The cones corresponding to each stripe have the same axis, which is called the axis of vision. This straight line being parallel to the rays of the sun, it follows that when the sun is in the horizon, the axis of vision is itself horizontal, and the rainbow appears in the form of a semi-circle. If the sun is raised above the horizon, the axis of vision is lowered, and with it the rainbow. Lastly, when the sun is 42° 2′ above the horizon, the rainbow disappears altogether below the horizon. Hence it is never seen except in the morning or evening. of "Finden's Tableaux:" and a series of papers called "Readings of Poetry, Old and New." Although her tragedies show great intellectual powers, and a highly cultivated mind, yet it is by her sketches of English life that she has obtained the greatest share of her popularity, and it is on them her fame will chiefly depend. In these descriptions Mary Mitford is unrivalled. Her manner is inimitable and indescribable, and sheds interest around the most homely subjects and coarsest characters. Who ever threw by a sketch of hers half read? No one who admired a spring daisy-or that most fragrant blossom, the wallflower, which beautifies every object, however rough, rude or ruinous, around which it wreathes. And though she does not trace the motives of conduct very deeply, or attempt to teach principles of moral duty, yet there is much in her sprightly and warm sketches of simple nature which draws the heart to love the Author of all this beauty; and much in her kind and contented philosophy to promote love and good feelings. She was a philanthropist, for she took pleasure in the happiness of others-a patriot, for she drew the people to feel the beauties and blessings which surround the most lowly lot in the "land of proud names and high heroic deed." "As a proof that we love her, we love her dog," says an American writer. "Walter Scott's stately Maida is not more an All that we have stated applies to the inner bow. With regard to the outer one, it is formed by rays which have undergone two reflections, as is seen in the ray s' id feo in the drop p. The angle s' 1 o, formed by the emerging and incident rays, is called the angle of deviation, as before. In the present case, however, this angle is not susceptible of a maximum, but of a minimum, which varies according to the different kinds of rays, and which has effective rays corresponding to it. It is proved by calculation, that for violet rays the minimum angle is 54° 7′, and for red rays only 50° 57', which explains why the red bow is in this case inside and the violet outside. As at each interior reflection in the drop of water there is a loss of light, the outer bow always exhibits fainter colours than the inner one. The outer bow ceases to be visible when the sun is more than 54° above the horizon. The moon produces rainbows as well as the sun, which are historical character than her springing spaniel, or Italian greycalled lunar rainbows, but they are very pale. BIOGRAPHY.-No. XXVIII. MARY RUSSELL MITFORD. THIS lady was born on the 16th of December, 1786, at Abresford, in Hampshire. Her father was of an old Northumberland family, one of the Mitfords of Mitford Castle; her mother the only daughter of the Rev. Dr. Russell of Ash, in Hampshire, and she was their only child. When still a young girl, about the year 1806, Miss Mitford published a volume of miscellaneous poems, and two volumes of narrative poetry after the manner of Scott, "Christina, the Maid of the South Seas (founded upon the story of the mutineers of the Bounty, afterwards taken by Lord Byron), and "Blanche, a Spanish Story." These books sold well and obtained a fair share of popularity, and some of them were reprinted in America. However, Miss Mitford herself was not satisfied with them, and for several of the following years devoted herself to reading instead of writing; indeed it is doubtful whether she would ever have written again had not she, with her parents, been reduced from the high affluence to which they were born to comparative poverty. Filial affection induced her to resume the pen she had so long thrown aside, and accordingly she wrote the series of papers which afterwards formed the first volume of "Our Village: Sketches of Rural Character and Scenery," about 1820. But so little was the peculiar and original excellence of her descriptions understood at first, that, after being rejected by the more important publications, they at last saw the light in the "Lady's Magazine." The public were not long in discovering the beauties of a style so fresh yet so finished, and in appreciating the delicate humour and the simple pathos of these tales; and the result was, that the popularity of these sketches outgrew that of the works of a loftier order from the same pen; and every nook and corner of the cluster of cottages around Three-Mile-Cross, near Reading, in Berkshire, is as well known as the streets and lanes around the reader's own home. Four other volumes of sketches were afterwards added; the fifth, and last, in 1832. Extending her observation from the country village to the market-town, Miss Mitford published another interesting volume of descriptions, entitled Belford Regis." She edited three volumes, called "Stories of American Life by American Writers." She also published a volume of "Country Stories;" a volume of "Dramatic Scenes;" an opera called "Sadak and Kalasrade," and four tragedies, the first entitled "Julian," which was represented in Londen, in 1823, Mr. Macready playing Julian. Her next was "Foscari;" then "Rienzi" and "Charles the First;" all were successful. "Rienzi," in particular, long continued a favourite. She also edited four volumes hound. If she began by being prosaic in poetry, she has redeemed herself by being most poetic in pastoral prose." In 1833 Miss Mitford's name was added to the pension list, a well-earned tribute to one whose genius has been devoted to the honour and embellishment of her country. After a long period of decline and helpless suffering, cheerfully borne, this eminent lady died lately at Swallowfield Cottage, near Reading, aged sixtv-six years. WHITSUN-EVE-MY GARDEN. "The pride of my heart and the delight of my eyes is my. garden. Our house, which is in dimensions very much like a bird-cage, and might, with almost equal convenience, be laid on a shelf, or hung up in a tree, would be utterly unbearable in warm weather, were it not that we have a retreat out of doors, and a very pleasant retreat it is. To make my readers fully comprehend it, I must describe our whole territories. cottage at one end; a large granary, divided from the dwelling "Fancy a small plot of ground, with a pretty low irregular by a little court running along one side; and a long thatched shed open towards the garden, and supported by wooden pillars on the other. The bottom is bounded, half by an old wall, and half by an old paling, over which we see a pretty distance of woody hills. paling, are covered with vines, cherry-trees, roses, honeyThe house, granary, wall, and suckles, and jessamines, with great clusters of tall hollyhocks running up between them; a large elder overhanging the little gate, and a magnificent bay-tree, such a tree as shall scarcely form the horizontal lines of the buildings. This is my garden; by matched in these parts, breaking with its beautiful conical and the long-pillared shed, the sort of rustic arcade which runs along one side, parted from the flower-beds by a row of rich geraniums, is our out-of-door drawing-room. "I know nothing so pleasant as to sit there on a summer afternoon, with the western sun flickering through the great elder-tree, and lighting up our gay parterres, where flowers and flowering shrubs are set as thick as grass in a field, a wilderness of blossom, interwoven, intertwined, wreathy, garlandy, profuse beyond all profusion, where we may guess that there is such a thing as mould, but never see it. I know nothing so pleasant as to sit in the shade of that dark bower, with the eye resting on that bright piece of colour, lighted so gloriously by the evening sun, now catching a glimpse of the little birds as they fly rapidly in and out of their nests-for there are always two or three birds'-nests in the thick tapestry of cherry-trees, honeysuckles, and China-roses, which cover our walls-now tracing the gay gambols of the common butterflies as they sport around the dahlias; now watching that rarer moth, which the country people, fertile in pretty names, call the bee-bird; that bird-like insect, which flutters in the Sphynx ligustri, privet hawk-moth. cos. CD: R:: cos. B: sin. B C D. Hence, cos. A cos. B:: sin. A CD sin. B C D. Cor. 3. The sines of the segments of the base are reciprocally proportional to the tangents of the angles at the base. For, by Theorem II., Also, sin. A DR:: tan, CD: tan. A. sin. BD: R:: tan. CD: tan. B. sin. A D sin. B D : tan. B: tan. A. Cor. 4. The cotangents of the two sides are proportional to the cosines of the segments of the vertical angle. For, by Theorem II., Cor. 2, hottest days over the sweetest flowers, inserting its long pro-Alsɔ, "What a contrast from the quiet garden the lively street! Saturday night is always a time of stir and bustle in our Village, and this is Whitsun-Eve, the pleasantest Saturday of all the year, when London journeymen and servant lads and lasses snatch a short holiday to visit their families. A short and precious holiday, the happiest and liveliest of any; for even the gambols and merry-makings of Christmas offer but a poor enjoyment, compared with the rural diversions, the Mayings, revels, and cricket-matches of Whitsuntide.' LESSONS IN TRIGONOMETRY.-No. V. OBLIQUE-ANGLED SPHERICAL TRIANGLES. THEOREM III. In any spherical triangle, the sines of the sides are proportional to the sines of the opposite angles. ! In the case of right-angled spherical triangles, this proposition has already been demonstrated. Let, then, A B C be an oblique-angled triangle; we are to prove that sin. BC: sin. A c :: sin. A: sin. B. Through the point c draw an arc of a great circle CD perpendicular to A B. Then, in the A D B Cos. A CD: cot. Ac:: tan. CD: R. Also, Cos. A CD cos. BCD cot. A c cot. B C. C 22 D B Let B Ca, Ac=b, BD=m, and AD = n. Then, by Theorem III., Cor. 1, cos. a: cos. b:: cos. m : cos. *. Whence, cos.a+cos. b: cos.a-cos. b:: cos.m+cos. n: cos. m—cos. n. But by Trigonometry, cos.a+cos. b: cos. a— cos. b:: cot. (a+b): tan. 1(a — b). Also, cos.m+cos. n: cos. m-cos. n:: cot. (m+n): tan. 1(m—n). Therefore, cot. (a+b): cot. 1(m + n) :: tan. (a - b): tan. 1(m — n) But, since tangents are reciprocally as their cotangents, we have, cot. 1(a + b) : cot. 1(m + n) : : tan. 3(m + n) : tan. Ha + 6). Hence, spherical triangle ACD, right-angled at D, we have, by Napier's cases may occur, viz. : rule, 1. Given two sides and an angle opposite one of them. 2. Given two angles and a side opposite one of them. 3. Given two sides and the included angle. 4. Given two angles and the included side. 5. Given the three sides. 6. Given the three angles. When we have given two sides and an opposite angle, there are, in general, two solutions, each of which will satisfy the conditions of the problem. If the side ▲ c, the angle A, and the side opposite this angle are given, then, with the latter for radius, describe an arc cutting the arc A B in the points в and B. The arcs CB, CB' will be equal, and each of the triangles AC, ACB' will satisfy the conditions of B B' B When we have given two angles and an opposite side, there are, in general, two solutions, each of which will satisfy the conditions of the problem. If the angle ▲, the side a c. and the angle opposite this side are given, then through the point o there may generally be drawn two arcs of great circles CB, C B', making the same angle with A B, and each of the triangles A B C, A B'o will satisfy the conditions of the problem. There is the same ambiguity in the numerical computation, since the side BC is found by means of its sine. In the preceding example, however, there is no ambiguity, because the angle A is less than B, and therefore the side a must be less than 6, that is, less than a quadrant. Ex. 2. In the oblique-angled spherical triangle ABC, the angle A is 128° 45', the angle c=30° 35′, and BC= 68° 50′. Required the remaining parts. AB Ans. AC B 37° 28′ 20′′. 40° 9' 4". 32° 37′ 58′′. CASE III. Given two sides and the included angle, to find the remaining parts. In the triangle A B C let there be given two sides, as ▲ B, A C, and the included angle A. Let fall the perpendicular c D on the side AB; then, by Napier's rule, R COS. A tan. AD cot. A C. the problem. There is the same ambiguity in the numerical Having found the segment" A D, the segment BD becomes sin. BD sin. AD: : tan. A : tan. B. The remaining parts may now be found by Theorem III. From the unknown angle draw CD perpendicular to D CASE IV. Given two angles and the included side, to find the remaining parts. In the triangle ABC let there be given two angles, as a and AB; thn will the triangle ABC be divided into two rightangled triangles, in each of which there is given the hypo-ACB, and the side A c included between them. From a let fall thenuse and the angle at the base. Whence we may proceed by Napier's rule, as in Case I. Ex. 1. in the oblique-angled spherical triangle ABC, there are given the angle 52° 20', в 63° 40', and the side b=83° 25'. Required the remaining parts. sin. B: sin. A :: sin. A C· sin. Bc 61° 19′ 53′′. Then, in the triangle ▲ C D, cot. AUR : cos. A: tan. A D 79° 18′ 17′′. Also, in the triangle B C D, Hence, cot. EO: R: Cos. B: tan. BD- 39° 3' 8". To find the angle AC B. sin. BC sin, AB :: sin. A: sin. A C B 127° 26 47". Also, by Theorem III., Cor. 2, sin. ACD sin. BOD:: cos. A: cos, B = 28° 15′ 47′′. Then, by Theorem III., sin. B: sin. ACB:: sin. AC: sin. A B76° 23′ 5′′. Ex. 2. In the spherical triangle ABC, the angle A the angle o 48° 30', and the side AC the remaining parts. Ans. AB 125° 20′, 83° 13. Required 56° 39' 9". 114° 30′ 24′′. B =62° 54' 38". The specimen of an interrogative sentence given above, is that of a direct interrogative. The sentence is called a direct interrogative sentence, because it simply and directly asks a question. If, however, I put the sentence thus, "I do not know whether the man is good," then I form what is called an indirect interrogative sentence; that is, a sentence in which a question is implied or involved. Thus the sentence, "I do not know whether the man is good," is equivalent to, "Is the man good?" and, "I do not know." An indirect interrogative sentence is, consequently, a compound sentence. Interrogative sentences are formed in Greek by means of interrogative words. Such words are numerous in Greek, if CASE V. Given the three sides of a spherical triangle, to find the only because the language has two forms of words, one for the angles. direct and one for the indirect interrogatory. The indirect interrogatives are formed from the direct, by prefixing to the latter the syllable o, by which it is indicated that the question rests on the foregoing sentence or clause. In the triangle ABC let there be given the three sides. R CO3. A tan, A D cot. A C. The other angles may now be easily found. A sentence is formed by the junction of a predicate with a and you ask of what subject a certain thing is to be predicated. Hence arise what are called noun-questions; that is, questions in which you ask for the noun. But your question may relate also to the predicate, and you then ask what is said Ex. 1. In the spherical triangle ABC, the side A B=112° 25', of the subject? Hence, who and what involve the substance Ac 60° 20', and BC 81° 10. Required the angles. 54° 26', 81° 16', and 118° 7′. From which, by Case V., the angles are found to be, Hence the sides of the proposed triangle are, of interrogations; as, who did it? what did he do? As the Causal interrogatives, or such as ask for the cause or reason of a thing, are formed by the interrogative pronouns, in connection with a preposition; as, dia ri; why? Tov éveka; on what account? ε T; on what condition? Indirect, diori, ÓTOV Éveka, ad' ory, etc. In the same way are formed some of the temporal interrogatives; as, μɛxpɩ тov; how long? so, μέχρι ποσου ; μέχρις όσου. Sometimes the direct interrogative is employed instead of the indirect, the question being put independently: e.g είπε μοι, ποῖον τι νομίζεις ευσεβειαν ειναι ; tell me, what do you consider piety to be? That is, "What do you consider piety to be? pray tell me." Sometimes the direct and the indirect are connected together: e.g. ου γαρ αισθανομαι σου, ὁποιον νομιμον η ποιον δικαιον λεγεις I do not learn from you what you call lawful, or what just. In the interchanges of conversation, the indirect question answers the direct in asking the question indirectly: e.g. In English, a question may be asked by merely inverting the order of the verb and the subject, as, eatest thou? This form, which is rare in English, is still rarer in Greek, in which questions are generally asked by means of certain interrogative, words placed at the head of the sentence. These interrogatives serve to denote the view, the object, or the feeling under which the question is put, though some of them have so slender a signification, as scarcely to admit of English equivalents. If we speak of them separately, we may remark that1. apa (corresponding to the Latin num), whether, implies something preceding as the ground of the question, and an anxiety on the part of the inquirer as to the answer. This is the most common form of interrogation; and often, by taking to itself the particle ovv, then, or the negatives ou and un, the particle involves its own answer: e.g. Simple Interrogation. ἄρα μου μεμνησθε ; do you remember me? ἄρ' ουχι μῶρον εστι τουγχείρημα σου άρα μη ιατρος βουλει γενέσθαι surely you do not wish to become a physician? "No." When a double question, or a question with an alternative member, is asked, άρα is superseded by πότερον οι ποτερα, which merely intimates that the question relates to two mutually excluding points: e.g. · πότερον μονῳ μοι βουλει διαλεχθηναι, η και μετα των αλλων ; do you wish to speak to me by myself, or together with the rest? 2., truly, shows that the interrogator has a special interest in ascertaining the true state of things, and may, consequently, be often rendered by "in truth," "really;" but it is often untranslateable: e.g. ὦ οὗτοι πολεμοι εισιν ; are those enemies? Other particles are adjoined to . These strengthen the original one, as, ǹ dŋ, ǹ dñra; or they weaken its force, as, TOU; or they ground the question on something else, and so give it more emphasis, as, yap, for truly; which, when it stands as an independent elliptical sentence, may be rendered, is it not so? 3. μv (formed out of un ouv, is it not then ?), indicates that the inquirer supports his question on something (ovv, then, therefore), but is uncertain whether thereby he shall hit the truth. Consequently, this particle conveys some uncertainty, and may be rendered by "perhaps," "it may be": e.g. "Yes." μwv μῶν τί σε αδικεί ; perhaps something injures thee? So with the negatives, μwv ov, "does not?" un, "surely not?" "No." 4. aλλo rɩ ŋ, forms the direct opposite of ur, literally, is it other than ? which amounts to a strong affirmation; the form intimates that the questioner has hit the right view of the matter, and accordingly expects the opposite (also indicated by alλo Ti) to be unconditionally denied: e.g. αλλο τι η αδικοῦμεν ; beyond a doubt, we are acting unjustly. Then is sometimes dropped without a marked alteration in the sense: e.g. αλλο τι; γεωργος μεν εἷς, αλλος δε τις ύφαντης the one is a farmer, the other a weaver-is it not so? 5. εἶτα and επειτα, also κᾆτα (και ειτα), and κάπειτα, so them, represent the question as called forth by something which excites surprise or dissatisfaction in the interrogator, and may often be Englished by, and now? and yet? what! e.g. επειτ' ουκ οιει θεους ανθρωπων φροντίζειν ; and so then, you do not think the gods have care of men? 6. Ti pawn (literally, learning what?), ri alov (literally, suffering what?), express dissatisfaction in the fact implied in the question: e.g. τι μαθών καταφρονεῖς των αμεινόνων ; τι παθόντες αδικεῖτε τους φιλους ; what has happened to you, that you injure your friends? Of indirect interrogative sentences the single are introduced by &, if, whether, tav, av; and μn, or not; and the double by ETE ειτε; less frequently by ει – είτε and είτε — 1, whether -07. In regard to moods, the same rules obtain for interrogative sentences as for affirmative. Consequently the indicative is employed when the questioner inquires after a fact as the basis of an opinion or judgment. If inquiry is made in regard to a circumstance which the inquirer does not regard as existing, since, in his view, the condition necessary to its existence does not exist, then, in the interrogative sentence, the indicative of the historical tenses with av, is employed. A sentence thus constructed has its basis in a supposed preliminary sentence, which is commonly expressed, but sometimes is merely understood, or implied from the tenor of what is said: e.g. ει τις σε ήρετο, όπως εσώθης, τί αν απεκρίνω ; if any asked thee how thou wast saved, what would you answer? τι αίσχιον και κακιον είη ; what could be more shameful and base? The particle av, as in the subjunctive, increases the uncertainty: e.g. τίς ουκ αν μαινεσθαι ὑμας νομίσειεν ; who would not consider you mad? In indirect interrogative sentences the employment of the moods is generally governed by the same rules as in direct interrogative sentences. The province of the indirect interrogative is more extended in Greek than in English, for verbs expressive of fear or care take after them a sentence (or clause) of that kind. The mood depends on the tense of the principal verb, and on the degree of doubt or uncertainty; even the indicative may be used after the accompanying μŋ, if full conviction is intended: e.g. νῦν φοβούμεθα μη αμφοτέρων ἅμα ἡμαρτηκαμεν now we fear, lest we have at once missed both. As peculiarities in the construction of interrogative sentences, observe a kind of intermingling of the indirect sentence and the principal sentence: e.g. το των χρημάτων, ποσα και ποθεν εσται, μαλιστα ποθεῖτε |