6. Draw a map of the Scandinavian Peninsula, marking the Dovre-feld range, and put in a dot to mark the position of:- Hammerfest, Bergen, Christiania, Stockholm, Carlscrona; mark also the Skagger-rack, the Cattegat, the Sound, the Lofoden Islands, and North Cape. 7. Give the foreign possessions, outside the limits of Europe, of France, Spain, and Holland. FRENCH. Thursday, 30th March, 1882. 10 A.M.-12.30 P.M. [Including Grammatical Questions and English Dictation.] Translate into English: I. Après la bataille de Nangis, avant de monter à cheval pour se rendre à Montereau, Napoléon écrivit à M. de Caulaincourt la lettre suivante :"NANGIS, le 18 février. "Je vous ai donné carte blanche pour sauver Paris et éviter une bataille qui était la dernière espérance de la nation. La bataille a eu lieu; la Providence a béni nos armes. J'ai fait trente à quarante mille prisonniers; j'ai pris 200 pièces de canon, un grand nombre de généraux, et détruit plusieurs armées. Votre attitude doit être la même; vous devez tout faire pour la paix, mais mon intention est que vous ne signiez rien sans mon ordre, parceque seul je connais ma position. En général je ne désire qu'une paix solide et honorable. Si les alliés eussent accepté vos propositions il n'y aurait pas eu de bataille; je n'aurais pas couru les chances de la fortune dans un moment où le moindre insuccès perdait la France, enfin je n'aurais pas connu le secret de leur faiblesse : il est juste qu'en retour j'aie les avantages des chances qui ont tourné pour moi." II. COMBAT DU TAUREAU. Le signal se donne, la barrière s'ouvre, le taureau s'élance au milieu du cirque; mais, au cris, à la vue des spectateurs, il s'arrête, inquiet et troublé; ses naseaux fument; ses regards brûlants errent sur les amphithéâtres; il semble également en proie à la surprise, à la fureur. Tout à coup il se précipite sur un cavalier qui le blesse et fuit rapidement à l'autre bout. Le taureau s'irrite, le poursuit de près, frappe à coups redoublés la terre et fond sur le voile éclatant que lui présente un combattant à pied. L'adroit Espagnol, dans le même instant, évite à la fois sa rencontre, suspend à ses cornes le voile léger et lui darde une flèche aiguë qui de nouveau fait couler son sang. Percé bientôt de toutes les lances, blessé de ces traits pénétrants dont le fer courbé reste dans la plaie, l'animal bondit dans l'arène, pousse d'horribles mugissements, et tombe enfin épuisé d'efforts de colère et de douleur. FRENCH GRAMMAR. 1. Give the feminines of Doux, malin, épais, frais, las, sec. 2. Put into French :-cighty horses; ninety men; 1000 leagues; in the year 1780; Henry II., King of France. 3. Write out the pres. indic., the imperf. fut., cond., pres. and imperf. sub. of craindre; and give the pres. part., 3rd sing. pret. def., and 3rd sing. cond. of aller, prier, s'asseoir, rester, haïr, naître. 4. Put into French :-He has just gone out: I was at your house today; He seems to be satisfied; You have done enough of it. ARITHMETIC, including Vulgar and Decimal Fractions, Proportion, and Simple Interest. Thursday, 30th March, 1882. 2 P.M.-5 P.M. [Including Dictation.] N.B.-You are particularly recommended to answer the questions in the order in which they are set; not omitting any one unless you are unable to do it. Do not lose time by copying out the questions, but refer to each question by its number. 1. Add together 11, 58, 2, and 37. 2. Subtract 159 from 18. 3. Multiply 7, 13, and 117. 4. Divide 44 by 731. 5. Add together 23.018706, 1.907, 07831, and 1.006785. 6. Subtract 28 306703 from 501 28601. 7. Multiply 67.891 by 04508. 8. Divide 4990107712 by 00608. 9. Reduce 1.095 of 3 days 13 hrs. 43 min. to minutes and the decimal of a minute. 10. Find the value of 2 tons 14 cwt. 1 qr. 21 lbs. if 14 ton cost £35. 11. Express 4,798,325 inches in miles, furlongs, &c. 12. Find the simple interest on £3740 for four years at £5 5s. per cent. per annum. 13. Add together 63, 74, 2, and 31. 14. Subtract 913 from 1113. 17. Add together 11 0857 hours and ⚫0167 of a week, and give the answer in seconds and the decimal of a second. 18. Subtract 3.2061 of 9 ozs. 13 dwts. from 1.0672 of 2 lbs. 5 ozs. troy, and give the answer in grains and the decimal of a grain. 19. Multiply 589 0067 by 3 1008. 20. Find the continued product of 15·08, 6·47, and 0905. 22. Divide 609 by 3.78. 23. If 17 gallons of brandy cost £26 178. 74d., how much can be bought for £30 08. 10d.? 24. In how many days of 10 hours each would 108 men complete 4th of the work that 147 men could do in 27 days of 10 hours each? 25. At what rate per cent. simple interest will £2085 amount to £2491 118. 6d. in 6 years? 26. What sum will amount to £1416 16s. in 5 years at 21 per cent. simple interest ? ANSWERS. ELEMENTS OF GEOMETRICAL DRAWING. N.B.-In reading dimensions, a single accent () signifies feet; a double accent (") inches. Sol. = Solution. (For the figures, see sheet at beginning of book.) Q. 1. Sol.-In this question a length of 2.15" represents a length of 17 furlongs, and it is required to make the scale long enough to show 5 miles or 40 furlongs, then the equation for the scale will be as follows: To obtain the representative fraction of the scale, we have to find the proportion between 2∙15" and 17 furlongs, then 2.15 17 x 220 × 36 134640 Thus 17 furlongs 2.15)134640·00(62623 1 62623 = the representative fraction. To construct the scale, we first draw a line A B = 5·058" long, and divide this into five equal parts to represent miles; then subdivide the first division on the left hand into eight equal parts, to show furlongs; and there being 10 chains to a furlong, we must draw ten parallel lines, as shown, to be able to measure single chains. To obtain the required measure, we first take the distance of 2 miles 3 furlongs on the lower line, then measure for chains on the line marked for 4 chains in the scale, as shown, from A to B. NOTE.-The method of obtaining the length of line required, viz. 2 miles 3 furlongs 4 chains, is shown by the position of the points A-B on the scale in the sheet of diagrams. = Q. 2. Sol.-First draw the indefinite line A B, then draw a line at right angles to it, and on this line measure off AB 1". Point A will be the centre for the first circle; then from A, the centre of the first circle, describe an arc with a radius equal to the radius of the first plus that of the second circle required; this will be 1"+ 1}" AD 24". Then we cut this arc by a line drawn from I on A B parallel to the indefinite line A B, and 11′′ from it, the intersection of this line and the arc struck from A as a centre will give the centre of the second circle E; then producing through this centre a line F H at right angles to AB, we mark off from E to H a distance equal to the radius of the second plus that of the third circle, thus 11"+1" EH 2"; then a line drawn from J on the line FH parallel to A B and 11" from it, intersecting the arc struck from E with a radius of 23", gives point K the centre of the third and last circle. = Q. 3. Sol.-First draw a line A B 8 inches long, the length of the given perimeter, then on point A as a centre describe a semicircle, divide this semicircle into as many parts as the ratios of the given angles equal (in this case 2:3:49). The semicircle must therefore be divided into nine equal parts. From point A draw a line A F through the third of these divisions, from point B draw a line B F, making the angle A B F equal to two of the divisions, we thus obtain a triangle ABF whose base A B = 8′′ and its angles are in the required ratio. To obtain the required triangle we draw line A E bisecting the angle B A F, then draw line B E bisecting the angle ABF; from the point of intersection E of these two bisecting lines we draw EC parallel to A F and ED parallel to BF; we thus obtain the triangle CD E, having a perimeter of 8 inches and its angles in the ratio of 23:4 as required. It will be seen that CE is equal to A C and ED equal to D B, and the sum of the sides of the smaller triangle DC, CE, ED= AB = 8". Q. 4. Sol.-First draw the scale of 3 French mètres to 1 inch. I have shown 15 mètres, which will be represented by a line A B 5 inches long. Draw a line at any angle to A B, divide it into three parts, and subdivide the division on the left hand into five parts, and we thus obtain single mètres. To construct the comparative scale of feet we proceed as follows:— 1 mètre 1.093 × 3 = 3.279 yards. Then 3 279 yards = 3.279 × 3 = 9.837 feet 3 mètres. 1.093 yards.. 3 mètres = To obtain the representative fraction, we find that a length of 9.837 feet is represented by a length of 1", then the fraction will be thus 1 = 1 9.837 × 12 118.044 = the representative fraction. To construct the scale, draw a line AB 5.08" in length, divide this primarily into 5 equal parts, and the first division towards the left hand into ten equal parts; these will show single feet, while the primary divisions will represent 10 feet. To measure 33 feet, take an opening of your compasses from 30 to the line showing 3 feet, as shown by the points ab on the scale. To construct a scale of yards as represented by the fraction :· 792 7 signifies that a line 1" long on a drawing represents an absolute length of 792" to be measured up or estimated for. 792 7 ..the scale of 22 yards to an inch, and supposing it be required to draw a scale long enough to measure 120 yards, then the equation will be as follows: Sol.-Draw a line A B 5.45" long, then draw a line to it at any angle, and divide the line A B as shown into 6 equal parts; each of these will give primary divisions of 20 yards. Subdivide the first division on the left band into 20 equal parts, and we thus obtain a means of measuring off single yards, and the scale is complete. Q. 5. Sol.-Draw an indefinite line, and on it mark off A B, 3" apart. With A as a centre, describe a circle of 1" radius, and with B as a centre a circle of 1" radius; then mark off on A B a distance A c' equal to the difference between the two given circles, and from A, the centre of the larger circle, describe another having A c' for its radius; bisect A B, and from the point of bisection as a centre describe a semicircle having A B for a diameter; draw a line A d through the point of intersection of the circumference of the circle A c' with this semicircle, and produce this line to E in the larger circle; join Bd, draw BF parallel to A E, then the line G H drawn through the points E F and parallel to Bd will be the required tangent to the two circles. Q. 6. Sol.-Draw the line A B = 4", then construct the angle ABC of 120° by taking any radius, and from point B describing an arc, on this arc from the point on its intersection with the line A B set off the radius of the arc twice at points 1 and 2 as shown, this will give the required angle of 120°; through the second division draw the line BC 24", and draw the corresponding parallel lines to complete the rhomboid A BCE (parallelogram); next determine the position of point D 11" from B. |