a

400

afterwards, a repetition of the process, when, in a future case, the object above varies in size and form from the one below, the difficulties will not be so great. Probably it will be advisable to recapitulate some of the work, to prevent failure. Make a b equal to the distance the object is to the left of the eye; draw b PS; make bf equal to the distance the nearest angle is within the picture; and because the line from b vanishes at PS, therefore the line from fƒ, to cut off the point within, must be drawn to DE', the distance point of E or PS, to determine the nearest part of the object c. (Some writers on Perspective call the DE the DPS, meaning the distance of the point of sight. It makes no practical difference, because DE1 or DE represents the space between the eye and the picture plane, that is, between E and PS; PS being on the picture plane, which is supposed to be in a perpendicular position; the line below, marked PP, being its base.-See Fig. 21, Vol. II., page 360.) Through c, directed from DVP', draw a line to r; make r s equal to the length of the block; draw from

s back again to DVP', which will cut the vanishing line from c to vpl in m; cm will then be the per. spective representation of the length of the block. Through c, directed from DVP2, draw a line to n; make no equal to the width of the block, and rule from o back again to DVP2; this will cut the line from c to VP2 in v; cv will be the width of the block. We trust the remainder of the work, including the thickness of the block, will present no difficulties.

We will make further use of this problem, by changing the proportions of the upper block to 4 feet long, and 2 feet wide; its plan being in the centre of the plan of the lower one. In this case a plan must be drawn both of the blocks and the PP, to show how the former are situated and con

and from the PP.

k

to the right of c d. Upon d m draw the plan of the lower block; afterwards the plan of the upper one, eh ik; all its sides being one foot within the larger plan. In Fig. 59 we have represented only the upper block; the lower one will be simply a repetition of the one in Fig. 57, which our pupils

PS PP

Fig. 58.

m

must not omit repeating when drawing Fig. 59. We will now commence with the HL, and proceed upwards. The E, DE, PP, and PS will be the same as in Fig. 57. The distance of the nearest angle a from the PP must be measured from b to c on the PP, and equal to PS c, taken from Fig. 58. The distance cf, of the point a within, must be equal to ƒ e (Fig. 58). Draw from a to VP1, and also the other way to the PP in m; a line from m perpen-dicularly to PP will be the line of contact, upon which to measure the thickness, m n, of the block. The length and breadth to be cut off on the lineswhich vanish to VP1 and VP2 must be taken from the plan, viz., eh for the length, and e k for the breadth, as shown in e h and o k (Fig. 59). It

Fig. 60.

DE

DE

HL

DVP2

PS

Dvp1

VP2

DO

PP

nected with the latter, and from which we obtain the proportions and distances of the several parts from one another Therefore Fig. 58 is the first consideration; it is a plan constructed according to the particulars given in the question. Draw the PP. Anywhere, say from a, draw the line a b, at an angle of 40° with the PP. Upon this last line find the point d, the nearest angle within the PP; draw d e perpendicularly with the PP; place PS 3 feet

DP found, and in all respects treated as are the vanishing lines of retiring sides.

PROBLEM XXXVI. (Fig. 60).-Two square slabs of different dimensions, the smaller of which is lying upon the other; the plans of their centres coincide; the nearest angle of the lower one touches the PP. The side of the larger slab is 4.5 feet; the smaller, 3 feet. Thickness of each, 1 foot. Angle of sight, distance, and height of the eye, as in the last problem.

A portion of the subject represented by the plan a must be constructed, for the purpose of obtaining the length of that part of the diagonal line between a and b. As the angles of the object are right angles, therefore the angle formed by the vanishing lines from E to the HL will be a right angle. Bisect it by the line Eo; E o will then be the vanishing line of the diagonal of the slabs, and o the VP. Find its distance point by drawing from o the arc E DO. After the lower slab, m c d e, is drawn according to previous instructions, produce the perpendicular me through v; make me and cv equal to the thickness of the slabs; in other words, mark their heights on the line of contact from m. Draw the diagonals m o, co, and vo; also the diagonal d e. Our object now is to determine the nearest angle of the upper slab. Upon the diagonal of the base, mo, we must cut off the distance of a b, in the plan A. Make mn equal to the line a b, and from n draw a line to DO, sutting the retiring diagonal m o in h; m h will then be the perspective distance of a b. From h draw the perpendicular hsr; this perpendicular, cutting the diagonal from c, gives the nearest angle of the upper slab in s; cv being the measured thickness of the upper slab, therefore s r is the perspective thickness. The diagonal d e, cutting the retiring base of the upper slab from s each way, gives the perpendicular edges at 1 and k. The remaining retiring lines must be directed to their respective vanishing points.

2. How many bricks 9 inches long, 4 broad, and 4 thick, will be required for a wall 30 feet long, 20 feet high, and 4 feet thick, allowing 64 per cent. of the space for mortar ?

3. When hay was £5 per ton, a well-to-do farmer hid himself in a load, and his weight, of course, was added in that of the hay. Before the hay was shipped, the trick was detected; and after another weighing, 7s. 6d. was deducted from the price. Find the farmer's weight.

4. A room is 20 feet long, 16 broad, and 12 high. If pure gold be worth £4 5s. per oz. Troy, and a cubic foot of gold weigh 19260 oz. avoirdupois, what is the value of the gold which will exactly fill the room?

5. A wine-merchant buys 12 dozen of port at 84s. per dozen, and 60 dozen more at 48s. per dozen; he mixes them, and sells the mixture at 72s. per dozen: what profit per cent. does he realise on his original outlay?

6. How many cubes of which the sides are 2 inches can be cut out of a cube of which the side is 22 inches ?

7. A young lady desires to paper her room with postagestamps, but being herself unable to calculate the number which will be required, she supplies the following data :-Her room is 14 feet 9 inches long, 9 feet 3 inches broad, and 10 feet 6 inches high; it contains two windows, each 5 feet by 4 feet, and three doors, each 6 feet by 3 feet; a postage-stamp is of an inch long, and of an inch broad. Make the calculation for her.

8. The daily issue of the Times is 60,000 copies. Three days of the week it consists of 3 sheets, and for the remaining three of 4 sheets. If a sheet be 3 feet long and 2 feet broad, find the number of acres which the weekly issue of the Times would

11. Find the length of the side of a square which is equal in area to the rectangle, the sides of which are 513 yards 1 foot 11 inches and 1628 yards 11 inches.

How much would it cost to cover the area with turf at 41d. per square yard ?

12. If 100 lbs. of tea be bought at 4s. 4d. and sold at 58., and 100 lbs. of sugar bought at 6d. and sold at 7d., what profit per cent. will be realised on the whole outlay?

13. The removal of a quantity of brick earth, 32 square yards in area and of a uniform depth of 2 yards, costs £2 2s. 8d.; what is the cost of the removal of a cubic yard ?

14. A person's average annual expenditure, from the year 1830 to the year 1850 inclusive, is £391 9s. 2d. He finds that in 1830 he spent £391 16s., and in 1851, £445 8s. 9d. What was his average annual expenditure from 1831 to 1851 inclusive?

15. In Austria 120 gulden (paper currency) are worth 100 silver gulder. What amount of paper money should be obtained for £10 sterling if the value of £1 be 9 gulden 30 kreutzers in silver (60 kreutzers 1 gulden) ?

=

16. What sum at £4 per cent. compound interest will amount in two years to £405 12s. ?

17. A room is 60 feet long by 29 feet wide; how many people can be seated in it on chairs 1 feet wide, and placed 2 feet apart from back to back, allowing a clear passage 3 feet wide down the middle of the room and a space of 15 feet deep at one end? 18. Divide 296-293 by 41.967 so as to have six decimal places in the quotient.

19. Find the length of the longest chain in terms of which 88 yards 2 feet 5 inches and 119 yards 2 feet 1 inch can both be expressed as integers.

20. By selling at 4 per cent. profit, a tradesman gained £47 148.; what was the prime cost of his goods?

21. The interest on a certain sum of money for two years is £71 16s. 7 d., and the discount on the same sum for the same time is £63 17s., simple interest being reckoned. Find the rate per cent. and the sum.

22. A barters some tea with B for flour which is worth 28. 34d. a stone, but uses a false pound weight of 15 oz. What value should B set upon his flour that the exchange may be fair?

23. A garrison consisting of 2000 men, fixds during a siege that it has provisions for six weeks; at the end of a fortnight 400 men are killed in a sally. How long will the provisions last?

24. Find the expense of painting a room 23 feet 6 inches long, 12 feet 7 inches high, and 17 feet 6 inches broad, at 3s. 6d. a square yard.

25. The gold procured from Australia in nine months in 1851 amounted to 313644 ounces. In 1861, the New Zealand gold. fields yielded 314438 ounces in the same time. What is the excess in weight and value (at £3 17s. 101d. per ounce) of the average monthly return from New Zealand over that from Australia?

26. Find the difference between the amount of £247 10s. for two years, and the present worth of the same sum due after two years at 5 per cent.

27. How many bricks, of which the length, breadth, and thickness are 9, 6, 3 inches respectively, will be required to build a wall whereof the length, height, and thickness are 72, 8, and 1 feet?

28. Express as the fraction of £10 the difference between £83 and £8 × ; and find the value of of a ton of sugar when of a ton is worth £6 5s.

29. Find two numbers whose greatest common measure is 179, and least common multiple 56385.

30. In which way had one better buy sugar, at 3 guineas per cwt., or at £2 16s. 4d. per quintal of 100 lbs. ? and how much is one buying when the gain by the more advantageous way is a guinea?

31. On what sum is the daily interest at 4 per cent. one penny? 32. If 16 darics make 17 guineas, 19 guineas make 24 pistoles, 31 pistoles make 38 sequins, how many sequins are there in 1851 darics ?

33. Which way had one better buy coffee, at 6 guineas a cwt., or at £5 12s. 4d. per quintal of 100 lbs. ? And how much is one buying, when the loss on the less advantageous way is £17

34. If 2 guineas make 3 napoleons, and 15 rix-dollars make 4 napoleons, and 6 ducats make 7 rix-dollars, how many ducats are there in £490 ?

35. Three per Cents. are offered at 901, Five per Cents. at 1504; in which should one invest ? And how much is one investing when the difference of income is £1?

36. How much ore must one raise that, on losing 13 in roasting, and of the residue in smelting, there may result 506 tons of pure metal ?

37. An analysis of the Board of Trade returns for 1861 respecting shipwrecked lives gives the following results :-Saved by lifeboats, 134 per cent.; by rocket and mortar apparatus, 8 per cent.; by ships' boats, etc., 62 per cent.; by individual exertion,per cent.; lost, 16 per cent. Determine the number of lives saved by the several means enumerated, corresponding to a loss of 864 lives.

38. A monolith of red granite in the Isle of Mull is said to be about 108 feet in length, and to have an average transverse section of 113 square feet. If shaped for an obelisk it would probably lose one-third of its bulk, and then weigh about 600 Determine the number of cubic yards in such an obelisk, and the weight in pounds of a cubic foot of granite.

tons.

39. A person invests £5187 10s. in the Three per Cents. at 83, and when the funds have risen to 85, he transfers three-fifths of his capital to the Four per Cents. at 96. Find the alteration

in his income.

40. Find the square root of 767376, and the length of the side of a square whose area is equal to that of a rectangle, the sides of which are 47·14 yards and 210 yards.

41. A and B contract to execute a certain order for £1245. A employs 100 children for 3 months, 80 women for 2 months, and 40 men for 1 month; B employs 120 children for 2 months, 60 women for 14 months, and 80 men for 24 months. If the work done in the same time by a child, a woman, and a man be in the ratio 1: 2: 3, find the sum of money which A and B must each receive.

42. The area of the coal-field of South Wales is 1000 square miles, and the average thickness of the coal is 60 feet. If a cubic yard of coal weigh 1 ton, and the annual consumption of coal in Great Britain be 70,000,000 tons, find the number of years for which this coal-field alone would supply Great Britain with coal at the present rate of consumption.

43. If the coal annually consumed in this country (70,000,000 tons) were piled up into a pyramid, having for base the great court of Trinity College, Cambridge, the dimensions of which are 110 by 90 yards, find the height of the pyramid. (N.B. The volume of a pyramid is equal to the area of the base multiplied into onethird of the height.)

44. A man invests £4297 10s. in the Three per Cents. at 95). He sells out one-third of his stock when the funds have fallen to 94, £1600 stock when they have risen to 964, and the remainder at par. What sum does he gain?

If he invest the proceeds in the French Three per Cents. at 67.50, what is the difference in his income, 25 francs being taken as equivalent to £1 ?

45. Gunter's Chain is taken along the line A D (920 links) in the six-sided field ABCDEF; the distances of the points B, C, E, F from A D are 182, 250, 190, 136 links, meeting it at points 120, 560, 750, 95 links from A. Find the acreage of the field. (N.B. The area of a triangle is half the rectangle contained by its base and its height.)

46. A ring weighs 1 dwt. 4 gr., and is worth £1 2s. If 1050 such rings be packed in a box weighing 3 lbs., what would it cost to convey them 144 miles at the rate of 5s. per ton per mile, insurance being demanded at the rate of per cent.?

47. If £1 exchanges for 24-8 francs, and the French Three per Cents. are selling for 70-2 francs, what amount of the latter stock will £539 buy?

48. A contractor engaged to make 2 miles of road in 84 days; but after employing 60 men for 54 days, he found they had only finished 880 yards. How many additional men must be employed to finish the work within the prescribed time? 49. The fall in the price of paper was 14d. per lb., and the weight of a certain book 14 lbs. The paper manufacturer realised 10 per cent. on his sale, and the publisher 20 per cent. on his outlay. What reduction might be made in the price of the book on the fall in the price of paper, allowing to each tradesman the same rate of profit as before?

50. How soon will a sum double itself at 12 per cent. compound interest ?

51. The external length, breadth, and height of a rectangular wooden closed box are 18 inches, 10 inches, and 6 inches respectively, and the thickness of the wood is inch. When the box is empty, it weighs 15 lbs.; and when filled with sand, 100 lbs. Compare the weights of equal bulks of wood and sand.

52. The sum of £177 is to be divided among 15 men, 20 women, and 30 children in such a manner that a man and a child may together receive as much as two women, and all the women together receive £60. What will they respectively receive ?

READINGS IN FRENCH.-XII.

JACOPO.

SECTION III.

ELISA, un peu rassurée par la promesse de son oncle, commença, d'une voix tremblante, son récit. Elle raconta comment elle avait renversé la petite paysanne, et comment ses œufs avaient été brisés.

"Allons! c'est très-bien, Élisa, tu as été franche ; comme ce chargeant(b) de solliciter aussi ta mère en ta faveur." n'est pas trop ton habitude, je veux t'en(a) récompenser en me

'Maman," dit alors Napoléon, "j'ai encore un grâce à vous demander. Vous me donnez dix sous par(c) semaine pour mes menus plaisirs. (d) Eh bien! achevez de payer les œufs de cette pauvre petite qui attend là ce que tout cela va devenir, (e) et vous ne me donnerez plus rien jusqu'à ce que nous soyons quittes."

"D'accord," (f) dit Madame Laetitia en faisant approcher la petite paysanne, et lui donnant un petit écu. "Napoléon, en voilà pour six semaines."

L'enfant courut à Napoléon, et voulut lui remettre les deux pièces de monnaie qu'elle avait reçues de lui au moment où l'accident était arrivé; mais il refusa.s

Cette probité plut(g) à Madame Bonaparte, qui alors interrogea la petite paysanne. Elle apprit que c'était la fille d'un pauvre pêcheur, que sa mère était malade," qu'elle demeurait dans une chétive cabane, 12 sur le bord de la mer, à quelque distance 13 de l'endroit où son panier avait été renversé.

"Ta mère est malade, dis-tu, mon enfant ? elle n'a pas de médecin qui la soigne, sans doute. J'irai la voir."

"Oh! maman, je vous en prie," s'écria Napoléon, allons-y tout de suite.15 Nous reconduirons Charlotte." "Volontiers," répondit Madame Bonaparte. "Allons, 16 mes enfants, partons."

Les enfants ne se le firent(h) pas répéter. Quelques instants après, ils arrivèrent au pied d'un rocher."7

18

"C'est là," dit Charlotte, en désignant une misérable cabane." Lorsqu'ils entrèrent, un jeune garçon de douze ans était occupé à faire un filet;19 une toute petite fille était assise à terre(i) et mangeait une croûte de pain; une enfant, beaucoup plus jeune encore, dormait dans un berceau cassé,20 couvert d'une vieille courtepointe presque en lambeaux.

Vous êtes malade, ma bonne femme," dit Madame Lætitia en s'approchant; "un médecin vous donne-t-il des soins?" "Ah! Madame, de pauvres gens comme nous ne doivent pas réclamer des soins qu'ils ne peuvent payer."

Pendant ce dialogue, Napoléon s'était approché de l'enfant qui faisait du filet, et n'avait pas tardé à faire avec lui plus ample connaissance.

Depuis ce temps, la cabane était souvent le but des promeJacopo, tel est le nom du fils du pêcheur, s'était surtout concilié les onnes grâces 1o de Napoléon, qui, sur ses menus plaisirs, trouvait toujours le moyen de mettre quelque chose de côté pour lui. Aussi était-il devenu pour Jacopo l'objet d'une sorte de culte et d'adoration; pour Napoléon, Jacopo aurait tout sacrifié,12 jusqu'à sa vie.

nades de Madame Laetitia et de ses enfants.

Cependant, lorsque Napoléon eut atteint(c) l'âge de dix ans, 13 il dut(d) quitter Ajaccio. Avant de partir, l'enfant alla faire ses adieux1 à la famille du pêcheur, et ce ne fut pas sans verser quelques larmes qu'il se sépara de Jacopo. Il avait une trèsjolie boîte en ébène, 15 de la grandeur à peu près d'une tabatière, à laquelle il(e) tenait beaucoup; il y grava son nom avec la pointe d'un canif, et 16 en fit cadeau à Jacopo, qui la reçut en sanglotant, et la plaça immédiatement sur son cœur. Jamais ce souvenir ne devait le quitter.

Nous ne suivrons point Napoléon dans les différentes phases de sa prodigieuse fortune.

Le deux décembre mil huit cent cinq,19 l'armée française était campée dans les plaines d'Austerlitz. Le soleil se lève; entouré de ses maréchaux, l'Empereur attend, 19 pour donner ses ordres, que l'horizon soit tout à fait éclairci.

"Soldats," s'écria-t-il, "il faut finir cette campagne par un 20 coup de tonnerre!" Et le combat s'engage aux cris de Vive l'Empereur!

KEY TO EXERCISES IN LESSONS IN FRENCH.

EXERCISE 146 (Vol. II., page 386).

1. M. votre beau-frère compte-t-il louer le rez-de-chaussée ? 2. Il compte louer deux appartements au second. 3. Combien de chambres M. votre fils compte-t-il louer ? 4. Il compte louer deux chambres au second. 5. Préfère-t-il demeurer au second? 6. Il préftre demeurer au rez-de-chaussée. 7. M. votre père veut-il venir diner demain avec nous ? 8. Il compte venir demain à deux heures. 9. Préférez-vous demeurer en haut ou en bas? 10. Je préfère demeurer en haut. Mlle. votre sœur sait-elle toucher le piano? 12. Elle sait jouer du piano. 13. Où comptez-vous demeurer? 14. Nous comptons demeurer chez M. votre père. 15. Voulez-vous monter dans ma chambre ? 16. Je descendrai chez votre père. 17. Désirez-vous demeurer au rez-deLaussée ? 18. Je désire demeurer au second. 19. Faut-il rester ici ?

11.

20. Il n'est pas nécessaire d'y rester. 21. Que pensez-vous faire de votre livre? 22. Je pense le donner à mon fils. 23. Que voulez-vous que je dise à ce monsieur? 21. Je veux le prier de me faire un plaisir. 25. Voulez-vous envoyer ce faisan à Mme. votre mère ? 26. Je désire le lui envoyer, elle est malade. 27. Mlle. votre sœur ne sait-elle pas jouer du violon? 28. Elle ne sait pas jouer du violon, mais elle sait. jouer de la guitare. 29. Mlle. votre sœur désire-t-elle demeurer en haut? 30. Elle préfère demeurer en bas. 31. Ne voulez-vous pas me faire ce plaisir ? 32. Je le ferai volontiers. 33. M. votre frère ne peut-il pas rester à dîner avec nous aujourd'hui ? 34. Il a promis à mon père de venir dîner avec lui. 35. Notre ami sait lire, écrire et compter.

LESSONS IN SHORTHAND.-IX.
METHOD OF PRACTICE.

134. The learner should not attempt, at first, to bring into use all practise, for two or three weeks, a rather lengthened style of Phonethe abbreviating principles here introduced. He should be content to graphy, making much use of the simple consonants, until he feels confidence in the use of the phonographic characters, and in the principle of phonetic spelling. He may then gradually adopt the double and treble letters, and the prefixes and affixes, etc., as he requires them; that is, as he feels that the style he is employing is not brief enough for the manual dexterity he has acquired. In selecting one out of two or more possible forms for any word, the student must recollect that great case in writing, and, consequently, the saving of time, is not secured by using hooked and grouped, and especially half-sized, letters, on all possible occasions; but he must learn to make a judicious selection, and employ those which are most readily made in any given case, and not adopt those forms that merely take up the least room.

135. The pupil should spend as much time in reading as in writing Phonography. Printed rather than manuscript Phonography should be selected for this purpose. To those who wish to excel in Phonography as an Art, the perusal of some shorthand volumes is recommended before a rapid style of writing is acquired, in order that the style may be formed on a correct model. When learning, the following method of practice will be found useful:-Take a specimen of printed shorthand, and copy it out in longhand; then transcribe the article into phonetic shorthand, from the longhand copy, and compare the shorthand exercise with the original : correct, if necessary, and re-write. This course should be continued until a correct style is obtained. Much advantage will also be derived from transcribing phonetic printing into shorthand. In this case the pupil has the phonetic spelling of each word provided to his hand. The "Phonetic Journal," published weekly, may be used for these purposes, as it contains both shorthand and phonetic priuting. In a class, after an exercise has been written from the dictation of the leader, let the books change hands, and each student read and correct the writing of another.

136. The pupil is now prepared to employ in his writing the full list of Grammalogues used in the Corresponding Style of Phonography:

137. Logograms that are written above the line (except horizontal and vowel logograms), or through the line, cannot be employed on unruled paper. These words should, in that case, have their remaining consonants or vowels inserted. They are employed in printed Phonography, although it is done on unruled paper, that it may serve as a guide to the writer of the Corresponding Style, and the line underneath, or through, such words, is dotted in. In manuscript Phonography it is less trouble to vocalise such words than to insert this dotted line. The additional grammalogues used in the Reporting Style (from 500 to 1,000, according to the rapidity of the speaker) are mostly single-stroke words whose vowels are omitted, and the words are placed in position in accordance with the rule given in paragraphs 139, 140. The learner will now do well to study with the utmost care the following table of grammalogues.

ft In the preceding Tables, some words are printed with a hyphen, thus, give-n; or, with a double termination; thus, importan; to intimate that the corresponding logograms represent both give and given, important and importance. The context will show which is meant.

Has, his may be written by placing the aspirate dot before the circles which represents as, is, or by thickening the circle on one side. Theoretically, you is (yoo), but the light sign (yoo) may be used because the latter sound does not occur in English. In like manner the circle is commonly written light, like s, and the heavy hook zhon (in vision) light, like shon (tion).

CH

which; each +

J

large; advantage

mr

jn

general

jnt

K

ms

gentleman, gentle- mp

can come

[men

mt

kl

с

call*, equal

kr

care

N

nr

M

r

are; our +

read* (pr.tense), word