In the north of Europe there are only two peninsulas worthy of particular notice, namely, the Great Scandinavian Peninsula, which includes Sweden and Norway, and lies between the Baltic Sea and the North Atlantic Ocean; and the Peninsula of Jutland, which includes continental Denmark, and lies between the Kattegut and the North Sea. It is joined to the continent by the isthmus of Sleswig, which is about 25 miles wide. In the south of Europe there are three peninsulas of great importance in history, namely, the Iberian or Hispanian Peninsula, including Spain and Portugal, which lies between the Mediterranean and the Atlantic, and is separated from the rest of Europe by the chain of the Pyrenean Mountains stretching from the Bay of Biscay to the Gulf of Lyons; and Greece (anciently, the Peloponnesus, the Island of Pelops), sometimes called the Morea, which is joined to the mainland, called Hellas (anciently Achaia), by the isthmus of Corinth; this isthmus being only about four miles wide at the narrowest part. To these peninsulas may be added the Crimea, which is the most southern part of Russia, and is joined to the mainland by the isthmus of Perecop, which is only about five miles wide at the narrowest part. In the preceding Table of the Countries of Europe we have endeavoured to comprise a great deal of information in the smallest possible space. In the first column, the countries marked in capitals are independent and self-governed; those marked in small letters are dependent on the others with which they are connected. The states of Germany are connected by a Confederation, in which each has a certain number of votes, amounting in all to 70; the number of votes belonging to each state is attached to its name in a parenthesis. The latitudes and longitudes of the capitals of some of the smaller states are taken from a map, and therefore are not so strictly accurate as those of the larger countries, which have been astronomically determined. The names of the rulers of each country or state is taken from a table inserted in the "Working Man's Friend," vol. II., No. 38, p. 179, col. 2. The form of government has been ascertained with the greatest care from various documents. Where the monarchy or sovereignty is not marked as absolute or limited, it is generally of a doubtful or an undetermined character; but in small states this is of little importance to the general tranquillity of Europe. H D B C Join the points A and B (Postulate 1, Book I.), and upon the straight line AB describe an equilateral triangle ADP (Proposition 1, Book I.) With the point в as a centre, and the straight line в c as radius, describe the circle C G H (Postulate 3, Book I.) Produce the straight line DB till it meets the circumference of the circle CGH in the point G (Postulate 2, Book I.) With the point D as a centre, and the straight line D G as radius, describe the circle G K L. Produce the straight line DA till it meets the circumference of the circle G K L in the point L. Then the straight line A L is equal to the given straight line B C. For, by Definition 15, Book I., the straight line Bc is equal to the straight line B G, and the straight line D L to the straight line But, by the construction and Definition 24, the straight line DA is equal to the straight line D B. Therefore, by Axiom 3, Book I., the straight line A L is equal to the straight line B G. Whence, the straight lines AL and BC are each equal to the straight line BG; and, by Axiom 1, Book I., the straight line AL is therefore equal to the straight line BC; and it is drawn from the point A as required. D G. The construction of this problem is here different from that of Euclid; and it is better than his. The student will at once see that the portions GP and LE of the straight lines D F and D E, as drawn in Euclid's construction, are superfluous, and that by this construction the straight line a L is drawn at once of the exact and proper length required. In some remarks which we made upon Dr. Thomson's edition of Euclid when it first appeared,―remarks which we made at his own request,-we pointed out to him this construction as preferable to Euclid's. He admitted the fact, but in his subsequent editions made no alteration. Perhaps as we ourselves have done in Cassell's edition--he retained the old construction, lest he should be charged with too much innovation. "I have taken care," said Dr. Thomson, in the first edition of his Euclid, "not to touch with too rude a hand a work which has stood for so many centuries." There is a species of conservatism followed even in mathematics! We shall rejoice, however, in giving our students the benefit of every new improvement that has been made in this science. The practical student,-the mechanic and the engineer, will, on perusing the above demonstration and remarks, very probably say to themselves: "What is the use of all this unnecessary parade of learning about such a simple matter as drawing one straight line of exactly the same length as another? Why not take a pair of compasses or dividers such as those described in the Lessons on Drawing, (6g. 57, page 250, col. 1,) and at once transfer the distance from в to c by their means, to any other place of the paper or plane that you wish, say from A to L; then draw a straight line joining the points A and L, and the thing is done?" Why not, indeed! For all practical purposes, this method is quite sufficient; to go through all the steps of Euclid's construction is wholly unnecessary for mechanical operations. What, then, it may be asked, is the use of Euclid's method? We answer, that it is useful as a training of the mind to accurate thought, conception, and reasoning; useful to the acquisition of a link in the great chain of geometrical demonstration; and useful to the certainty of the geometrical process of argumentation, in which nothing is to be taken for granted which is not laid down in postulates, and agreed upon between the student and the professor before they enter upon the earnest study of this exact science. Without Euclid's method, it would be necessary to demand as a postulate that “ a distance or length of a straight line can be transferred from one place to another, or from one part of a plane to another part of it;" and, in this case, reference to the first proposition of this book would be rendered unnecessary in the second proposition, which would then virtually become the first, and Euclid's order would be destroyed. Even in the construction of the first proposition, the complete circles ACE and BCD, fig. 1, are not necessary; all that is wanted being a single point of intersection, which may be obtained from two small arcs or portions of these circles drawn nearly over the middle of the straight line A B. The exercise appended to this proposition is, "Draw the figures and show the application of the construction and demonstration to different positions of the points and the straight line; such as when the given point is situated above the straight line or below the straight line; also, when in the straight line of itself, at the extremities, or at any point between them." In order to perform this exercise, the student has only to assume the point A a little above the middle of в C, fig. 2, or a little below the middle of B C, and I make precisely the same construction, using the same letters in every way; by so doing, he will find that as the equilateral triangle ABD may be constructed on opposite sides of AB, he will thus have the power to draw the straight line A L in four different directions. Again, he may assume the point a in the straight line itself; if in or near the middle of B C, then A B will be part of B C, and the joining of AB will be unnecessary; but, by following precisely the same construction, and using the same letters, he will obtain two different directions for the straight line A L, according as he constructs the equilateral triangle A B D on one side or other of AB. Next, if he assumes the point B for the point A, the equilateral triangle ABD, and the second circle G KL, become both unnecessary, for the circle GCH will be sufficient for the purpose of drawing AL, any radius of this circle being the line required. If the point c, the other extremity of BC, be employed as the point to which the given point A is to be joined, then there will be just double the number of the preceding varieties in the construction. The expense of cutting the figures prevents us from exhibiting all these varieties of construction to the eye of the student; but with the preceding hints he will now be fully able to draw them for himself. Llanefydd; A. Coats, Glasgow-have sent us accurate drawings and expla Several of our students-among whom may be mentioned J. C. Jones, nations of these different diagrams. The first proposition of this book may be varied in its enunciation so as to exercise the ingenuity of the learner; thus, it may be put under either of the following forms :-"To find a point at the same distance from two given points, that these points are from each other;" or, "to find three points equally distant from each other." From the consideration of the latter form, there might arise in the mind the problem to find four points equally distant from each other; a solution of this problem is given in vol. I., at p. 79, col. 2, art. 6. If the inquiring and ingenious student wishes to find more than four points equally distant from each other, he will find that the problem is impossible, and he will be clever if he can assign a satisfactory reason. The second proposition above discussed might be put in the following form:-"To find the locus of all the points which are at the same distance from a given point, that two other given points are from each other." By locus here is meant the place or line, straight or curved, in which if any point be taken, it will be found to be at the required distance from the given point. In the preceding figure, if a circle were described from the point A as a centre with the straight line A L as radius, this circle would be the locus required. PROPOSITION III. PROBLEM. From the greater of two given straight lines to cut off a part equal to the less. From Fig. 3. D C In fig. 3, let A B and c be the two given straight lines of which A B is the greater, and from which a part is to be cut off equal to o the less. the point a draw a straight line A D equal to c by the preceding proposition, and from the same point as a centre, with a D as radius, describe the circle DEF (Post. 3), cutting A B in the point E. Then the part AE, of the straight line A B, is equal to C. E B For, by Definition 15, the straight line AE is equal to the straight line A D, and by construction, the straight line c is equal to the same straight line. Therefore, by Axiom 1, the straight line A E is equal to the straight line c, and it is cut off the straight line A B as required. Page 338, col. 1, vol. I.-ENGLISH-LATIN. Sitierunt; esuriam; praeceptis meis non obedies; pueri garriunt; pari non obedierunt; nescio cur patri non obesiverint; nemo dubitat quin boni pueri patri obediant; verba mea memo iâ custodivit; curae mihi erit ut verba mea memoria custodias; veniunt urbem munitum; ars scribendi utilis est; domus suae parietes coronis ornant; non prius dormiam quam negotia finivero; negotia finivistine? puerum puniebat, quum scholam intrabam. Page 388, col. 2, vol. I.-LATIN-ENGLISH. The father takes care that (u) his son is well instructed; the father took care that (ut) his son was well instructed; the citizens fear that the camp is fortified by the enemies before the city; the eyes have been clothed with very thin membranes; when the king was entering the city, the houses of all the citizens were clothed and adorned with chaplets and flowers; we shall not sleep until (before that) your business is (shall have been) finished; as soon as the camp is (shall have been) fortified, the soldiers will prepare for the fight; we feared that the city had been blockaded by the enemies; let the wicked be punished; a good scholar strives to be instructed in the knowledge of letters; the city, having been blockaded, is punished by many evils; a cultivated man not only benefits himself but others also; boys must be diligently instructed. Page 388, col. 2, vol. 1.-ENGLISH-LATIN. Custodiuntur; urbs custoditur; urbs custodietur; urbs custodita est; curo ut urbs custodiatur; nemo dubitat quin urbs bene custodiatur; cives urbem custodire debent; cur cives non urbem custodiunt? nescio cur cives non urbem custodiant; metuo ut cives urbam custodiant; ad pugnam se expedierunt; domûs parietes foribus vestiti sunt. Page 410, col. 1, vol. I.-LATIN-ENGLISH. My friends cannot be received in one house; tell us, by what consolation the troubled mind of the friend has been soothed? the narrow limits of your breast cannot contain so great a character, t ken by me); you must teach; teaching boys, you will be much nor will the world contain thee; I must take food (food must be loved; say, why the boy has been punished? the war came to an end; see that the state receives no injury (not anything of injury); tell me, what has been written to you by your sister? no vice is In the construction of this problem, the student should go more vile than avarice, especially in rulers who manage (managing) through the process required by the preceding proposition in order the state; thinking of heavenly things, we despise these our own as to obtain the straight line a D. He would then see that the whole insignificant; the class of men who reproach (reproaching) kind construction actually required is considerably more complex than actions is hateful; a draught of cold water is hurtful to one sweatit appears to be in fig. 3; and unless he does this, he will not have ing from the effect of labour; a good man assists a good man a clear geometrical idea of this proposition. The practical geo-1nds, are assembled in one spot; a great multitude of men are without his entreating it; storks, about to migrate into foreign meter, in solving this problem, would do here as in the preceding collected in the city, for the purpose of seeing the public games; proposition, take the distance or length of c in his dividers, fix it all griefs (which are) borne patiently are less bitter; the general with the screw, and then lay it off upon A B at once, when the point dismisses the soldiers, after praising them (having been praised) E would be obtained, and the part A E as required; but, as we on account of their distinguished valour; many youths, havobserved above, this would be a mechanical solution, not a geo-ing been badly educated in their early boyhood by their parents, metrical one. The solution of the exercise appended to this proposition will be given in our next lesson. rush to destruction; in the reign of Xerxes (Xerxes reigning), the Greeks obtained a most splendid victory over the Persians; there is friendship between good men and God, nature uniting them; when winter approaches (winter approaching), many birds seek milder A KEY TO THE EXERCISES IN THE regions; peace being recovered, the arts flourish; when kings LATIN LESSONS. (Continued from page 239, Vol. II.) By JOHN R. BEARD, D.D. Page 388, col. 1, vol. I.-LATIN-ENGLISH. The soldiers hungered and thirsted duting the whole day; Nature has clothed the eyes with very thin membranes; why have you adorned and clothed the walls of your house with chaplets? yu had pleased your teachers, because you had always obeyed their commands; scarcely had our soldiers fortified the camp, when Caesar formed a line of battle; we shall not sleep until (before that) we have finished our business; when the soldiers have fortified the camp, they will prepare for the fight; take care, boys, that you do not chatter; the laws of the Spartans have this object, to instruct that they may instruct) the youth in labours; no one doubted that you had always taken care of the boys; tell me, by what consolation you have soothed the troubled mind of your friend? I know not why you have punished the boy; I did not doubt that you had kept my precepts in memory; do not chatter, daughters; I come to ask you, to walk (that you may walk) with me; the soldiers ought to guard the city; wisdom is the art of seeing; we must obey the precepts of virtue; the art of sailing is most useful. were banished (kings being banished), the Romans laid the foundation of a free state; though the country is changed (the country being changed), the characters of men are not changed; since the laws of God have been religiously observed (the laws of God having been religiously observed), our life will be happy. Page 410, col. 1, vol. I.-ENGLISH-LATIN. Veri amici angu tâ domo capi possunt; non capiunt angustiae hujus domûs tautam personam; dic mihi quid pater tibi dixerit; fer matri aquam; avaritia in parentibus domos gerentibus magnum vitium est; avaritiâ deletâ, vitium deletum est; cogitans patriam, miles periit; timenti amicus magnae consolationi est; republicà turbatâ, quis beatus esse potest? ingens hominum multitudo venerunt, potitura vinum; milites laudati, dimissi sunt; Regnante Victoria, Educator Popularis institutus est; libro mutato, non sententias mutas. (End of the Key to Vol. I.) Page 9, ccl. 2, vol II.-LATIN-ENGLISH. Who does not admire the splendour and beauty (for puilchri tudinemque read pulchritudinemque) of virtue? the general encouraged the soldiers to attempt to throw into confusion the enemies' line; already the enemies attempted to attack the city, when suddenly they were driven back by the citizens; when you have despised pleasure, then, at length, you will be happy; survey the noble examples of virtue which have been recorded in history; I come to accompany you into the garden; dreams are difficult to be explained; Socrates accounted himself an inhabitant and a citizen of the whole world; learn willingly (being willing); what is sweeter than to learn many things? riches accompany a learner, honours accompany (a learner); the wicked man will at length remember his vices with grief. Page 9, col. 2, vol. II.-ENGLISH-LATIN. Mulierum pulchritudinem admiratus sum; hominem hortati sunt; rex milites hortabitur ut hostes propulsent; improbum pater filium arbitrabatur; quis signa interpretetur? tum demum Dei signa interpretaberis, quum sapiens et bonus eris; virtutis exempla facilia sunt interpretatu; ille me in horto comitabatur, quum tu venisti; eo patrem comitatum; pater me in provinciam comitatum venit; honores bonos et sapientes comitabuntur; pueri, discite libentes, et admiratione afficiemini. Fage 11, col. 1, vol. II.-LATIN-ENGLISH. Sabinus having encouraged his (troops), gives the signal; your benefits exhort me to obey your command; Caesar exhorted his soldiers to (strive after) glory; they encouraged them to become friends (towards joining friendship); I exhort you again and again Concerning the same things on which I have exhorted you in a former letter; we will not cease to advise Pompey (for Pomperium read Pompeium) to shun great dishonour; he exhorts them not to fail in courage; I, then (for tune read tunc) fearful, advised shameful flight; I, indeed, cease not to recommend peace. Page 11, col. 1, vol. II.-ENGLISH-LATIN. Magister ad diligentiam discipulos hortari non desinit; magister discipulos ad diligentiam hortabatur; magister discipulos ad diligentiam hortatus, omnibus oscula dedit; sapientia tua me hortatur ut imperio tuo paream; hortabitur eos in amicitiam jungendam ; pater tuus te iisdem de rebus hortatur, quibus ego fratrem meum hortabor; hortor te ne animo deficias; sororem tuam hortati sunt, ne animo deficiat; pudendam fugam hortabor nunquam; bellum hortari non desinit. Page 23, col. 1, vol. II.-LATIN-ENGLISH. You had scarcely confessed your fault, when your father pitied you; you had already admitted that you had erred, when you denied it again; we had not yet entreated your assistance, when you promised it to us; we had scarcely confessed our want, when you most freely promised us your assistance (praesidium); there is great power in philosophy when it heals our minds, and removes vain anxieties; the arts afford us great assistance when they seve rally support themselves independently; teachers serve (merentur) their country well (deserve well of their country), when they instruct the youth (juventutem) by the study of useful letters; when philosophy heals our minds, we ought to give up ourselves wholly and thoroughly to it (for medeturei read medetur ei, and strike out the comma before tradere); all pitied you, since you were in wretched (circumstances), not in consequence of wickedness, but on account of fortune; since the soldiers feared dangers, they dared not to fight with the enemies; the covetous (man), though he is extremely rich, will not admit that he has enough; take pity on us; O citizens, relieve our want; let each defend his son; no one, beholding the whole earth, will doubt concerning the providence of God; the citizens, thinking that the enemies were about to attack the city, strove most energetically to drive them back; I come to promise (about to promise) you my assistance; it is the duty of a young man to reverence his elders; you ought in every way to relieve the want of the citizens; who knows not that you have served the republic well? (that you have deserved well of the republic); I hope that you will pity me. Page 23, col. 1, vol. II.-ENGLISH-LATIN. Peccata sua fassi sunt; peccata sua fatebuntur; fassine erunt peccata? peccata sua non fatebitur; soror mea peccata fassa est; adolescentes negant se peccata fassuros esse; religio hominum animis medetur; solum religio vera hominum animis mederi potest; religio semper bonorum animos sanavit O mi pater, miserere mei; O Deus, miserere nostri; O Deus, hominum cunctorum miserere; conjux quisque tuetor uxorem suam; adolescentes, milites domos suas oppugnaturos rati, prae metu se interfecerunt; artes ipsae singulae artifices tuentur; tuenturne artes ipsae se? artes artifices tuitae sunt, et tuentur, et tuebuntur; intuere coelum, et Deum vereberis; virtutem intuentes, homines fiunt sapientes; praeclare de republica meritus est; regina praeclare de republicâ merebitur; milites praeclare de patria meriti sunt; praeclare de domo mereri non possum; intuetur virtutis exemplar; fatetur peccata, et veniam impetrat; confessi peccata veniam impetravēre; quum peccata confessi sitis, veniam impetrabitis. Page 23, col. 2, vol. II.-LATIN-ENLISH, selves wish to be feared; we venerate you, Romans, and if you so Why do we not fear the veterans? because not even they themdesire, we even fear you; let her not be afraid to enter into the house of another; I fear that I am walking out with this ornament for the sake of (exciting) love rather (than for anything else); I shall not cease to be apprehensive about Carthage, until I have ascertained that it is demolished; I fear that Dolabella will not be able to benefit us sufficiently; I received your letter, by which I understood that you were afraid, lest the former (letter) had not been delivered to me; he was afraid, lest he should hurt the mind of Divitiacus by the punishment of that man; I fear if I begin to explain this thing, I shall seem not to be narrating a life, but to be writing a history; I do not fear that I shall satisfy you by writing; I do not fear you will do anything timidly, anything foolishly; I do not fear that the moderation of my life will prevail too little against false rumours. Page 23, col. 2, vol. II.-ENGLISH-LATIN. Verentur parentes, regem timent; tyranni timentur; tyrannos timebunt; parentes meos verebor; non vereor ne verbis te expleam; timetis in hostium castra introire; vereor ne frustra legam; de patriâ metuunt ne excidatur; timeo ne mater veniat; quid times ne mater veniat? quia contra praecepta sua ago; metuunt ne patruus mortuus sit; metuo ne Dei ira in hanc urbem incidat; vita tua contra calumniam valebit; ne verearis ne vita tua contra malorum calumniam non valeat; vereris ut tibi prodessc possim; ne verearis nequid stulte faciam; frater meus non veretur nequid stulte faciam. SOLID TREASURES. Seek wisdom's treasures in her fields, Those hidden treasures which she yields Those treasures raise the meanest soul, Around the checquer'd scenes of life, They chase the dreary gloom of strife, With nobleness of mind, despise The little he already knows See how the great and good have gain'd A height, like theirs, may be obtained Now, let the toils of others prove For cowards fail, they will not move, Come then, this pow'rful aegis take, And gain those trophies which will make W. F. (amended.) ANSWERS TO CORRESPONDENTS. J. P. (Hackney): By the ratio of Metius given in our Lessons on Geometry, No. XI., the diameter of a circle is to the circumference as 113 to 355; and by the rule of Archimedes given in Lesson No. XII., the area of a circle is equal to half the diameter multiplied by half the circumference; therefore 113X355 113 SHORT-HAND.-J. G-K: All right but "potato," character," and "improbability." J. G. seems to have overlooked the repeater in the first and last of these. In the second, the t is short, and the word cannot therefore be "caricature." You must write letters with no preceding vowel much smaller. Your kinkelso" is longer than the 1, see the rule given in a note in the fourth lesson.-A YOUNG LEARNER: "G soft" requires no separate alphabetic character. It is a combination of d and sh. Ch," in 355 represents the area of a circle whose diameter is 113; and chair, is the breath correspondent of "G soft,"-a combination of t and sh. See the words" page, knowledge, chapter, and handkerchief," illustrated in 113 2×2 the second lesson. The characters may be written either upwards or down-113X113X452 represents the square of the diameter. wards according to the taste and convenience of the writer. The learner is fettered with no rule in this particular. The recapitulative table in the fourth lesson will serve to explain and simplify the list of prefixes. Whence, as X 355: 113 355 355 355 4 355 the circle; therefore -X113: X1420, or 355: 1420:: the area of a circle: the square of its circumference. See Walkinghame on the square root. AMICUS POPULI (Richmond): For information on Electricity and Galvanism, we recommend "Peschell's Physics," vol. III.-JEUNE ANGLAIS (Swansea): Thanks.-I. T. G. (Leeds) should revise his former studies first; he may go on with Music as a recreation.-YOUNG SAILOR (Manchester): "Norie's Navigation" (price 16s.) is the best.-G. D. (Tilly) is quite right on the proportion given in Hutton's Mathematics, viz., As any one side is to square of the circumference; and -X113 represents the area of the sine of its opposite angle, so is any other side to the sine of its opposite angle:" this proportion is heterogeneous, and therefore erroneous, see Cassell's Euclid, Book V., Definition V., p. 98. It should be stated as he has said, viz., "Any one side is to any other side, as the sine of the angle opposite the former side is to the sine of the angle opposite the latter side."-ULTRA PERGERE (Belfast): We dissuade him from the learned professions as he calls them; but we advise him to acquire learning by all means. The course pointed out in the Regulations of the University of London, is among the best for him.-M. B. SMITH (Shelf): Dr. Beard's Lessons in English are superior to all the grammars he has mentioned.-G. WILKINSON (Earby): His letter has been overlooked.-SUBSCRIBER (Whitby) should study the P. E. The second course of the French Lessons is begun.-A. W. CLITHERO: We can't tell.-S. J. R. (Strand): A perpendicular means a straight line at right angles to another in any position; a perpendicular to the horizon means a straight line at right angles to a horizontal straight line.-J. HOARE (Bridport) informs us that Mr. Budgett's salary during the three years mentioned in the Biography, was £40, £50, and £60, and that he saved out of the whole £100, not £300. sixpenny series of Lessons in French before he takes up the lessons in the Communications have been received from E. J. BREMNER (Carlisle); D. C. (Glasgow); J. LOVETT (Ashfordby); C. T. JONES (Bushy Heath); J. HAYWOOD (Edgware-road).-HUM BRAZILEIRO: As soon as we can.-W. S. (Sydney-street (wishes to know a good, plain, and inexpensive book on costume, armour, &c., English in particular.-T. and E. DENNISS (Edwinstowe): The last edition of Keith on the Globes (Longmans and Co.) is the best, and is greatly improved.-W. N. B. should pursue his own plan; it is very good. PATHWAY should first study English, Penmanship, and Arithmetic in regular order. A FRENCH SCHOLAR (Perthshire): We cannot, on principle, give opinions to scholars, which might prove unfavourable or injurious to their teachers ; we believe that in the latter position, every man does his best; and for the members of the scholastic profession we have the deepest sympathy.-E. O. (Fleetstreet): In time.-R. M. W.: Thanks for his correction.-G. GORDON (Edinburgh): We are glad that a Co-Instruction Society has been formed at Buchanan's Coffee-house, High-street, to meet on Tuesdays, at half-past 8 P.M.; and that it is to begin with the "Lessons in French;" we hope the members will increase so as to render the study valuable and interesting to many. -F. SCRIVEN (Leominster): Yes, the "French Manual" contains Reading Lessons.-PUNCTILIO (Buckland): 1. No; 2. Yes; 3. No.-J. C. L. (Montrose): According to the Greek Scriptures, called the Septuagint, the flood of Noah took place 2,262 years after the creation of Adam, and the advent of the Saviour 3,216 after the flood; hence, the latter event took place 5,478 years after the creation, see vol. I., p. 96, col. 1, line 6 from the bottom. Flox is a Greek word signifying a flame; flos is the Latin word signifying a flower.-G. S. S.: We thank him for the sketch of the Corinthian order; we have examined, and find we are right.-M. THIMHISON (Otley): See the second answer above this. W. E. WILLIAMS (Merthyr Tydvil), and J. DONALD (Aberdeen); F. BUXTON (Salford): Their solutions are partly right and partly wrong; we strongly recommend them to study Cassell's Euclid, as well as his Arithmetic.-THOMAS (Malton): Withering's Botany, by Macgillivray, is a work which contains-in a Dictionary form-the names of plants, their descriptions, and the places where they may be found.-F. ROBINSON (London): The use of therefor instead of therefore is simply pedantic and unusual, and therefore erroneous; for common usage is the rule that establishes the right spelling of a language. If the proper meaning of the word were to be the guide to its spelling, it should be written thisfor, as the word therefore simply means for this. W. M'INTYRE and POOR SCHOLAR (Glasgow): For the pronunciation of the French words, see Cassell's Lessons in French" republished from the "Working Man's Friend;" price 6d., or 7d. by post.-J. NICOL (Glasgow), Instructions in Mapping will be given. The Latin arrangement will be explained.-E. CROSSLEY (Littleborough): Study the Lessons in Drawing in the P. E. as they appear.-W. HYMERS (Barnard Castle): To "accede to London;" to "acquit themselves of a bad habit;" and to "be adequate to the rich;" are expressions which cannot be tolerated in English composition.-E. J. (Reading) will, by studying the Second Part of the Lessons in French, attain her wisher-JOHN MARTIN (Stroud): See vol. I. of the P. E., page 407, col. 2.-J. A. O. (South Molton); A SHOP BOY (Isley): Their penmanship is not near enough to our Court-hand.-A. W. HAMILTON (Hull): We do not know.-J. B (Hulme): The term compter is from the French verb compter, to reckon; it means a place where a person is put in order to be reckoned with, or taken to account (accompt).-C. W. F. (London): His attempt at poetry is pretty fair; but it wants more amendments than we have time to make upon it.-J. LEE (Westminster); We can't say yet.-E. C. COOKE (Holloway): Ilis suggestion is good. JOHN WILKIE (Fulham): "To find two numbers whose sum is half their product;" let x+y=a, and xy=2a, then solving this by quadratics, or otherwise, you have ■=} {a+√ (a2—8a)} and y=} {a−√ (a2—8a)}; in which, by substituting any possible number for a, you may obtain the numbers required. ERRATA. 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THE ILLUSTRATED EXHIBITOR AND MAGAZINE OF ART-The First Part of a new and improved Series of this work, under the title of the ILLUSTRATED MAGAZINE OF ART, is now ready, price One Shilling. Each Weekly Number is now enclosed in a neat wrapper, price 3d. In addition to numerous Engravings in the text, each number contains a fine Engraving, worked on Plate Paper. With this Part is presented a splendid View of the Interior of St. Paul's Cathedral, during the Interment of the late Duke of Wellington, printed upon fine Plate Paper, measuring eighteen inches by thirteen. in addition to four separate Engravings, and a large number of choice Illustrations. Printed and Published by JOHN CASSELL, 9. La Belle Sauvage-yard, LESSONS IN PHONETIC SHORT-HAND.--No. V. By ALEX, MELVILLE BELL, F.R.S.S.A., Professor of Eloction and Vocal Physiology, Member of the British Phonetic Council, Author of the "Principles of Speech and Elocution""The Elocutionary Manual "—" Steno-phonography,"-&c. 49. WITH this lesson we introduce a new principle of abbreviation, applying to all the subordinate classes of words-articles, pronouns, prepositions, secondary adverbs, conjunctions, and auxiliary verbs. These words are written without full-sized characters. This has the effect of giving them a distinctive appearance to the eye, while, by the force of contrast, it throws into emphatic prominence the leading words of a sentence, which retain a full notation, in accordance with the principles detailed in the preceding lessons. 50. The principal words in sentences are nouns and verbs; and the next in importance are the words that qualify nouns and verbs-namely adjectives and adverbs. The last of these classes includes two different species of words--adverbs that qualify verbs, and those that qualify adjectives or adverbs. Of these, the former is, of course, the primary species: the latter we call secondary adverbs. is, that all the minor marks of punctuation may be omitted, without danger of ambiguity in deciphering. The grouping is itself a valuable species of punctuation; indeed, for the commas, semicolons, &c. With this principle of notation, it purposes of effective reading, far more valuable than that by is simply necessary in writing to indicate the greater divisions of composition, such as are generally marked by periods and paragraphs. For this purpose, a line of three or more dots, best sign for catching the eye, and for simplicity of execution. ranged "horizontally,' or a short zig-zag line, will be the No other mark of punctuation can be at all necessary; but, it may be well to add, that there is nothing in the system to prevent the writer, who chooses to do so, from inserting all the ordinary signs. In this case, to secure against ambiguity, the comma and full stop would require to be either well "spaced off" from the writing on either side, or encircled by a small ring. The other marks would need no alteration. 51. The subordinate words are-besides being contracted-acquainted with the grammatical classifications of words, and WRITTEN CONSTRUCTIVELY; that is, above or below the leading words to which they refer, and with which they are accentually connected in ordinary utterance; so that, both by size and position, their comparative inferiority is plainly indicated. 52. This plan of grouping the subordinate with the principal words gives a highly rhetorical effect to the writing, similar to that which is produced in printing by the use of italic and CAPITAL letters. It is at once a source of great brevity in writing, and of perspicuity and effectiveness in reading. It also reduces the possibilities of ambiguity between words of the same "articulate skeleton"-by confining the reader's choice to principal words only; and thus enables him with the most perfect confidence to leave out vowels in ordinary notation-indeed rendering their insertion, in the vast majority of cases, altogether superfluous. 53. The following passage exemplifies, in type, the effect of the grammatical grouping, in distinguishing between principal and subordinate words. The syllables enclosed in brackets are contracted Prefixes and Affixes. as this 55. In the ready and accurate application of the grouping principle, those learners will have an advantage who are best of these subjects will not prevent any person from writing the rules for the construction of sentences; but entire ignorance constructively, though he may not perhaps group with perfect accuracy. To the ungrammatical reader it may be enough to say that all the little words of common occurrence, and those which in pronunciation he passes lightly over, are to be reduced in writing to as small a size as possible, and placed after-the more important words with which they are conabove or below-as they happen to be pronounced before or nected in utterance. That is, the little and generally unemphatic words which, in a greater or less degree, enter into the composition of every sentence, are not to occupy space separately in the line of writing, but to be clustered about the leading and emphatic words, which constitute the new and essential parts of the sentence. 56. No group should contain two leading words; each will contain one, except when a very large collection of subordinate words coming together may render it inconvenient to add the principal word, which will then stand by itself. 57. It is of great importance to attach a definite outline to all the subordinate words, by invariably writing each in its may to the own appropriate mode, that the possibility of confusion between philosoph[ical] lead general words containing the same letters may be entirely obviated. Such words as am, me, my, may; either, other, there, through; this, thus; these, those; ever, over, very, every, &c., will thus be distinguished by a different arrangement of the letters that schools. study make up their " articulate skeleton." All compound and derivative words, too, preserve the outline of the simple words from which they are formed, with alphabetic additions for the new syllables. of the art of stenography to attractive nature young persons. that would never become in The Occas[ional] exercises, the for of expenditure time, a practical facility the we in 58. In arranging Abbreviations for the subordinate words, "labour delight physics the ALPHABET has been almost uniformly adhered to; so that the learner who is well acquainted with the First Lesson will experience very little difficulty in making himself master of all the contractions. There are, for instance, not more than FIVE marks that can be considered as arbitrary, employed in representing the whole category of subordinate words. The words denoted by them are an, the, and; more and derivatives, no-not. in the of such an tages to every secure schoolboy before he is to called enter The or the at such a would be 59. No distinction in writing is necessary between the intellectual advan- nominative and objective forms of pronouns, as he, him, &c.; the different persons or numbers of auxiliary verbs, as am, art, is, are; may, may'st, &c.; or the infinitive and the past participle of such verbs, as do, done; be, been, &c. The governing words in the context leave no room for ambiguity in such art possessed 54. Another advantage gained by the principle of GROUPING VOL. II. cases. 47 |