L-dish ztic redi- _'si- gen- lrlly the ll.'1‘lIE.I-TIC-L.] Barents,” under Lieutenants de Bruyne and Koolemans lleynen, made a useful reconnaissance of the Barent’s Sea; while Professor N ordenski'o'ld left Sweden in July 1878, in the well-equipped steamer “ Vega, ” to achieve the North- liast Passage. In August he rounded Cape Chelyuskin, the most northern point of the Old World, and reached the mouth of the Lena. But much work remains to be done in the polar regions, in order to complete the connexion between Aldrich’s furthest in 1876 and M‘Clintock’s in 1851, to complete the discovery of the north side of Greenland, to explore the northern bounds of Franz Josef Land, and to discover lands north of Siberia. There is one great branch of physical geography which has only been effectively studied within the last thirty years, namely, the physical geography of the sea. Mathew Fontiine .Iaury, by his wind and current charts, by his trade wind, storm, rain, and whale charts, and above all by his charming work The I’/L3/sz'«:al Gc’0[/)'((.p/1._1/ of the Sea, gave the first impulse to this study. It was Captain Maury who organized the first deep—sea soundings in the North Atlantic, which up to that time was deemed to be unfathomable ; and when his work was published, the illustrious Humboldt declared Maury to be the founder of a new and important science—the meteorology of the sea. He first took charge of the Washington Observatory in 1h‘l'3 ; he resigned that post under a deep sense of duty in April 1861, aftera career of great usefulness; and he ended a noble and well-spent life in 1872. The investigations into the physical geography of the sea, which were com- bined into a system by Maury, have since been ably and zealously continued by others, among whom the names of Dr Carpenter, Sir Wyville Thomson, and Professor Mohn of Christiania are pre-eminent. The voyage of the “Chal- lenger ” from 1873-1876, under Captains Nares and Thomson, with Sir Wyville Thomson as chief of the scien- tific staff, was organized with the object of examining and mapping the bottom of the ocean, of describing ‘the fauna of the great depths, of ascertaining the temperatures at various depths, and of solving questions relating to oceanic circulation. The area thus explored in the Atlantic, Antarctic, Pacific, and Indian Oceans is of vast extent, and the researches, ably and zealously conducted, have resulted in an important addition to geographical knowledge. In this rapid sketch of the history of geographical dis- covery, the labours of numerous explorers during many generations have been enumerated; but its perusal will show that, notwithstanding all this work, there is much remaining to be done. Vast areas round both poles, and in the interior of Asia, Africa, South America, and New Guinea, are still unknown, even more extensive regions have only been partially explored, and millions of square miles remain to be surveyed, before the work of geographers is complete. (0, R, 31,) II. MATIIEMATICAL GEOGRAPHY. All our knowledge of the planet on which we live, whether obtained fron1 the explorations of travellers, the voyages of navigators. or the discoveries of astronomy in modern times, goes to confirm the doctrine held and taught by philosophers in a remote antiquity that the earth is spherical. What is spherical, however, is not the actual surface of the earth, but rather that of the sea produced in imagination to pass through the continents. That the surface of the sea is convex any one may—at a seaside station where there is a high clifi‘—convince himself, by noting with a telescope at the top of the cliff the exact appearance of a ship in, or slightly beyond, the horizon, and then, immediately after, repeating at the foot of the cliff the same observation on the same ship. GEOGRAPHY l the eartl1’s rotation. By a more , through 360" in 21: hours. 197 precise observation of the sea horizon from a known alti- tude one may even calculate the radius of the earth. Let m (fig. 1) be a point on the top of a mountain ; Imlc a portion of the earth’s surface ; mm a line drawn from m towards the centre of the earth ; I mh a tangent from m to the spheri- cal surface ; and ml a horizontalline II . through m, that is, ml is perpen— /L ]' dicular to mv. Then by the mere _V measure of the angle lmk, or the F18- 1- depression of the sea horizon, one can, knowing mu, calculate very simply the radius of the earth. Let the height mn=lL, the angle lmk=8, and the radius of the earth=7- ; then since the angle subtended at the earth’s centre by /no is 8, it is clear that (/a+r) cos8=r, which gives r in terms of It and 8, known quantities. In fact, since It and 8 are both small, r=?3h—:— sin"’31,8. But here we have assmned that the ray of light proceeding from II. to m takes a rectilinear course; this is not true however, for the path is curved, its concavity being turned towards the earth—-a consequence of terrestrial refraction. From the laws of terrestrial refraction, which have been very minutely studied, we know that the formula last written down should be r='422h+sin'-’%8. Now to take an actual case—the depression of the sea horizon at the top of Ben Nevis is 64' 48" (this is the mean of several observations, taken with special precautions for the express purpose of this experimental calculation), and the height of the hill is 4406 feet, or '8345 of a mile. The formula gives at once r=3965 miles, which is remarkably near the truth. But this method is not capable of precision on account of the variableness of terrestrial refraction. In connexion with the appearance of the sea horizon from a height the following formulze are useful :——hbeing the height in feet, 8 the depression or dip of the horizon in minutes, 3 the distance of the horizon in miles, then 5=(1 -$)'/IL; s=§~/h. Thus, for instance, to a spectator 011 the top of Snowdon, which is 3590 feet in height, the distance of the sea horizon is about 80 miles. The first great fact in the description of the earth being that it is spherical (or at any rate so nearly so that, were a perfect model of it constructed, no one could, by unaided vision, discover that it is not spherical), the next points to be noted are,——secondly, that the earth rotates uniformly round_an axis passing through its centre, and fixcd, or very nearly fixed as to direction, in space; and thirdly, that its figure is not spherical but spheroidal, the surface being that found by the revolution of an ellipse round its minor axis, the axis of figure corresponding with the axis of diurnal rotation. The spheroidal figure is a necessary consequence of the rotation. The rotation of the earth once in 24- hours, although made evident by the rising and setting of the heavenly bodies, is rendered perhaps more distinctly visible by Foucault’s pendulum experiment. Let a heavy ball be suspended by a fine thread, free from tension, from a fixed point. Let it be drawn aside fron1 the position of equili- brium and then dropped so that it commences to oscillate in a vertical plane passing through the point of suspension. - Then a careful observation of the pendulum will show that its plane of oscillation is not fixed, but has a uniform rota- tion in a direction opposite to that of the earth’s rotation. Suppose, for instance. that the pendulum were suspended at the north pole and that it were set oscillating in a plane passing through any one fixed star, then it will continue to oscillate in that same plane notwithstanding Consequently, to the observer there the plane of the pendulum’s oscillation will appear to rotate
At the equator, since there is