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7.0000 ( 2-64
pleted divisor into the last figure of the root must not exceed Stamford Raffles and others, but since 1840 it has been conthe dividend. Hence, in finding the figure to be placed in the siderably extended by the investigations made by Sir James root, care must be taken to observe whether, when the multi- Brooke in the Eastern or Asiatic Archipelago. plication is effected, the product will exceed the dividend or not. The story of the adventurous career of this gentleman may Thus, in the last example, in the case of the dividend 334, the be told in a few words. He was an Indian officer who was partial divisor 4 will go eight times in 33, but since the product severely wounded in the Burmese war of 1824-26, and shortly 8 X 48 is greater than 334, 7 is the next figure of the root, and after quitted the service. During a voyage to China in 1830, 200 8.
he saw for the first time the islands of the Asiatic Archipelago, 7. In the case of a decimal, if the number of decimal places and soon became convinced that they offered a splendid field be odd, it should always be made even by annexing a cipher, in for enterprise and research. Disliking an idle life, and being a order that the last period may be completed.
wealthy man and well able to follow up any scheme on which EXAMPLE.—Find the square root of 41 34156.
he had set his fancy, he determined to devote his energies and Here, adding a cipher, we point the decimal thus :
his means to the attempt of civilising the Malay races, and im41.311560 (6-429
parting to them the benefits of commerce, gathering at the same time information about the geography and natural history
of these almost unknown regions. Returning to England, he 124 ) 534
made himself acquainted with the practical duties of a sailor, 496
and having purchased the Royalist, a schooner yacht of 150
tons, he equipped her and furnished her with costly instruments 1292) 3815
for surveying, etc., and sailed again for the Eastern Archipelago 2561
in 1838, arriving off the coast of Borneo, August 1, 1839. Here
he became acquainted with the Rajah Muda Hassim, the uncle 12849) 125160
of the Sultan of Borneo, and immediately commenced a survey 115641
of the north-west coast of the island, which he relinquished in 9519
consequence of a rebellion of the Dyaks in that part of Borneo. And there will be 3 decimal places in the square root obtained.
He then visited Celebes and surveyed the Gulf of Boni, and Here there is a remainder, or the given decimal is not what is that island. In 1840 he returned to Borneo, and having ren
made a large collection of the quadrupeds, birds, and plants of called a complete square. By adding, however, more ciphers, dered considerable assistance to Muda Hassim in the suppresmore and more figures can be obtained in the root, to any extent sion of the rebellion, he was rewarded with a large tract of land of approximation.
called Sarawak, on the north-west coast, and received the title This is a similar case to that of v7 spoken of in Art. 2.
of rajah. He now turned his attention to the suppression of To approximate to the square root of 7, we should proceed piracy in the Malay waters, and in this he was successfal, thus :
though the means at his command were but small. Ultimately he was instrumental in procuring the cession of Labuan, an island also on the north-west coast of Borneo, to Great Britain,
which is still retained as a British dependency, although the 46 ) 300
British Government, as lately as 1858, declined to purchase Sir
James Brooke's province of Sarawak. 524 ) 2400
In Australia, prior to 1840, the explorations had been chiefly confined to surveys of the coast, and short excursions inland for distances varying from fifty to one hundred miles from the shore
-such as the expedition of Lieutenants Grey and Lushington By continually adding ciphers we can carry the approximation to any in 1839, which resulted in the discovery of the Glenelg River on degree of nearuess.
the north-west coast-except in New South Wales and South 8. Similarly, in the case of any whole number which is not a Australia, where the researches of the colonists had been pashed complete square root, an approximation to the root by means of farther inland with the view of discovering suitable localities decimals can be obtained.
for settling and pasture lands fit for sheep-farming. In 1841, The integral part of the root obtained is, of course, the square Mr. Edward John Eyre left Fowler Bay, on the south coast of root of the largest integral complete square, which is less than South Australia, on February 25, and reached St. George's the given number,
Sound, a distance of 1,040 miles from the point whence he
started, on July 7, having had no other companion during the LESSONS IN GEOGRAPHY.-X.
last half of his journey than a native Australian. The first
attempt to traverse the interior of the country, and ascertain its DISCOVERIES OF THE NINETEENTH CENTURY.
general character, was made in 1844 by Captain Sturt, who had In tracing the discoveries that have been made in different proposed to go through the length and breadth of the country parts of the world, and the fresh details of foreign countries from north to south and from east to west. His scheme was that have been added to our knowledge of geography during found to be impracticable from its magnitude ; but the British the last forty years, or thereabouts, from 1830 to the present Government supplied the necessary funds for the equipment of time, our best course, after noting the progress of discovery an expedition under Captain Sturt's command, to proceed along and exploration in Asia, which was done in the last lesson, will the Darling as far as Laidley's Ponds, and to try to go thence be to glance at Oceania, which comprises the whole of our northwards across the country to the Gulf of Carpentaria
. colonial empire on the south-western borders of the Pacific, and The expedition, however, was à failure as far as crossing the see what has been effected by travellers, voyagers, explorers, continent was concerned, but Captain Sturt reached a spot in and adventurers in that portion of the world's surface.
latitude 24° 5' south, longitude 138° 15' east, about 200 miles Lying along the equator, and pretty nearly within a belt from the centre of the continent, beyond which it was found boanded by the tenth degree of north latitude on one side, and impossible to penetrate, owing to the impracticable character of the tenth parallel of south latitude on the other, are a number the country and the want of food and water for the horses. He of large islands, which form a long chain between South-Western was therefore reluctantly compelled to retrace his steps and Asia on the north and Australia on the south. These islands, abandon his explorations. which belong chiefly to the Dutch, are rich in vegetable and Another Australian traveller, Dr. Ludwig Leichardt, was more mineral produce of all kinds. Chief among them is Borneo, snecessful. Proceeding from Moreton Bay to Jimba, the farthest the largest island in the world (since geographers are now agreed station on the Darling Downs, Dr. Leichardt, accompanied by in considering Australia as a continent), peopled by a ferocious a party of seven persons, quitted this point on October 1, 1844, race of savages, who, like all the inhabitants of the seaboard and made his way through the interior by a route nearly parallel of the islands of Malaysia, are greatly addicted to piracy. Our to the coast to the south-east corner of the Gulf of Carpentaris, knowledge of this part of Oceania, more especially the islands and thence to Port Essington, a distance of 1,800 miles, arriving of Java and Sumatra, has been gathered from the works of Sir at his destination on December 17, 1845, after a journey of a
little more than fourteen months. Many rivers were discovered, of so barren and desolate a character as had been imagined from among which was the Mackenzie, on whose banks some good the discovery of the great central desert by Captain Sturt in coal-fields were found, and several tracts of country were 1844. crossed consisting of rich arable land, admirably adapted for To Burke and his companions belong the honour of having agricultural purposes. His subsequent expeditions, however, been the first to make their way from south to north, across the were not attended with the same good fortune. In 1847 he set trackless centre of the Australian continent; but three out of out on a journey across the Australian continent from Sydney the four were doomed to purchase the distinction they had so to Swan River, which he was compelled to abandon by events gallantly won, at the cost of their lives. Having feasted their over which he had no control, after reaching as far as the downs eyes with the sight of the blue waters of the Gulf of Carpenof the Upper Mackenzie and Peak River. Nothing daunted by taria, the adventurers, worn and weakened by the privations the unsuccessful result of his attempt to traverse Australia, he they had endured, and the fatigues and hardships they had started once more on his great undertaking about the beginning undergone in their journey northwards, turned to retrace their of 1848, from Moreton Bay, only to meet with fresh failure and steps. Gray died soon after commencing the march home death. From that time nothing has been heard either of the wards; but the three survivors struggled on till, in April, they
leader of the expedition or his companions, and although a few reached Cooper's Creek, a stream that crosses the boundary line traces of their route after quitting the west bank of the Con. between South Australia and New South Wales, towards its
, , ,
definite respecting their fate and what led to the failure of the in charge of a store of provisions. By some sad fatality, the expedition has ever been discovered.
man who had been placed at the head of the little party left to The principal journeys of discovery in Australia since the guard the depôt, weary of awaiting the return of the travellers, disappearance of Dr. Leichardt have been the expeditions of and thinking that they had all perished, had left the spot only Mr. Angustus C. Gregory, in West, North-West, and North Aus. a few hours before Burke and his companions reached it. tralia in 1856 and 1858, in which many important discoveries Knowing that it would be utterly useless to try to overtake were effected, and the perilous march of Richard O'Hara Burke, them, Burke and his friends directed their steps towards Mount and his companions Gray, King, and Wills, across the continent Hopeless, a short range on the west side of Lake Blanch, where from Melbourne to the Gulf of Carpentaria in 1860-61. The they found some settlers who had “squatted” in that locality in cyploring party started from Melbourne on August 10, 1860, as wretched a condition as themselves, without clothes and and reached the Gulf of Carpentaria, near the embouchure of without food, endeavouring to prolong existence by searching in the Cloncurry River, on February 11, 1861, having passed the marshes and swamps for a plant called nardou, which they for miles and miles through a fertile and well-watered country, knew was frequently eaten by the natives when nothing better thas proving that the whole of the interior, at all events, is not could be had. Again disappointed of procuring aid, and a
able to advance any further, Burke and Wills soon died of
RÉSUMÉ OF EXAMPLES. exhaustion, and King himself was at the point of death, when connaissez-vous le monsieur qui Do you know the gentleman who he was discovered by a party of the natives, who treated him parle à notre cousin ?
speaks to our cousin ? with the utmost kindness, and, when he was sufficiently re
Je connais celui qui lui parle. I know him who speals to him. covered, brought him on his way towards Melbourne, which he Comprenez-vous ce que je vous dis ? Do you understand vhat I say to you:
Who has spoken to you of this ajsair! reached in safety towards the close of the year, having met with Qui vous a parlé de cette affaire ?
The Englishman of whom you speak an expedition which had been sent out to see if any traces L'Anglais dont vous parlez est ici.
is here. could be discovered of the missing travellers.
L'Espagnol dont la seur est ici. The Spaniard those sister is here. In other parts of Oceania, little of any importance besides Que faites-vous ce matin? What do you do this morning? surveys of the coast and different parts of the waters of the Que dites-vous à notre ami ? What do you say to our friend! Pacific has been effected of late years, nor have any further Nous faisons ce que vous nous dites. We do that which you say to an discoveries been made with regard to the outlying lands of the Pour qui faites-vous cet habit ? For whom do you make this cout 1 Antarctic continent that is supposed to encircle the South Pole, De quoi parlez-vous à votre frère ? Of what do you speak to your brother?
Nous faisons ce que nous pouvons.
We do what we can. girdled by volcanic ranges that seem to forbid all access to whatever may lie beyond, although it may be mentioned that a Nous parlons de ce dont vous parlez. We speak of that of achich you speak. theory has been broached to the effect that within the belt of
VOCABULARY. burning mountains that line its gloomy ice-bound shores, it is Arriv-er, 1, arrive. Habillement, m., dress, 1 Nom, m., name. possible there may be a country in which human life may be Avec, with.
Plaisir, m., pleasure. sustained, and in which may be found productions suitable to Coffre, m., trunk. Hollandais, -e, Dutch. Presque, almost. its soil and clime, that are amply sufficient for man's require- Command-er,1, to order. Linge, m., linen. Rien, nothing. ments.
Ecossais, -e, Scotch, Monsieur, m., gentle Soulier, m., shoe.
Vrai, -e, true.
1. Qui connaissez-vous ? 2. Nous connaissons les Hollandais SECTION XXX-RELATIVE PRONOUNS [S 38].
dont vous nous parlez. 3. Quelles leçons apprenez-vous ? 4. 1. Qui, used as nominative, may relate to persons or to Nous apprenons les leçons que vous nous recommandez. 5. Co things.
que je vous dis est-il vrai. 6. Ce que vous nous dites est vrai.
7. De qui nous parlez-vous ? 8. Nous vous parlons des Écossais Les fleurs qui sont dans votre The flovers which in your qui viennent d'arriver. 9. Savez-vous qui vient d'arriver: 10. jardin,
12. Elles ne font presque rien, 2. Qui, used as the object of a verb, can only be said of per. 11. Vos seurs que font-elles ? It is used interrogatively with or without a preposition.
elles n'ont presque rien à faire. 13. Que mettez-vous dans votre coffre ? 14. Nous y mettons ce que nous avons, nos habillements
y Qui votre frère voit-il ? Whom does your brother see?
et notre linge. 15. N'y mettez-vous pas vos souliers ? 16. De qui parlez-vous ce matin ? Of whom do you speak this morning? Nous y mettons les souliers dont nous avons besoin. 17. De
18. Nous avons besoin de ce que nous 3. Quo may be said of persons or things. It can never be quoi avez-vous besoin ? understood, and must be repeated before every verb [Sect. fait et ce qu'il dit. 21. Ne voulez-vous pas le leur dire : 23
19. Cet enfant sait-il ce qu'il fait ? 20. Il sait ce qu'il XVIII. 1].
Avec beaucoup de plaisir. 23. Faites-vous ce que le marchand Les personnes que nous voyons, Tho persons whom ice see.
vous commande ? 24. Nous faisons ce qu'il nous dit. 25. Il Les langues que nous apprenons, The languages which we learn.
parle de ce dont vous parlez. 4. Ce que is employed for that which, or its equivalent whot.
EXERCISE 56. Ce que vous apprenez est utile, That which you learn is useful.
1. Have you what (ce dont) you want? 2. We have what we Trouvez-vous ce que vous cherchez? Do you find what you seek ?
want. 3. Is the gentleman whom you know here? 4. The
lady of whom you speak is here. 5. Is she just arrived ? • 5. Que answers to the English pronoun what, used absolutely (Sect. XXV. 2)? 6. She is just arrived. 7. Do you know that before a verb.
gentleman ? 8. I know the gentleman who is speaking with
9. Do you know his name? 10. I do not know Que pensez-vous de cela ? What do you think of that?
his name, but I know where he lives (demeure). 11. What do 6. Quoi, when not used as an exclamation, is generally pre- you do every morning? 12. We do almost nothing; we have ceded by a preposition, and relates only to things.
very little to do. 13. Does the tailor make your clothes ? 14.
He makes my clothes, my brother's, and my cousin's. 15. Do De quoi voulez-vous parler ? Of what do you wish to speak ? you know what you say ? 16. I know what I say, and what I A quoi pensez-vous ? Of what do you think? do. 17. Do you know the Scotchman of whom your brother
19. What does he put into his ?: Lequel, m., laquelle, f., lesquels, m. pl., lesquelles, f. pl., speaks? 18. I know him well.
trunk ? which, or which one (Sect. XVII. 6), or which ones, relate to per
20. He puts his clothes. 21. Is that which you say
true ? sons or things. They may be preceded by a preposition.
22. What I say is true. 23. Do you understand that
which I say to you ? 24. I understand all that you say. 25. Lequel avez-vous apporté ?
Which one have you brought ? Of whom does your brother speak ? 26. He speaks of the Duquel parlez-vous ? Of which one do you speak?
gentleman whose sister is here. 27. Is your brother wrong to 8. Dont, of which, or of whom, whose, may relate to persons or
do what he does ?
28. He cannot be wrong to do it. things, in the masculine or feminine, singular or plural. It can
What are you doing? 30. I am doing that which you do. 31. never be used absolutely, and must always be preceded by an
Where do you put my books ? 32. Into (dans) your brothers antecedent. It is preferable to de qui or duquel, etc.
trunk. 33. Is your brother here ? 34. He is not here. 35.
He is at my brother's, or at my father's.
SECTION XXXI.-IDIOMATIC USES OF METTRE, ETC. vous parle, sister speaks to you.
1. The verb mettre is used in the same sense as the English 9. PRESENT OF THE INDICATIVE OF THE IRREGULAR VERBS.
to put on, in speaking of garments. Mettre le couvert means
to lay the cloth, or set the table. DI-RE, 4, to say. FAI-RE, 4, to make, to do. I METT-RE, 4, to put.
Quel chapeau mettez-vous ?
What hat do you put on? Je dis, I say, də cay, or Je fais, I make or do, I | Je mets, I put, do put, Votre frère met son habit noir, Your brother puts on his black cout. am saying.
am making or doing. ! or an putting, Le doinestique va mettre le couvert, The servant is going to lay the clothe Tu dis. Tu fais.
2. Ôter means to take off, to take away, to take out.
Non domestique öte son chapeau, My servant takes off his hat.
Take away that book from the table. Ils disent. i Ils font. Is mettent. N'a-t-on pas êté le diner?
Have they not taken away the dinne!
3. The verb faire is used before another verb, in the sense of away the things every day. 11. Do you intend to have a coat to have, to cause.
made ? 12. I intend to have a coat made. 13. I am going to Votre frère fait-il bátir une maison? Does your brother have a house built? have a coat and a vest made. 14. Does your brother have his Il en fait bâtir plus d'une, He has more than one built.
boots mended ? 15. He has them mended. 16. What does
your son mean? 17. I do not know what he means. 18. I. 4. It may be used in the same sense before its own infinitive.
he angry with me or with my brother ? 19. He is neither angry Je fais faire un habit de drap ? I have a cloth coat made.
with you nor with your brother. 20. Is he afraid to spoil his Vous faites faire des souliers de You have leather shoes nyado.
coat? 21. He is not afraid to spoil it. 22. Does the diuggist cuir,
want money? 23. He does not want money. 24. Has your 5. Vouloir (Sect. XXVII. 6] followed by dire is used in the sister taken my book from the table ? 25. She has not taken it sense of to mean.
away. 26. Why do you take off your shoes ? 27. I take them
off because they hurt me. 28. Do you intend to have a house Que voulez-vous dire ? What do you mean?
built ? 29. I intend to have one built. 30. Does the tailor Votre sour que veut-elle dire ? What does your sister mean?
spoil your coat? 31. He does not spoil it. 32. Who spoils RÉSUMÉ OF EXAMPLES.
your clothes ?
33. No person spoils them. 34. What hat do Ne mettez-vous pas vos habits ?
35. I wear a black hat.
you wear ? Do you not put on your clothes ? J'ai peur de les gâter.
I am afraid of spoiling them. Ne portez-vous jamais votre habit Do you never wear your black coat ? noir ?
LESSONS IN DRAWING.–X. Je le mets tous les Samedis. I put it on every Saturday. Pourquoi n'otez-vous pas votre Why do you not take ojf your cloak ? We must now direct the attention of the pupil to shading and manteau ?
foliage; but before commencing, let us earnestly advise him to J'ai trop froid, j'ai peur de l'ôter. I am too cold, I am afraid to take it go over the previous lessons again, so that he may be well pre.
pared to follow us in a course of instruction that will require all Faites-vous raccommoder vos sou. Do you have your shoes mended ?
the knowledge he can possibly obtain, and a considerable amount liers? Je fais raccommoder mes habits.
of practice in using the pencil, to give him power, confidence, I have my clothes mended. Je fuis faire une paire de bottes. I have a pair of boots made.
and freedom of execution, combined with truth of representaJe fais creuser un puits. I have a well dug.
tion. We have already warned him against sketching before he can Votre frère que veut-il dire ? What does your brother mean?
draw well; the danger of falling into a slovenly manner is now Que veut dire cela ? What does that mean?
before him. He must be careful and slow at first in that which Cela ne veut rien dire. That means nothing.
he is about to undertake, for when shading and foliage are introOtez-vous vos souliers et vos bas ? Do you take off your shoes and stock duced, he must bear in mind that in proportion to the care, per
severance, and patience he bestows upon his work, will be the Je n'ote ni les uns ni les autres, I take oft" neither these nor those. Le diner est prêt; le domestique Dinner is ready; the servant is going carelessness of execution will degenerate into coarseness and
beauty and effectiveness of the result; while, on the other hand, 12 mettre le couvert.
to lay the cloth. Voulez-vous ôter le couvert ?
scribble. He will, in the one case, prove himself to be a clever Will you take away the things from the table !
and satisfactory draughtsman, or, in the other, one totally inJe vais mettre le couvert. I am going to lay the cloth.
capable of producing anything worthy of admiration, or fit to be Je vais ôter le couvert. I am going to take away the things. employed for any useful purpose.
The following observations relating to shadows will be found VOCABULARY.
important, as containing principles that influence their treatment Apothicaire, m., drug- Gên-er, i, to squeeze, | Prêt, -e, ready. under very common and frequent circumstances ; they may be gist.
Raccommod-er, 1, to classed as positive or decided shadows, and half tints. Decided Après, after. Gilet, m., waistcoat. mend.
shadows may be divided into broad shadows and cast shadows. Cave, f., cellar.
Grand, -e, large, very. Remett-re,4, to replace, Broad shadows are the shadows upon the object. In Fig. 72, a is Crens-er, 1, to dią. Manteau, m., cloak. to put on again.
the broad shadow. Cast shadows are those which are caused Dimanche, m., Sunday. Midi, noon, midday. Tout-à-l'heure, immodinner. Noir, -e, black.
by the object, and are thrown upo. the ground, or upon some Faché, -e, sorry, angry. Pantoufle, f., slipper. Uniforme, m., uniform. other object. In Fig. 72, b is the cast shadow. As a general rule, Gát-er, I, to spoil. Pourquoi, why.
Velours, m., velvet. for their difference of tone or depth, the cast shadow is darker
than the broad shadow, simply because the cast shadow being in EXERCISE 57.
most cases thrown upon a more extensive surface (the ground, 1. Le Général N. met-il son uniforme ? 2. Il ne le met point. for instance), there is then round about the cast shadow a sur3. Pourquoi ne portez-vous point votre manteau noir ? 4. J'ai face receiving the rays of light which refracts thein, or throws peur de le gâter. 5. Mettez-vous vos souliers de satin tous les them back again, with less power upon the side of the object matins ? 6. Je ne les mets que les Dimanches. 7. Il est midi; in broad shadow; this lowers its tone. When it occurs that no le domestique met-il le couvert ? 8. Il ne le met pas encore; il cause for refraction is present, then the broad and cast shadows va le mettre tout-à-l'heure. 9. Le dîner n'est-il pas prêt? 10. are equal in tone. In Fig. 72 the rays of light coming from the Le domestique ôte-t-il le couvert ?. 11. Il ne l'ôte pas encore, direction of s fall upon the ground at g 9 g, and are thrown back i n'a pas le temps de l'ôter. 12. Ôtez-vous votre habit quand again with less power upon a, causing the broad shadow a to be vous avez chaud ? 13. Je l'ôte quand j'ai trop chaud. 14. lighter than the cast shadow b, which cannot receive the refracted Faites-vous faire un habit de drap ? 15. Je fais faire un habit rays from g 9 g, being the same surface or plane upon which the de drap et un gilet de satin noir. 16. Ne faites-vous point light falls. Again, the highest light and darkest shadow are raccommoder vos pantoufles de velours ? 17. Ne faites-vous generally together; this will be considered more fully in its par creuser une cave ? 18. Je fais creuser une grande cave. place presently, when we take up the subject of half tint. 19. L'apothicaire que veut-il dire ? 20. Il veut dire qu'il a The pupil's first essay will be a very simple way of making a besoin d'argent. 21. Savez-vous ce que cela veut dire ? 22. Cela flat tone, before he attempts crossing lines; this simple method he Teut dire que votre frère est fâché contre vous. 23. Avez-vous will soon understand, and afterwards find to be an easy introducenvie de mettre votre manteau ? 24. J'ai l'intention de le tion to the crossing or cross-hatching system. When the surface mettre, car j'ai grand froid. 25. Je vais l'ôter, car j'ai chaud. of the shadow is large, fill it up with close perpendicular lines of
unequal lengths, not permitting the ends to lap over one another, EXERCISE 58.
or terminate on the same level; but if the surface is small, draw 1. Do you take off your coat? 2. I do not take off my coat, continuous lines to the full extent of the shadow, at the same
3. Do you take off your cloak when you are cold ? time observing the tone must be regulated by the strength or 4. When I am cold, I put it on. 5. Does your little boy take pressure used in the execution. Draw the square, Fig. 71, in off his shoes and stockings ($ 21. 4]? 6. He takes them off, which is shown the method when a broad surface is to be covered but he is going to put them on again. 7. Does that little girl by a flat tint of broken lines, as explained above. Fig. 72 is lay the cloth? 8. She lays the cloth every day at noon. 9. given to represent the continuous lines, commencing carefully Does she take away the things after dinner ? 10. She takes and evenly from one side of the shadow, and terminating exactly
I put it on.