volume, just issued, is well printed, and is sold for 2s. 6d. bound in cloth. It is important in ordering this work, that John Cassell's edition should be specially named. THE ALTAR OF THE HOUSEHOLD: a Series of Services for Domestic Wor ship for every Morning and Evening in the Year: Select Portions of Holy Writ, and Prayers and Thanksgivings for Particular Occasions; with ar Address to Heads of Families. Edited by the Rev. John Harris, D.D., Principal of New College, St. John's Wood; Author of The Great Teacher;" "Mammon;""Pre-Adamite Earth," &c. &c., assisted by eminent contributors. The following are among the Ministers engaged in the preparation of THE ALTAR OF THE HOUSEHOLD:-The Rev. J. Sherman, the Rev. W. Urwick, D.D., the Rev. W. H. 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THE SELF AND CLASS EXAMINER IN EUCLID, containing the Enunciations of all the Propositions and Corollaries in Cassell's Edition, for the ast of Colleges, Schools, and Private Students, is now ready, price 3d. J. M. N. (Malta): His solutions to the questions in Cassell's Arithmetic are correct. We believe the P. E. will be found at Halifax in America.S. EMBLETON (Blyth), and H. R. K. (Kingsland): Under consideration.NIL DESPERANDUM: A fortiori, means much more therefore, or for the stronger reason; a priori, means for a reason founded on the nature of the thing, or for a reason exactly such as we might expect; a posteriori, means for a reason founded on some previous argument, statement, or fact: admitted to be true; prima facie, means at first sight: a prima facie argument is a specious or imposing argument. If a man "cannot know what conscience is, until he knows something of metaphysics," he is much to be pitied! Every transgressor of a righteous law must both know and feel what conscience is (see Rom. chap. II, verse 11 and 15, and indeed the whole chapter). ARTHUR SHARP: We thank him for his lines; but it would look like a wish for flattery to insert them.-JEAN J. T. S. (Leeds): The "French Manual," published by Mr. Cassell, price 38., is a substitute for the "Reading Book," to which he refers; he will also find in the P. E. in the "French Extracts" sufficient to engage his attention for a time.-J. C. C. (Clapham) may obtain the numbers he wants by calling on the Editor about the 5th March, at the office of the P. E.--N. M. L. (Barnard Castle): His last exercise is better than the former.-Y. A. S.: Her verses might be improved.-T. J. W. had better make up his mind from our columns. GEORGIUS: We are instructed to say that the whole 16 vols. of Mr. Cassell's Library will be in print within a fortnigt.,-that is, reprinted.-T. GUY (Broomside): Go, in the passage "Go to the ant, thou sluggard," &c is not an interjection, but the 2nd person singular of the imperative mood of the verb to go. In the passages quoted from James, the words go to are the translation of the Greek age, which, like the Latin age, signifies, literally, to do, or to be doing, or to hold, weigh, or consider; they might, therefore, be translated, CONSIDER, OF WEIGH WELL, what I am going to say, it is, therefore, used adverbially, like the words behold, see, look, come now, well, &c. The same words, go to, in the passages quoted from Genesis, are the translation of the Hebrew haba, which signifies, literally, to give place, or set, that is, to put yourselves in the attitude of attention; as much as to say hearken, listen, &c., and is used adverbially just like the preceding words. As to the translation of Exod. xxxii. 35, it is so literal as to be obscure; it should be "they were the originators of the calf which Aaron made." The fact is, they compelled him to make it, and he submitted to them through fear. LITERARY NOTICES. GIN AND WATER; a pair of pictorial designs by Kenny Meadows, portray- Have ever been echoed in minstrel lays; These pictures, which should be framed and hung over every cottage chimney-piece, and on the walls of every factory, and workshop, and ragged school throughout all the land, can be obtained of every bookseller for one shilling. They are exquisitely engraved on wood, by Messrs. Henry Linton and William Measom. H. F. MCPHERSON (Grimsby): The error is now corrected. See also No. 46, p. 300, col. 1, line 60.-H. FISHER: In order to write "eleven 'thousand, eleven hundred and eleven," remember that eleven hundred is one thousand one hundred; so that the proper expression is twelve thousand, one hundred, and eleven. THE ANSWERS TO ALL THE QUESTIONS IN CASSELL'S ARITHMETIC for the use of Private Students, and of Teachers and Professors who use this work in their classes, is just issued, price 3d. THE LADIES' WORK BOOK, containing full instructions for every kind of Ladies' Work, in Point Lace, Knitting, Netting, Embroidery, Crochet, &c., forming the most splendid Book for the Work-table ever issued. This werk contains an immense number of the newest Designs for Ladies' Work, of every description, and is produced in a style perfectly unique. Price 2.64. THE LADIES' DRAWING-ROOM BOOK, in which are introduced the choicest Engravings from the "Illustrated Exhibitor and Magazine of Art," and the "Ladies' Work Book;" the whole forming a beautiful Volume fie the Drawing-room. The work is printed on fine Plate Paper, and got up in the first style of Art. Price 10s. 6d. R. L. A.: Phonography signifies writing according to sound; stenography means writing in a small compass. The origin and structure of the Low Islands extending from the Society Islands towards Cape Horn is the following: Coralline plants, growing at the bottom of the ocean, harbour a class of lithophytic (stone producing) insects, which, during their life, form round them a substance which after their death becomes hard as a stone. The rock-work of one generation affords a foundation to that of the succeeding, and layers are thus placed over each other till they reach the surface of the water and form islands. As soon as the rock is exposed to the air the insects quit the surface, leaving it perforated by numerous hollows; but they work for some time laterally (sideways), forming immediately under the water concealed table-reefs, which have given occasion to numerous and fatal shipwrecks. Meantime, from amid the interstices of the surface plants spring THE ILLUSTRATED EXHIBITOR AND MAGAZINE OF ART-The First Twy up, which, on their decay, are converted into soil, and thus by degrees the Parts of a new and improved Series of this work, under the title of the new island is covered with luxurious vegetation.-J. MCKEEVER (Wigton): ILLUSTRATED MAGAZINE OF ART, are now ready, price One Shilling each. Under consideration.-J. GODFREY (Worksop) will see in the Literary Weekly Numbers are now enclosed in a neat wrapper, price 3d. In addition Notices of the P. E. such books as will be useful to him and his friends; to numerous Engravings in the text, each number contains a fine Engravand by ordering them of the person who supplies him with the P. E. he willing, worked on Plate Paper. With the first Part was presented a splendid most readily obtain them. View of the Interior of St. Paul's Cathedral, during the Interment of the late Duke of Wellington, printed upon fine Plate Paper, measuring eightees inches by thirteen, in addition to four separate Engravings, and a large number of choice Illustrations, with which each Part is embellished. The PATHWAY, a Religious Magazine, price 2d. each Number, enclosed in a neat wrapper. The Fourth Volume has just commenced-Vols. I. and II. price 28. 3d. each, Vol. III., price 2s. 9d., neatly bound, are now ready. UNCLE TOM'S CABIN, with Twenty-seven Illustrations on wood, by George Cruikshank, and an excellent Portrait of the Authoress.-Three Editions of this popular work are now on sale at our office-a Drawing Room Edition, demy 8vo., price 4s. 6d. elegantly bound, with gilt edges; crown 8vo., neatly bound, gilt edges, 3s. 6d., or plain binding, 3s. Printed and Published by JOHN CASSELL, 9, La Bella Sauvage-yard, Professor of Elocution and Vocal Physiology, Member of the British Phonetic Council, Author of the “Principles of Speech and Elocution"_" The Elocutionary Manual "-" Steno-phonography,"—&c. REPRESENTED BY A SIMPLIFICATION OF THEIR ALPHABETIC FORM. by ܩܐ har*dly ...... 68. The subordinate words given in the preceding lesson once, after all, quite so, quite as, quite enough, quite alone, were uncontracted, except in size; written with all their quite another, except that, except as, except among, except elements, only without full-sized characters. The following indeed, except.only, except some, except this, except which, list contains such words as are represented by a simplification except such, little less, little (or) none, large enough, as large as, perhaps so, perhaps always, perhaps indeed, accordingly of their alphabetic form, as ft, for after ; r ring, for round; therefore, rather than, rather far, rather near, rather better, bh, for behind; dr, for under, &c. rather less, rather soon, rather that, rather large, rather much, 69. The letters printed in italics in the list are those used to hardly (so) much, such as, as such, as much as, as little as, denote the words. Illustrations of the different forms are given, altogether, together with, whichever, her own, by and bye, though, as they are all merely alphabetic, the student should thenceforward, thitherward, every one, very soon, very far, very little, very well. be able to supply them for himself from the descriptive print- II.-Write the following words, by adding the letters in ing; and he is recommended to write them from this,-cover- italics to the subordinate words, omitting the letters within ing down the marks,-as the readiest means of fixing them brackets :upon the memory. One thing), someth(ing), same thing), someth(ing) else, [As in the preceding lesson, an asterisk (*) after s, indicates anything), justly, larger*, largesť, largely, likew’is*e, underthe hook s; after r, the horizontal r; after m, n, or ng, a ring : far(the)r*, far(the)st, never(the)less, here(to)fore. n*eath, sometime), someti ime)s*, same t(ime), oftent(ime)s*, (') signifies write upwards ; and (), write backuards). 72. Contracted letters never having vowels before them in full alphabetic writing, the addition of a dot before any small 70. List of SUBORDINATE WORDS character, simple or compound, will furnish a distinctive symbol for any word to which it may be appropriated. This principle is employed to distinguish the past from the present form of the auxiliary verbs do, can, may, shall , and will. Thus. น did. could. b'eyond in or*der that may (m') is might. shal (shl) is should. is (D.) under* will (wl) would. 73. The same principle of distinction is applied to a few dur*ing* o:her words. Let the learner supply the symbols. Thus :A dot before l (all) is let. just [dzhust] f (off) is if. accordingly ń (he, him) is who, whom. (F.) after h 3* (his) is whose. before a ring (am, &c.,) is i.e. (id est, that is). nected] (K.) can [kan] is 9 (ago) e.g.or ex.gr. (Exempli gratia By way of example). quite [kwite] round d t (to, it) is rather th (they,thein) is though. except (eks *ept] น thr* (there, their) is through. Such [s*utsh] threl (thereat) is throughout. Ecross (akr*os] w (we) is away. is uhl (while) T'ogether a while. l'k (like) is alike. (L.) little et cetera (ts*(] r, ring (round) is around. already 74. Another similar and equally simple principle of distincwhich (whit'sh] tion is employed in the notation of the words at, thou (thee, large (lar* dzh] thy), thine, us, ye, and doun. These words are individualised, betw'ixt and preserved from confusion with to, they, then, so, &c., by the between addition of a little angular tick to the letters. Thus :Much [m* utsh] Thither immediately t ye y m*ean* while (W.) notwiths*t'and. down d Y j EXERCISES. THE VERB TO HAVE. 71. I.-Write the following compound words and phrases, by uniting the subordinate symbols. 75. A full-sized H is used to represent the verb Have. This character is perfectly distinctive, as it never occurs in ordinary Forasmuch, inasmuch, just so, just as, just about, just because, English notation. In the word 'ahoy the final vowel would be just like, just this, just thus, just that, just then, just one, just l indicated by a dot. VOL. II 51 مم۳ out. ...... کے ) wu 5 at us |