292 



THE POPULAE EDUCATOR. 



pkted 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 multi- 

 plication 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 '341 56. 



Here, adding a cipher, we point the decimal thus : 



41-341560 ( 6-429 

 36 



124) 534 

 496 



1282 ) 3815 

 2564 



12840 ) 125160 

 115641 



9519 

 And there will be 3 decimal places in the square root obtained. 



Here there is a remainder, or the given decimal is not what is 

 called a complete square. By adding, however, more ciphers, 

 more and more figures can be obtained in the root, to any extent 

 of approximation. 



This is a similar case to that of */7 spoken of in Art. 2. 

 To approximate to the square root of 7, we shpuld proceed 

 thus : 



7-0606 ( 2-64 

 4 



46)300 

 276 



521) 2400 

 2096 



304 

 By continually adding ciphers we can carry the approximation to any 



degree of nearness. 



8. Similarly, in the case of any whole number which is not a 

 complete square root, an approximation to the root by means of 

 decimals can be obtained. 



The integral part of the root obtained is, of course, the square 

 root of the largest integral complete square, which is less than 

 the given number. 



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 expleration 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 

 eee 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 con- 

 siderably 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, 

 hp 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 im- 

 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 

 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 

 made a large collection of the quadrupeds, birds, and plants of 

 that island. In 1840 he returned to Borneo, and having ren- 

 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 Start, 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 Start'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 Start reached a spot ia 

 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 



