pleted divisor into the last figure of the root must not exceed the dividend. Hence, in finding the figure to be placed in the root, care must be taken to observe whether, when the multiplication is effected, the product will exceed the dividend or not. Thus, in the last example, in the case of the dividend 334, the partial divisor 4 will go eight times in 33, but since the product 8 x 48 is greater than 334, 7 is the next figure of the root, and not 8.

7. In the case of a decimal, if the number of decimal places be odd, it should always be made even by annexing a cipher, in order that the last period may be completed.

EXAMPLE. Find the square root of 41.34156. Here, adding a cipher, we point the decimal thus :41-341560 (6.429

LESSONS IN GEOGRAPHY.-X.
DISCOVERIES OF THE NINETEENTH CENTURY.

IN tracing the discoveries that have been made in different parts of the world, and the fresh details of foreign countries that have been added to our knowledge of geography during the last forty years, or thereabouts, from 1830 to the present time, our best course, after noting the progress of discovery and exploration in Asia, which was done in the last lesson, will be to glance at Oceania, which comprises the whole of our colonial empire on the south-western borders of the Pacific, and see what has been effected by travellers, voyagers, explorers, and adventurers in that portion of the world's surface.

Lying along the equator, and pretty nearly within a belt bounded by the tenth degree of north latitude on one side, and the tenth parallel of south latitude on the other, are a number of large islands, which form a long chain between South-Western Asia on the north and Australia on the south. These islands, which belong chiefly to the Dutch, are rich in vegetable and mineral produce of all kinds. Chief among them is Borneo, the largest island in the world (since geographers are now agreed in considering Australia as a continent), peopled by a ferocious race of savages, who, like all the inhabitants of the seaboard of the islands of Malaysia, are greatly addicted to piracy. Our knowledge of this part of Oceania, more especially the islands of Java and Sumatra, has been gathered from the works of Sir

Stamford Raffles and others, but since 1840 it has been considerably extended by the investigations made by Sir James Brooke in the Eastern or Asiatic Archipelago.

The story of the adventurous career of this gentleman may be told in a few words. He was an Indian officer who was severely wounded in the Burmese war of 1824-26, and shortly after quitted the service. During a voyage to China in 1830, he saw for the first time the islands of the Asiatic Archipelago, and soon became convinced that they offered a splendid field for enterprise and research. Disliking an idle life, and being a wealthy man and well able to follow up any scheme on which he had set his fancy, he determined to devote his energies and his means to the attempt of civilising the Malay races, and imparting 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 made himself acquainted with the practical duties of a sailor, and having purchased the Royalist, a schooner yacht of 150 tons, he equipped her and furnished her with costly instruments for surveying, etc., and sailed again for the Eastern Archipelago in 1838, arriving off the coast of Borneo, August 1, 1839. Here he became acquainted with the Rajah Muda Hassim, the uncle of the Sultan of Borneo, and immediately commenced a survey of the north-west coast of the island, which he relinquished in consequence of a rebellion of the Dyaks in that part of Borneo. He then visited Celebes and surveyed the Gulf of Boni, and that island. In 1840 he returned to Borneo, and having renmade a large collection of the quadrupeds, birds, and plants of dered considerable assistance to Muda Hassim in the suppres sion of the rebellion, he was rewarded with a large tract of land called Sarawak, on the north-west coast, and received the title of rajah. He now turned his attention to the suppression of piracy in the Malay waters, and in this he was successful, 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 British Government, as lately as 1858, declined to purchase Sir James Brooke's province of Sarawak.

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 in 1839, which resulted in the discovery of the Glenelg River on the north-west coast-except in New South Wales and South Australia, where the researches of the colonists had been pushed farther inland with the view of discovering suitable localities for settling and pasture lands fit for sheep-farming. In 1841, Mr. Edward John Eyre left Fowler Bay, on the south coast of South Australia, on February 25, and reached St. George's Sound, a distance of 1,040 miles from the point whence he started, on July 7, having had no other companion during the last half of his journey than a native Australian. The first attempt to traverse the interior of the country, and ascertain its general character, was made in 1844 by Captain Sturt, who had proposed to go through the length and breadth of the country from north to south and from east to west. His scheme was found to be impracticable from its magnitude; but the British Government supplied the necessary funds for the equipment of an expedition under Captain Sturt's command, to proceed along the Darling as far as Laidley's Ponds, and to try to go thence northwards across the country to the Gulf of Carpentaria. The expedition, however, was a failure as far as crossing the continent was concerned, but Captain Sturt reached a spot in latitude 24° 5' south, longitude 138° 15′ east, about 200 miles from the centre of the continent, beyond which it was found impossible to penetrate, owing to the impracticable character of the country and the want of food and water for the horses. He was therefore reluctantly compelled to retrace his steps and abandon his explorations.

Another Australian traveller, Dr. Ludwig Leichardt, was more successful. Proceeding from Moreton Bay to Jimba, the farthest station on the Darling Downs, Dr. Leichardt, accompanied by a party of seven persons, quitted this point on October 1, 1844. and made his way through the interior by a route nearly parallel to the coast to the south-east corner of the Gulf of Carpentaria, and thence to Port Essington, a distance of 1,800 miles, arriving at his destination on December 17, 1845, after a journey of a

little more than fourteen months. Many rivers were discovered, among which was the Mackenzie, on whose banks some good coal-fields were found, and several tracts of country were crossed consisting of rich arable land, admirably adapted for agricultural purposes. His subsequent expeditions, however, were not attended with the same good fortune. In 1847 he set out on a journey across the Australian continent from Sydney to Swan River, which he was compelled to abandon by events over which he had no control, after reaching as far as the downs of the Upper Mackenzie and Peak River. Nothing daunted by the unsuccessful result of his attempt to traverse Australia, he started once more on his great undertaking about the beginning of 1848, from Moreton Bay, only to meet with fresh failure and death. From that time nothing has been heard either of the

of so barren and desolate a character as had been imagined from the discovery of the great central desert by Captain Sturt in 1844.

To Burke and his companions belong the honour of having been the first to make their way from south to north, across the trackless centre of the Australian continent; but three out of the four were doomed to purchase the distinction they had so gallantly won, at the cost of their lives. Having feasted their eyes with the sight of the blue waters of the Gulf of Carpentaria, the adventurers, worn and weakened by the privations they had endured, and the fatigues and hardships they had undergone in their journey northwards, turned to retrace their steps. Gray died soon after commencing the march home. wards; but the three survivors struggled on till, in April, they

leader of the expedition or his companions, and although a few traces of their route after quitting the west bank of the Condamine River and Fitzroy Downs have been found, nothing definite respecting their fate and what led to the failure of the expedition has ever been discovered.

The principal journeys of discovery in Australia since the disappearance of Dr. Leichardt have been the expeditions of Mr. Augustus C. Gregory, in West, North-West, and North Australia in 1856 and 1858, in which many important discoveries were effected, and the perilous march of Richard O'Hara Burke, and his companions Gray, King, and Wills, across the continent from Melbourne to the Gulf of Carpentaria in 1860-61. The exploring party started from Melbourne on August 10, 1860, and reached the Gulf of Carpentaria, near the embouchure of the Cloncurry River, on February 11, 1861, having passed for miles and miles through a fertile and well-watered country, thus proving that the whole of the interior, at all events, is not

reached Cooper's Creek, a stream that crosses the boundary line between South Australia and New South Wales, towards its northern limit, where, the year before, Burke had left a few men in charge of a store of provisions. By some sad fatality, the man who had been placed at the head of the little party left to guard the depôt, weary of awaiting the return of the travellers, and thinking that they had all perished, had left the spot only a few hours before Burke and his companions reached it. Knowing that it would be utterly useless to try to overtake them, Burke and his friends directed their steps towards Mount Hopeless, a short range on the west side of Lake Blanch, where they found some settlers who had "squatted" in that locality in as wretched a condition as themselves, without clothes and without food, endeavouring to prolong existence by searching in the marshes and swamps for a plant called nardou, which they knew was frequently eaten by the natives when nothing better could be had. Again disappointed of procuring aid, and u

Votre frère fait-il batir une maison? Il en fait batir plus d'une,

Does your brother have a house built? He has more than one built.

4. It may be used in the same sense before its own infinitive.

Je fais faire un habit de drap? Vous faites faire des souliers de

cuir,

I have a cloth coat made.

You have leather shoes made.

sense of to mean.

Que voulez-vous dire ?

Votre sœur que veut-elle dire?

What do you mean?
What does your sister mean?

Ne portez-vous jamais votre habit Do you never wear your black coat? noir?

Je le mets tous les Samedis. Pourquoi n'ôtez-vous pas votre manteau ?

J'ai trop froid, j'ai peur de l'ôter.

I put it on every Saturday.
Why do you not take off your cloak?

Faites-vous raccommoder vos sou. Do you have your shoes mended? liers ?

Je fais raccommoder mes habits.
Je fais faire une paire de bottes.
Je fais creuser un puits.

Votre frère que veut-il dire ?
Que veut dire cela ?

Cela ne veut rien dire.

I have my clothes mended.

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 built? 29. I intend to have one built. 30. Does the tailor spoil your coat? 31. He does not spoil it. 32. Who spoils your clothes? 33. No person spoils them. 34. What hat do you wear? 35. I wear a black hat.

I have a pair of boots made.
I have a well dug.

What does your brother mean?
What does that mean?
That means nothing.

il

10.

1. Le Général N. met-il son uniforme ? 2. Il ne le met point. 3. Pourquoi ne portez-vous point votre manteau noir ? 4. J'ai peur de le gâter. 5. Mettez-vous vos souliers de satin tous les matins? 6. Je ne les mets que les Dimanches. 7. Il est midi; le domestique met-il le couvert ? 8. Il ne le met pas encore; va le mettre tout-à-l'heure. 9. Le dîner n'est-il pas prêt? Le domestique ôte-t-il le couvert ? 11. Il ne l'ôte pas encore, Il n'a pas le temps de l'ôter. 12. Ôtez-vous votre habit quand Vous avez chaud? 13. Je l'ôte quand j'ai trop chaud. 14. Faites-vous faire un habit de drap? 15. Je fais faire un habit de drap et un gilet de satin noir. 16. Ne faites-vous point raccommoder vos pantoufles de velours? 17. Ne faites-vous pas creuser une cave? 18. Je fais creuser une grande cave. 19. L'apothicaire que veut-il dire ? 20. Il veut dire qu'il a besoin d'argent. 21. Savez-vous ce que cela veut dire ? 22. Cela veut dire que votre frère est fâché contre vous. 23. Avez-vous envie de mettre votre mantean? 24. J'ai l'intention de le mettre, car j'ai grand froid. 25. Je vais l'ôter, car j'ai chaud. EXERCISE 58.

1. Do you take off your coat? 2. I do not take off my coat, I put it on. 3. Do you take off your cloak when you are cold? 4. When I am cold, I put it on. 5. Does your little boy take off his shoes and stockings [§ 21. 4] 6. He takes them off, but he is going to put them on again. 7. Does that little girl lay the cloth? 8. She lays the cloth every day at noon. 9. Does she take away the things after dinner? 10. She takes

The following observations relating to shadows will be found important, as containing principles that influence their treatment under very common and frequent circumstances; they may be classed as positive or decided shadows, and half tints. Decided shadows may be divided into broad shadows and cast shadows. Broad shadows are the shadows upon the object. In Fig. 72, a is the broad shadow. Cast shadows are those which are caused by the object, and are thrown upon the ground, or upon some other object. In Fig. 72, b is the cast shadow. As a general rule, for their difference of tone or depth, the cast shadow is darker than the broad shadow, simply because the cast shadow being in most cases thrown upon a more extensive surface (the ground, for instance), there is then round about the cast shadow a surface receiving the rays of light which refracts them, or throws them back again, with less power upon the side of the object in broad shadow; this lowers its tone. When it occurs that no cause for refraction is present, then the broad and cast shadows are equal in tone. In Fig. 72 the rays of light coming from the direction of ƒ fall upon the ground at g 9 g, and are thrown back again with less power upon a, causing the broad shadow a to be lighter than the cast shadow b, which cannot receive the refracted rays from 9 9 g, being the same surface or plane upon which the light falls. Again, the highest light and darkest shadow are generally together; this will be considered more fully in its place presently, when we take up the subject of half tint.

The pupil's first essay will be a very simple way of making a flat tone, before he attempts crossing lines; this simple method he will soon understand, and afterwards find to be an easy introduction to the crossing or cross-hatching system. When the surface of the shadow is large, fill it up with close perpendicular lines of unequal lengths, not permitting the ends to lap over one another, or terminate on the same level; but if the surface is small, draw continuous lines to the full extent of the shadow, at the same time observing the tone must be regulated by the strength or pressure used in the execution. Draw the square, Fig. 71, in which is shown the method when a broad surface is to be covered by a flat tint of broken lines, as explained above. Fig. 72 is given to represent the continuous lines, commencing carefully and evenly from one side of the shadow, and terminating exactly