"Out of," meaning, removed from, beyond and outside of, is respect to; además de, besides; a pesar de, in spite of, notwithrendered by fuera de; meaning on account of, by por; meaning standing; cerca de, near to; frente á, or en frente de, opposite; from, by de; as, en orden d, with regard to; junto á, adjoining; por el medio de, across; durante, during. Out of danger, fuera de peli the ground, tengo habas The preposition entre, between, when it comes before per. gro. que están fuera de tierra. sonal pronouns, does not govern them in the objective case in Out of my power, fuera de Out of friendship, por amistad. Spanish, but is followed by them in the nominative; as, entre mis alcances. He-drinks out of a tumbler, tú y yo (and not entre tí y mi), between thee and me. I have beans that are out of bebe de un vaso, Prepositions, as in English, are placed before the word which they govern. “ Over" is rendered by encima de when it means above; and Care must be taken to distinguish the use of the same word otherwise by sobre ; as, in English, whether employed as a preposition or an adverb or conjunction. Thus in the phrases, after breakfast, before Over the window, encima de la | He-wept over the city, lloró dinner, the words after and before are prepositions, and are to ventana. sobre la ciudad. be rendered by despues de and antes de, respectively; while in the phrases, after I had departed, before I had dined, the • Through," meaning from one end or side to another, or on words after and before are adverbs, and are to be rendered by account of, is rendered by por ; when it means by reason of, despues que and ántes que. by de; as, Segun, when used before a verb in Spanish, is not a prepo sition, but an adverb, meaning, according as; as, segun creo, He-travelled through Spain, la muerte estaban en servi- according as I believe ; segun pareció, according as it-appeared. viajó por España. dintre toda la vida, Through the fear of death | She trembles through fear, they were in bondage all ella tiembla de temor, OF THE INTERJECTION. their life, por el temor de “Till" is rendered by hasta; as, The position of the interjection in a sentence is determined by no fixed rules, but is allowed to vary, as in English, accord ing as harmony and propriety may require. The office is open till ten o'clock at night, la oficina está abierta The interjection ete, lo, behold, is used with the first objechasta las diez de la noche. tive case of the personal pronouns only, being joined to them "To," when preceded by from, in such phrases as, from bad and forming one word; as, to worse, from time to time, is rendered by en; when it means of, by de; and in other cases generally by á; as, ; Eteme ! ¡Etelos que vienen! lo they i Etele ! behold hiin! come! From day to day, de dia en dia. | An uncle to John, un tio de ; Etela! behold her! A friend to his country, un Juan. amigo de su patria. He-gave the inkstand to Mary, The interjection he, see, behold, is prefixed to the first dió el tintero á Maria. objective case of personal pronouns, and precedes adverbs, such as aqui, here, alli, there; as, “ Towards” is rendered by hácia; as, ¡Hele aqui! here he is ! 1 i Hela aqui! here she is. Here comes towards us the lady of the house, aqui viene hucia ¡ Helos allí! there they are ! nosotros la señora de la casa, More literally these exclamations might be rendered, "see “Under" is rendered by debajo de or bajo; as, him here!" "see her here !'' “behold them there!" Under the bridge, debajo del puente. When adjectives are employed as interjections, they are Under the table, bajo la mesa. followed by the preposition de, if a noun or pronoun come after; as, "Under" is rendered by so in the following phrases, 60 capa de, under cover of ; so color de, under colour of; 80 pena de, under i Desgraciado de mi! unlucky me! (or, unfortunate that I am !) penalty of; so pretexto de, under pretext of. “With,” when meaning of, or from, or by, is rendered by de; noun or pronoun; as, The interjection ay is followed by de when used before a in most other cases by con; as, We-are covered with dust, stroke, Juan le mató de un i Ay de mi! alas for me! (or, woe to me!) estamos cubiertos de polvo. sablazo, We are-dying with cold, nos With permission of the capmorimos de frío. tain, con permiso del capiJohn killed him with a sabre. tan. LESSONS IN TRIGONOMETRY.-No. VI. “Within" is rendered by dentro de; as I-shall-need it within three days, lo necesitaré dentro de tres dias. TRIGONOMETRICAL FORMULÆ. “Without," meaning destitute of, with exemption from, is Let ABC be any spherical rendered by sin; and when it means outside of, or beyond, by triangle, and from the angle B fuera de; as, draw the arc B D perpendicular to the base AC. Represent Treat me without ceremony, | To-buy without money, com the sides of the triangle by trúteine vmd. sin ceremónia. prar sin dinero. a, b, c, and the segment ad by They-cast him without the city, le echaron fuera de la ciudad. then will cd be equal to Sin in Spanish is regarded as a negative preposition, and is therefore often followed by a negative conjunction; as, By Theorem III., Cor. 1, Sin otro fin ni motivo, without another end or (nor) motive. cos, c: cos, 0 :: cos. 2 : cos. There are other prepositions in Spanish, which, as they can be rendered in most cases by the corresponding English prepo cos. 6 cos. x + sin. b sin. x sition, offer no difficulty to the learner. Such are para con, in B D R Ans. tan. r = COS, C. COS. AS sin. B, But, Whence, We thus find the angle B = 59° 16' 46". and c=131° 28' 36". R cos. a cos. X=0.8.b cos. C Cos. + sin. b cos. c sin, s'; or, dividing each term by cov. &, we obtain, Es. 2. In a spherical triangle there are given a = 1150 20', R? cos. a = K (s. b cos. c + sin, b cos. c tan. X. 6 = 57° 30', and c= 82° 28'. Required the three angles. But, by Theorem II., Cor. 2, we have, A=126° 35' 2". B = 490 3!' 42". cos. A sin.c = 61° 43' 58". By means of the polar triangle, we may convert the preIIence, rocos. A= r cos. E cos. c + sin. ) sin. e cos, A, (1) celing formulæ for angles into formulæ for the sides of a trifrom which all the formule necessary for the solution of angle, since the angles of every triangle are the supplements spherical triangles may be deduced. of the sides of its polar triangle. Let, then, a', b, c, A', B', c', represent the sides and angles of the polar triangle, and we From this equation we obtain, by transposition, shall have, no cos. (I - Rcos, l cos.c A' = 180° a, B' = 1890 – b, c' = 180°C, m. b sin, c. a' = 1800 A, b' = 180o – B, C = 1802 Therefore, cos. A' = cos. ( 90° — a) = sin. Ja, a formula which furnishes an angle of a triangle when the sin. 6' = sin. (1809. three sides are known. sin. c' =sin. (180° -- () = sin. C, If we add r to each member of this equation, we shall have, Also, if we put s' = half the sum of the angles of the polar R? cosa + R sin. b sin. ( - cos.bos.c triangle, we shall have, 1 + cos. A = sin. b sin, c s' = 270o – 8, and sin, s' = 2 cos.?!A sin. (9' – a') = sin. [90° — (8 — A)]=cos. 18 – ). 1 + cos. A = By substituting these values, formula (3) becomes, And, cos. (8 - 1) cos. ($ - c) r sin. 6 sin. c -- R cos. b cos. c =-1: cos. (b + c). cos, da =R (1) sin, B sin, o Hence, by substitution, we obtain, and formula (2) becomes, 2 cos. ?JA R” (cos. a - cos. (b + c) cog, s cos. (8 A) sin. b sin, c. sin. Ja = =RV (5) 2 n sin. d(a + b + c) sin. ?(3 + 4- a) which formulæ enable us to compute the sides of a triangle sin. b sin. c when the three angles are known. If, then, we put : = (a+b+c), we shall find, By means of the polar triangle, we derive from formula (1), sin, 8 sin. (8 R? cos. A = cos. a sin. B sin. C - E COS. B cos. C. (6) cos. Ja =R (2) sin, b sin. c Ex. 1. In a spherical triangle a BC, there are given a=130° 30%, By subtracting cos. A from k instead of adling, we shall B = 30° 50', and c= 32° 5. Required the three sides. obtain, in a similar manger, IIere half the sum of the angles is 96° 42' 30" =s sin. (8 - b) sin. (8 Also, - 33° 47' 30". 65° 52' 30". 64° 37' 30". Either formula (2) or (3) may be employed to compute the Using formula (4), we have, angles of a spherical triangle when the three sides are known. log. cos. (8 — B), 65° 52' 30" Ex. 1. In a spherical triangle there are given a = 63° 50', log. cos. (s --C), 64° 37' 30" 1 = 80° 19', and c= 120° 47'. Required the three angles. - log. sın. B, 30° 50' Ilere half the sum of the sides is 132° 28' = 8. - loz. sin. c, 32° 59 Also, 8 -- a= 65° 38'. Using formula (2), we have, log. cos. }a, 36' 40' 1" log. sine s, 132° 28' 9.867862 log. sine 8 - a, 68° 38' Hence the side a= 73° 20' 2". 9.969075 - log. sine b, 80° 19' comp. 0:006232 The remaining sides may be found by Theorem III., or by --- log. sine c, 120° 47' comp. 0.065952 a formula similar to formula (4). R $1. B sin, C 8-A- 9.611435 9.631992 comp. 0•290270 comp. 0-274781 Sam 19-S0S178 9.904239 Sum 19.909121 V log. cos. A, 25° 45' 19" 9.954560, Hence the angle A = 51° 30' 38". The remaining angles may be found by Theorem III., or by a formula similar to formula (2). cos. (8 - A) cos. (8 -cos. 1b = RV sin. A sin. C We thus find the side 6 = 40° 13' 12", and C = 42° 0'12". Ex. 2. In the spherical triangle A B C, the angle a=129° 30', 1 = 54° 35', and c = 63° 6'. Required the three sides. a=120° 57' 5". 64° 55' 37". C 82° 19' 0". that is, THE TREASURE THAT WAXETH NOT OLD. COS. a Formula (1) will also furnish a new test for removing the grace or vigour of thought or speech he has acquired,--all shall ambiguity of the solution in Case I. of oblique-angled triangles. I tell fully, nobly, if he will give heed to the conditions. And For we have, one condition, the prime one, is, that he be a true man, and no cos, a. --- Rcos, b cos, o recognise the obligation of a man, and go forth with heart and COS. AS will, and every gist and acquirement dedicated, lovingly and sin. I sin c resolutely, to the true and the right. These are the terms ; Now if cos, a is greater than cos. b, the sign of the second which an ingenuous mind can desire, or which a sound and and apart from these there is no success, no influence to be had member of this equation will be the same as that of cos, a: far-seeing mind would dare to scek. Hence cos. A and cos, a will have the same sign; or A and a will be of the same species when cos. a>cos.b, or sin. a <sin.b; to obtain a substantial success, and an abiding, influence, Indeed, it is not an easy thing, nay, it is not a possible thing, except on these terms. A factitious popularity, a transient If the sine of the side opposite to threquired angle is less than notoriety, or, in the case of shining talents, the doom of a the sine of the other giren side, there will be but one triangit. damning fame, may fall to bad men. But an honoured name, enduring influence, a sun brightening on through its circuit, But if cos. a is less than cos. b, then whether the right-hand more and more, even to its serene setting,-this boon of a truc member be plus or minus will depend upon the magnitude of success goes never to intellectual qualities alone. It gravitates cos.c; or cos.c will have two values, corresponding to + cos. A slowly but surely to weight of character, to intellectual ability and COS. A ; hence, rooted in principle.- George Putnam. If the sine of the side opposite to the required angle is greater" than the sine of the other given side, there will be two triangles. Oh! I have loved, in youth's fair vernal morn, Formula (6) will furnish a test for removing the ambiguity To spread imagination's wildest wing, n Case II. of oblique-angled triangles. For we have, The sober certainties of life to scom, And seek the visioned realms that poets sing, - Where Nature blushes in perennial spring, Where streams of earthly joy exhaustless rise, sin. B sin, o Where Youth and Beauty tread the choral ring, And shout their raptures to the cloudless skies, from which it follows, as in the preceding case, that if cos. A While every jovial hour on downy pinion flies. is greater than cos, B, A and a will be of the same species. But if cos. A is less than cos. B, then c may be taken so 48 to But, ah! those fairy scenes at once are fled, render cos. e positive or negative. Hence, if the sine of the Since stern experience waved her iron wand, engle opposite to the required side is less than the sine of the other Broke the soft slumbers of my visioned heal, giren angle, there will be but one triangle; but if the sine of the And bade me here of perfect bliss despond. angle opposite to the required side be greater than the sine of the And oft have I the painful lesson conned ; other given angle, there will be two triangles. When Disappointment mocked my wooing heart, And from forbidden pleasures loth to part, And is there naught in mortal life, I cried, Can soothe the sorrows of the labouring breast? No kind recess where baffled hope may hide, And weary nature lull her woes to rest? Oh! grant me, pitying Heaven, this last request, -- Oh! give me yet, in some recluse abode, now, but few of our educated men are privileged Encircled with a faithful few, to dwell, Where power cannot oppress, nor care corrode, Nor venomed tongues the tale of slander tell; Oh! bear me to some solitary cell, Beyond the reach of every human eye; Society has work for us, and we must forth to do it. Full And let ine bid a long and last farewell carly and hastily we must gird on the manly gown, gather up To each alluring object ’neath the sky, the loose leaves and scanty fragments of our youthful lore, and And there in peace await my hour, --in peace to die. go out among men, to act with them and for them. It is a “Ah, vain desire !" a still small voice replied, practical age; and our Wisdom, such as it is, “must strive "No place, no circumstance can Peace impart: and cry, and utter her voice in the streets, standing in the She scorns the mansion of unvanquished Pride,places of the paths, crying in the chief place of concourse, at Sweet inmate of a pure and humble heart. the entry of the city, and the coming in at the doors.” Take then thy station,--act thy proper part; This state of things, though not suited to the tastes and A Saviour's mercy seek,-his will perforın : qualities of all, is not, on the whole, to be regretted by educated His word has balm for sin's envenomed sinart, men as such. It is not in literary production only, or chiefly, His love, diffused, thy shuduering breast shall warm, that educated mind finds fit expression, and fulfils its inission in honour and beneficence. In the great theatre of the world's His power provide a shelter from the gathering storm." affairs, there is a worthy and a sufficient sphere. Society needs Oh! welcome hiding place! Oh! refuge meet ihe well-trained, enlarged, and cultivated intellect of the For fainting pilgrims, on this desert way! scholar in its midst; needs it, and welcomes it, and gives it a Oh! kind Conductor of these wandering feet .place, or, by its own capacity, it will take a place of honour, Through snares and darkness, to the realms of day! influence, and power. The youthful scholar has no occasion So did the Sun of Righteousness display to deplore the fate that is soon to tear him from his studies, His healing berms; each gloomy cloud dispel : and cast him into the swelling tide of life and action. None While on the parting mist, in colours grey, of his disciplinary and enriching culture will be lost, or useless, Truth's cheering bow of precious promise fell, even there. Every hour of study, every truth he has reached, And Mercy's silver voice soft whispered, -—"All is well.” and the toilsome process by which he reached it: the heightened D. Huntington. THE YOUNG MARINER'S DREAM. His hammock swung loose at the sport of the wind; But, watch worn and weary, his cares flew away, And visions of happiness danced o'er his mind. He dreamed of his home, of his dear native bowers, And pleasures that waited on life's merry morn; While memory each scene gaily covered with flowers, And restored every rose, but secreted its thorn. Then fancy her magical pinions spread wide, And bade the young dreamer in ecstacy rise ;-Now far, far behind him, the green waters glide, And the cot of his forefathers blesses his eye. The jessamine clambers, in flower, o'er the thatch ; And the swallow sings sweet from her nest in the wall ; All trembling with transport, he raises the latch ; And the voices of loved ones reply to his call. A father bends o'er him with looks of delight; His cheek is impearled with a mother's warm tear ; And the lips of the boy in a love-kiss unite, With those of the sister his bosom. holds dear. The heart of the sleeper beats high in his breast, Joy quickens his pulses,-his hardships seem o'er; And a murmur of happiness steals through his rest, “0 God! thou has blest me; I ask for no more." Ah! whence is that flame which now bursts on his eye? Ah! what is that sound which now larums his ear: 'Tis the lightning's red glare, painting wrath on the sky! 'Tis the crashing of thunders, the groan of the sphere ! He springs from his hammock,-he flies to the deck,- Amazement confronts him with images dire, The masts fly in splinters,-the shrouds are on fire ! In vain the lost wretch calls on mercy to save ; Unseen hands of spirits are ringing his knell, And the death angel flaps his broad wing o'er the wave. O sailor boy! woe to thy dream of delight! In darkness dissolves the gay frost-work of bliss : Where now is the picture that fancy touched bright, Thy parents' fond pressure, and love's honied kiss? () sailor boy! sailor boy! never again Shall home, love, or kindred, thy wishes repay; Unblessed, and unhonoured, down deep in the main, Full many a score fathom, thy frame shall decay. Or redeem form or fame from the merciless surge ; And winds, in the midnight of winter, thy dirge ! Around thy white bones the red coral shall grow; Of thy fair yellow locks, threads of amber be made, And every part suit to thy mansion below. And still the vast waters above thee shall roll: Dimond. THE VICTOR ANGELS. S) warned he them, aware themselves, and soon "VANGUARD, to right and left the front unfuid , Milton. LITERARY NOTICES. CASSELL'S LATIN DICTIONARY. BEARD), D.D., and C. BEARD, B.A. Part II. - Exolisu-LATIN, price 4s., in paper covers ; 5s, cloth. Cassell's SHILLING EDITION OF First LESSONS IN LATIN. By Pro A KEY TO CASSELL's Lessons in Latin. Containing Translations of all the Exercises. Price Is. paper covers, or 18.6d. cloth. Cassell's CLASSICAL LIBRARY.-The First Volume of this work price 18. 6d. cloth, consists of a LATIN READER, adapted to " Cassell's First cloth. - Volume III. contains Tue ACTS OF THE Apostles in the Original Greek, with copious Notes and a Lexicon, price 2s.6d, neat cloth. cloth. END OF VOL. VI. JUIN CASSELL, I'KIATEK, LUDGATE HILL, LONDON. |