εκινδύνευσε τον εσχατον κινδύνον. Τας των φαύλων συνηθειας | dust your empire but a grave your martial pomp a black ολιγος χρονος διελυσεν. Πριν αν αμφοιν μύθον ακουσης, μη funereal pall - your palace trampled by your meanest slave. To-day is thine - improve to-day, nor trust to-morrow's δικάζε. Οἱ Λακεδαιμονιοι Πλαταιας κατελῦσαν. Τίς αν distant ray. πιστευσαι (πιστεύσεις) ψευστη; Ακουσαις (ακουσειας) μου, ω For some time the struggle was most amusing φιλε. Ο άγγελος επηγγελλεν, οτι οἱ πολέμιοι τη στρατια pulling, and the bird screaming with all its might επιβουλευσαιεν (επιβουλευσειαν). Ακουσον μου, ω φιλε. Εταιρος | attempting to fly, and the other to swim from its invisible the gander at one moment losing and the next Την πολιν λεγουσι μεγαν κινδύνον enemy regaining his centre of gravity. ἑταιρῳ πιστευσάτω, κινδυνεύσαι. ENGLISH-GREEK. The general will free the city from the enemy (plural); good men plant for their offspring also; good men will plant for their children (ac); the messengers report many things; the enemy plot against the king; the enemy will plot against me; I announce inany things to the citizens; Achilles is angry with Agamemnon; Achilles will be angry with Agamemnon; thou art angry with thy brother; I was angry (first Aorist) with the enemy; I will entreat my judges; Socrates will not entreat his judges; the good citizens will not entreat their judges; the enemy are destroying Platea; the soldiers will destroy Platea; the soldiers destroyed the city; hear (Aorist) me, O my offspring (plural). One friend believes another (eraipos traipy); one friend will believe another; one friend did believe another; they believed; they did believe; they believe; they will believe; thou wilt believe; they two believed; we shall believe; we believe; thou wilt believe; the soldier prevails much by his strength; I prevailed much by my strength. the fish - the one 54. The dash is sometimes to be read as a period, with the falling inflection of the voice. The favoured child of nature, who combines in herself these united perfections, may justly be considered as the masterpiece of creation as the most perfect image of the Divinity here below. Now launch the boat upon the wave- - the wind is blowing off the shore - I will not live a cowering slave, in these polluted islands more. The wind is blowing off the shore, and out to sea the streamers fly-my music is the dashing roar, my canopy the stainless sky — it bends above, so fair a blue, that heaven seems opening to my view. He had stopped soon after beginning the tale - he had laid the fragment away among his papers, and had never looked at it again. The exaltation of his soul left him he sunk down- and his misery went over him like a flood. - Mr. Playfair was too indulgent, in truth, and favourable to his friends and made a kind of liberal allowance for the faults of all mankind except only faults of baseness or of cruelty; against which he never failed to manifest the most open scorn LESSONS IN READING AND ELOCUTION.-No. V. and detestation. (Continued from page 371, Vol. IV.) THE DASH. 48. The Dash is a short straight line which occurs in reading, and which is placed between the sentences in such a manner as to be parallel to the top or the bottom of the page. 49. The dash is sometimes used to express a sudden stop, or change in the subject. 50. The dash requires a pause sometimes as short as that of a comma, and sometimes one as long as, if not longer than, that of a period. 51. The dash is frequently used instead of crotchets or brackets, and a parenthesis is thus placed between two dashes. 52. The dash is sometimes used to precede something unexpected; as when a sentence beginning seriously ends humorously. 53. In the following examples, the dash is used to express a sudden stop, or change of the subject. Examples. If you will give me your attention, I will show you-but top, I do not know that you wish to see. Alas! that folly and falsehood should be so hard to grapple with-but he that hopes to make mankind the wiser for his labours, must not be soon tired. Please your honours, quoth Trim, the inquisition is the vilest. Prithee, spare thy description, Trim; I hate the very name of it, said my father. The fierce wolf prowls around thee-there he stands listening -not fearful, for he nothing fears. The wild stag hears the falling waters' sound, and tremblingly - o'er his back he bends his stately horns noiseless ground his hurried feet impress not and his track is lost amidst the tumult of the breeze, and the leaves falling from the rustling trees. The wild horse thee approaches in his turn. His mane stands he snorts up erect his nostrils burn he pricks his ears and starts aside. There was silence not a word was said their meal was before them God had been thanked, and they began to eat. -- for their eyes are They hear not - see not know not covered with thick mists they will not see. And ye like fading autumn leaves will fall; your throne but Towards women he had the most chivalrous feelings of regard and attention, and was, beyond almost all men, acceptable and agreeable in their society. though without the least levity or pretension unbecoming his age or condition. 55. The dash is sometimes to be read like a comma, with the voice suspended. I have always felt that I could meet death with composure; but I did not know, she said, with a tremulous voice, her lips quivering I did not know how hard a thing it would be to leave my children, till now that the hour is come. And Babylon shall become she that was the beauty of kingdoms, the glory of the pride of the Chaldeans as the overthrow of Sodom and Gomorrah by the hand of God. Our land the first garden of liberty's tree- - it has been, and shall yet be, the land of the free. Day after day prepares the funeral shroud; the world is gray with age: the striking hour is but an echo of death's summons loud the jarring of the dark grave's prison door. devouring all kings and the friends of Into its deep abyss kings alike must fall. She made an effort to put on something like mourning for her son; and nothing could be more touching than this struggle between pious affection and utter poverty: a black ribbon or humble attempts to express by outward signs that grief that so a faded black handkerchief, and one or two more such passeth show. God, whom you see me daily worship, whom I daily call upon to bless both you and me and all mankind; whose wondrous acts are recorded in those Scriptures which you constantly read, God, who created the heavens and the earth; who appointed his Son Jesus Christ to redeem mankind: - God, who has done all these great things, who has created so many millions of men, with whom the spirits of the good will live and be happy for ever; this great God, the Creator of worlds, of angels, and of men, is your Father and Friend. It is not, therefore, the use of the innocent amusements of life which is dangerous, but the abuse of them; — it is not when they are occasionally, but when they are constantly pursued; when the love of amusement degenerates into a passion; and when, from being an occasional indulgence, it becomes an habitual desire. In every pursuit, whatever gives strength and energy to the mind of man, experience teaches to be favourable to the interests of piety, of knowledge, and of virtue; in every pursuit, on the contrary, whatever enfeebles or limits the powers of the mind, the same experience ever shows to be hostile to the best interests of human nature. From the first hour of existence to the last, from the cradle of the infant, beside which the mother watches with unslumbering eye, to the grave of the aged, where the son pours his bitterest tears upon the bier of his father, in all that intermediate time, every day calls for exertion and activity, and moral honours can only be won by the steadfast magnanimity of pious duty. They say they have bought it. Bought it! Yes; - of whom?-Of the poor trembling natives, who knew that refusal would be vain; and who strove to make a merit of necessity, by seeming to yield with grace, what they knew they had not the power to retain. It is not the lifeless mass of matter, he will then feel, that he is examining, it is the mighty machine of Eternal Wisdom : the workmanship of Him, in whom every thing lives, and moves, and has its being. When suffering the inconveniences of the ruder parts of the year, we may be tempted to wonder why this rotation is necessary; why we could not be constantly gratified with vernal bloom and fragrance, or summer beauty and profusion. Then a spirit passed before my face; the hair of my flesh stood up: it stood still, but I could not discern the form thereof: an image was before mine eyes : -There was silence, and I heard a voice Shall mortal man be more just than God? -- 58. The dash is sometimes to be read as a note of interrogation. Is it not enough to see our friends die, and part with them for the remainder of our days- to reflect that we shall hear their voices no more, and that they will never look on us again -to see that turning to corruption, which was but just now alive, and eloquent, and beautiful with all the sensations of the soul? world, and demi-gods of fame? Is this your triumph — this your proud applause, children of truth, and champions of her cause? Was there ever a bolder captain of a more valiant band? Was there ever but I scorn to boast. - And what if thou shalt fall unnoticed by the living — and no friend take note of thy departure? Seest thou yon lonely cottage in the grove with little garden neatly planned before its roof deep-shaded by the elms above, moss-grown, and decked with velvet verdure o'er? What shall we call them? piles of crystal light - a glorious company of golden streams - lamps of celestial ether burning bright suns lighting systems with their joyous beams. -- 59. The dash is sometimes to be read like a note of exclamation. What dreadful pleasure! there to stand sublime, like shiprecked mariner on desert coast, and see the enormous waste of vapour, tossed in billows lengthening to the horizon round, now scooped in gulfs, with mountains now embossed - and hear the voice of mirth and song rebound, flocks, herds, and waterfalls, along the hoar profound! The chain of being is complete in me; in me is matter's last gradation lost, and the next step is spirit-Deity! I can command the lightning, and am dust! Above me are the Alps, the palaces of Nature, whose vast walls have pinnacled in clouds their snowy scalps, and throned Eternity in icy halls of cold sublimity, where forms and falls the avalanche-the thunderbolt of snow! How has expectation darkened into anxiety-anxiety into dread-and dread into despair! Alas! not one memento shall ever return for love to cherish. All that shall ever be. known is, that she sailed from her port, and was never heard of more. A measure of corn would hardly suffice me fine flour enough for a month's provisions, and this arises to above six score bushels and many hogsheads of wine and other liquors have passed through this body of mine-this wretched strainer of meat and drink! And what have I done all this time for God and man? What a vast profusion of good things upon a useless life and a worthless liver! Extraneous, sea-water, semi-circle, demi-gods, Seething-hall, Moss-side, plane-trees, bed-side, Birk-knowe, over-canopied, toil-hardened, gray-haired, to-morrow, Sabbath-day, Sardanapālus, ill-requited, thunder-cloud, European, Epicurean, pine-covered, clay-cold, snow-clad, parish-clerk, night-steed, moon-eyed, azure, all-wise, edict, fellow-creatures, icy, wellfounded, omega, fellow-feeling, uniform, prophesy, earth-born, far-wandering, storm-clouds, hymeneal, chamber, either, fairy, lēver, apiary, culinary. ELLIPSIS. 64. Ellipsis means an omission of some word or words. Sometimes a sentence is unfinished, or some parts of it are purposely omitted; and the mark which indicates an ellipsis is put in the place of that which is left out. 65. An ellipsis is sometimes indicated by a long straight line, thus, which resembles a lengthened dash. 66. Sometimes the ellipsis is denoted by asterisks, or stars, thus, 67. Sometimes the ellipsis is marked by small dots, or periods, thus 68. Sometimes the ellipsis is indicated by hyphens, | powers of 2 will be the natural numbers, and the indices of those thus, to his kinsman's aid. I would not wound thee, Douglas, well thou knowest; but thus to hazard on desperate a cast thy golden fortunes Still must I wonder; for so dark a cloud Oh, deeper than thou think'st I've read thy heart. Your grace will pardon me for obeying Say no more, my child; you are yet too raw to make proper distinctions. Let them or suppose I address myself to some particular sufferer- there is something more confidential in that manner of communicating one's ideas -as Moore says, Heart speaks to heart-I say, then, take especial care to write by candle-light. To such unhappy persons, in whose miseries I deeply sympathise Have I not groaned under similar horrors? That spares manual labour-this would relieve from mental drudgery, and thousands yet unborn But hold! I am not so sure that the female sex in general may quite enter into my views on the subject. MATHEMATICAL ILLUSTRATIONS.-No. III. CRITHMETICAL LOGARITHMS. NATURE AND USE OF LOGARITHMS. 15. The powers of any assumed invariable number or root constitute a series of numbers which are denominated the natural numbers. The indices of those powers are called artificial numbers or logarithms; and taken collectively, a system of logarithms. The assumed constant number, or root, is called the base of the system. 16. The logarithm of a given number is precisely defined, the index of that power of the base of the system, which is equal to the given number. 17. Any number may be assumed as the base of a system of logarithms. If the number 2 be assumed as the base, then the powers will be the logarithms of the natural numbers. If these definitions be applied to the numbers and their indices in the table of powers, Art. 8, the expression in Art. 14 being also taken into consideration, the construction of the following table will be rendered manifest: By means of this table, logarithmic calculations may be exemplified on a small scale, in the following manner. 18. First. To multiply two or more numbers together. It the logarithm of the product (see Art. 10). Thus, to multiply the logarithms of the factors be added together, the sum is 128 by 8, add 7 and 3 together, the logarithms of the factors; the sum 10 is the logarithm of the product 1024. Again, to multiply 4, 8 and 16 continuously together, add 2, 3 and 4, together, the logarithms of the factors; the sum 9 is the logarithm of the product 512. logarithm of the divisor be subtracted from the logarithm of 19. Secondly. To divide one number by another. If the the dividend, the remainder is the logarithm of the quotient rithm of the divisor from 8, the logarithm of the dividend; the (see Art. 11). Thus, to divide 256 by 64, subtract 6, the loga. remainder 2 is the logarithm of the quotient 4. 20. Thirdly. To find a fourth proportional to three given terms. If the logarithms of the second and third terms be added together, and from the sum, the logarithm of the first term be subtracted, the remainder is the logarithm of the fourth term. Thus, to find a fourth proportional to 8, 32 and 64; if 8: 32 64 the fourth term, then add 5 and 6 together, the loga rithms of the second and third terms, and from the sum 11 subtract 3, the logarithm of the first term, the remainder 8 is the logarithm of the fourth term 256. logarithm of the number be multiplied by the index of the 21. Fourthly. To find any power of a number. If the required power, the product is the logarithm of that power (see Art. 12). Thus, to find the square of 16, multiply 4, the logarithm of the number, by 2, the index of the square; the product 8 is the logarithm of the square 256. 22. Fifthly. To find any root of a number. If the logarithm of the number be multiplied by the index of the required root, or be divided by its denominator, the quotient is the logarithm of that root (see Art. 13). Thus, to find the cube root of 64, divide 6, the logarithm of the number, by 3, the denominator of the index of the cube root; the quotient 2 is the logarithm of the cube root 4. 23. The nature and use of logarithms having been thus illustrated and exemplified in the system of which the base is 2, we shall now give a full explanation of the system in common use. COMMON SYSTEM OF LOGARITHMS. 24. The number 10 has been assumed as the base of the common system of logarithms, because it is the root of the decimal scale of notation, and on this account possesses certain advantages which have led to its universal adoption by mathematicians. 25. The powers of the number 10 being respectively unity with as many ciphers annexed as are denoted by the indices of the different powers, the construction of the following table is sufficiently evident to the student : Cube root of 1.08902 1.02883, index = etc. 27. If unity, the first natural number, be divided by the successive natural numbers in the preceding table, the quotients will be a series of decimal fractions, viz., 1, 01, 001, etc. The logarithms of these quotients will be found by subtracting On this principle the following table is constructed: the logarithms of the natural numbers from 0, the logarithm of unity (see Art. 11). Now, though it be impossible, arithmetically, to subtract the logarithms 1, 2, 3, etc., from the logarithm 0, yet the operation that should be performed is indicated by placing the sign of subtraction before each of these logarithms, thus: 1, 2, 3, etc. Hence, the construction of the following table of decimal fractions, with their logarithms, is evident to the student: Table of Odd Roots. 10 2.15443 The cube root. 10 1.29155 The ninth root. 102' 1.08902 The 27th root. 10 Fr 1.02883 The 81st root. Second Skeleton Table of Logarithms. 10243 1.00952 The 243rd root. Natural Numbers. 10745 •1 Lo garithms 1 1.00316 The 729th root. Fanny arracha l'èpine, non sans peine, lava le sang qui coulait de la blessure; puis, prenant son mouchoir, elle en fit un bandage avec lequel elle enveloppa la patte du patient, qui, se sentant soulagé, léchait le cou et les mains de sa petite bienfaitrice, en faisant entendre un grogne28. These logarithms, being of an opposite character to the ment de plaisir; puis il se coucha à ses pieds jusqu'au former, are called negative, while the former are denominated moment où les enfants se disposèrent à regagner l'habitapositive. From the remarks in the preceding article, it is tion. Quand ils se remirent en route, il alla se placer evident that the logarithm of every proper fraction is essentially negative, and that the logarithms of such fractions à côté de Fanny,5 en fixant sur elle des yeux expressifs et numerically increase in proportion as the fractions themselves qui semblaient l'interroger. Elle lui fit signe de la suivre. decrease in value, compared with unity. Hence, when the Alors, oubliant sa blessure, faisant un bond de plaisir, yalue of a fraction is indefinitely small, its logarithm numel'animal forma cortège à la petite troupe, qui ne tarda pas rically considered must be indefinitely great; and when the à rentrer dans la cour de l'habitation. value of a fraction is infinitely small, so as to be reckoned equal. A peine avaient-ils franchi la barrière, que le chien prit -Enfin te voilà retrouvé, mon brave Moustache, s'écria-t-il en flattant le chien. 10 sa course et se précipita vers un groupes rassemblé autour châtaignier, on fut très surpris de ne le point voir avec d'une sorte de marchand ambulants qui, ayant ouvert plu- Auguste et Fanny.10 On l'appela, on le chercha de tous sieurs ballots, étalait ses marchandises devant les personnes côtés; bientôt tout le monde fut sur pied. Alfred ne paruti qui se trouvaient là, en les invitant à faire quelques acqui-pas. Le père et la mère, tous les domestiques parcoururent sitions. Le marchand poussa un cri de joie: en vain les alentours; 12 ils n'en découvrirent aucune trace; 13 désespérés de cet événement, ils se partagèrent en plusieurs bandes; ils allèrent avec leurs voisins, qu'ils avertirent du malheur qui leur était arrivé, à la découverte, et ils s'enfoncèrent dans la forêt qu'ils battirent en tout sens avec la plus scrupuleuse attention.15 Mille fois ils appelèrent l'enfant par son nom, ils n'en reçurent aucune réponse.16 Cependant, les dernières lueurs du jour n'éclairaient plus que faiblement les recherches, et rien encore n'était venu calmer les inquiétudes de M. et de Mme Dérambert: les approches de la nuit redoublèrent leurs alarmes. Dans leur désespoir, ils ne voulurent jamais consentir à retourner dans leur domicile.19 Ils allumèrent des torches de résine et firent retentir les bois, les vallées, du nom chéri d'Alfred.20 Alors il se mit à raconter, qu'en traversant la forêt, son chien s'était élancé à la poursuite d'un animal sauvage," qu'il ne s'était aperçu que long-temps après sa disparition, qu'alors il l'avait vainement appelé; Moustache n'était pas Il avait alors supposé, qu'entraîné par son ardeur son chien s'était égaré,12 ou bien encore, qu'ayant attaqué quelque bête féroce, il avait succombé dans la lutte. revenu. -Je ne m'étais pas tout à fait trompés ajouta-t-il, car je vois que Moustache a été blessé. Mais quis done a eu la bonté de le secourir, de panser sa blessure? s'écria-t-il en apercevant le mouchoir qui enveloppait la patte de Moustache. A ces mots, le chien, comme s'il eut compris ce que venait de dire son maître, se mit à courir au devant des trois enfants 15 qui se dirigeaient de ce côté, et se plaçant près de Fanny, il ne la quitta pas d'un instant, qu'elle ne fût arrivée à l'endroit où se trouvait le marchand.17 9. Que faisait le marchand am. 10. Que dit son maître en 11. Que raconta le marchand? 15. Comment le chien sembla-t- 8. Où courut-il après avoir fran- 16. Où se plaça-t-il ? NOTES AND REFERENCES.-a. from faire; L. part ii., p. 92. b. L. S. 36, R. 5.-c. from remettre; L. part ii., p. 102.-d. from faire.-e. forma cortège, escorted.-f. from prendre; L. part ii., p. 100.g. marchand ambulant, itinerant merchant, pedlar.-h. te voilà, here you are.-i. flattant, caressing.-j. il se mit, he commenced; L. S. 68, R. 3.--k. trompé, mistaken; L. S. 37, R. 2.--. from comprendre ; L. part ii., p. 82.-m. L. S. 25, R. 2.— n. see note j. above.-o. quelle ne fût, until she was. SECTION III. 17 -Alfred, mon Alfred! où es-tu? s'écriait la mère de l'accent de voix le plus déchirant; mais c'était en vain. Je n'essaierai pas non plus de vous peindre le désespoir d'Auguste et de Fanny 2 pleurant, sanglotant. Le châtaignier, le ruisseau, les frais bocages qu'ils parcouraient ensemble ne présentaient aucune trace d'Alfred. 7. Que permit-il à ses enfants 8. Que demanda à M. Déram- 9. Qu'arriva t il trois mois mère et tous les domestiques? 13. Trouvèrent-ils le petit garçon ? 14. Comment firent-ils ensuite? 15. Examinèrent-ils bien la forêt ? 16. Leur recherche eut-elle quelque succès ? 17. Quelle heure était-il alors? 18. Quel fut l'effet des approches de la nuit, sur les parents de l'enfant ? 19. Voulurent-ils rentrer chez 20. Que firent-ils ensuite? 10. A quelle heure s'aperçut-on 2-h. from mettre ; L. part ii., p. 96.-i. L. S. 34, R. 1, 2.—j. SOLUTIONS. Alors, remuant la queue et regardant tour à tour Fanny, $49, R. (1).g. s'étaient écoulés, had elapsed; L. S. 44, R. et son maître, Moustache sembla la désigner comme celle qui lui avait donné ses soins. Le marchand apprit alors des enfants ce qui s'était passé ; le pauvre homme ne savait comment leur témoigner sa reconnaissance, car dans ses longues courses, Moustache était non seulement pour lui un compagnon de route, c'était un véritable ami, un brave défenseur qui l'avait préservé de mille dangers. Il voulait mettre à la disposition des enfants toute sa petite cargaison; mais M. Dérambert s'opposa à ce qu'il fit aucun sacrifice onéreux; seulement, comme il tite que ce refus l'affligeait,' il permit à ses enfants d'accepter quelques jouets de peu de valeur. Le lendemain, le marchand partit en demandant à M. Dérambert la permission de revenir dans quelque temps visiter son habitation, ce qui lui fut accordé de grand cœur. Trois mois à peine s'étaient écoulés depuis cette époque, lorsqu'un jour, Alfred, s'étant mis à la poursuite d'un papillon, s'écarta sans qu'on fit attention à sa disparition." Sur les dix heures du matin, heure à laquelle les trois enfants avaient l'habitude d'aller à la vallée déjeuner à l'ombre du ANSWER TO THE "FOUR BALL" QUERY, If the four balls be placed in contact with each other, and planes be supposed to pass through every three of their centres, they will constitute a tetrahedron, or solid whose four faces are four equal equilateral triangles, and whose edges (the sides of these triangles) are, in this case, each equal to 10 inches. The distant from its four angular points, which are the centres of centre of the fifth ball is a point within this tetrahedron equally the four balls; and the first question is to find the distance of this point from each of the said angular points. In the figure, iet A B C D be the tetrahedron, each of the triangles ABC, ABD, ACD, and B CD, being equilateral. Let |