to observe carefully the difference between the time shown by the chronometer and the local time, which can be accurately fixed by an observation of the sun at noon. The longitude is then easily calculated (1 hour = 15°, 1 minute = 15', 1 second = 15"). Thus, Paris time is 9 minutes 20 seconds before Greenwich mean time; the exact longitude of Paris then is 2° 20' 22" E. Longitude may also be found at night by observing the position of the moon among the stars. The heavens are, as it were, a clock, of which the moon may be regarded as an index, and as the moon's place in the heavens can be accurately predicted for years in advance, the navigator or traveller has only to compare the observed distance of the moon from a particular star with that given in the Nautical Almanac to find the exact time at Greenwich, and thus calculate his longitude. Determination of Latitude: There are numerous ways of determining latitude. The determination of longitude is, as we have seen, simply a question of time. We can find the latitude of a place by observing the altitude of the pole above the horizon. The so-called Pole Star is not exactly at the Celestial Pole, or directly over the North Pole of the earth; but supposing it were so, to an observer at the equator it would appear on the horizon, that is, its altitude or height in the heavens would be o. For every degree he advances north, the Pole Star would rise to a corresponding elevation in the heavens; in the latitude of London its altitude or declination would be 51%, which, therefore, is the latitude (or distance from the equator), of London. At the Pole, the star would appear directly overhead, i.e., 90° above the horizon. The star known as the Pole Star is not, however, at the actual pole of the heavens, but at a distance of 1° 24′ from it. Navigators and travellers have thus to find the latitude by other methods, e.g., by observing circumpolar stars at their greatest and least altitude above the horizon-the mean of the two observations showing the height of the true pole above the horizon, and hence the latitude; or by observations of the sun, moon, and the principal stars, the declination (i.e., latitude) of which is given in the Nautical Almanac for every day in the year. Provided with a compass, a chronometer, and a sextant-the latter an instrument for making minutely. accurate measurements of angles, and with the indispensable Nautical Almanac, the navi. gator boldly traverses the waste of waters, and the traveller presses forward across great deserts or through dense forests with the confidence that the course they are following will lead to their "desired haven." The Positions of Places on the earth's surface are thus accurately and unmistakably indicated by their Latitude and Longitude. A given parallel and meridian can only intersect or cut one another at one point; and while a large number of different places may have the same latitude or the same longitude, no two places can possibly have the same latitude and the same longitude. For example, the parallel of 50° N. encircles the globe, and passes through a large number of different places; and, similarly, the meridian of 20° E. passes half-way round the world; yet it is only at one particular and unmistakable point that the 50th parallel N. and the 20th meridian E. intersect or cut one another, and the place said to be at 50° N. latitude and 20° E. longitude is at that point and nowhere else. Methods of Representing the Earth: The largest pictures, even of the most extensive "views," show, after all, but a comparatively insignificant part of the earth's surface, and the hills and mountains, lakes or rivers, long lines of coast, or whatever the 'subject' of the picture may be, are all shown as they appear to the eye, i.e., in perspective. Objects in the 'foreground' are thus drawn much larger than objects of the same or even larger size in the 'background,' for the reason that near objects seem larger than those further off, and the more distant an object is the smaller it looks. A plan, on the other hand, though not so effective as a picture, is necessarily more accurate, in that it indicates the true positions and relative distances of the various places or things shown. Thus, a picture and a plan of a school are very different things; the former shows the apparent, and the latter the real dimensions and positions of the various parts of the building. Maps and Globes: Both pictures and plans, however, show at the best but comparatively small areas, and we must therefore have some convenient means of representing larger portions of the earth's surface, and also the whole of it. This we can do by means of maps and globes. Globes: The earth, being a sphere, is therefore most faithfully represented by a globe. The reason of this is evident. Any lines, circles, etc., drawn on the surface of a sphere can be exactly reproduced only on another spherical surface, as it is absolutely impossible to obtain a perfect representation on a flat surface of any part of a curved surface. Consequently, we can rightly represent the earth as a whole only by means of globes, and it is on a globe alone that the true configuration of the land-masses, the courses of rivers, the positions of towns, etc., can be correctly marked. As, however, artificial globes are both inconvenient for constant use, and, if large, very expensive, map-makers do not attempt to use them generally to show the details so much more easily and conveniently given in the handier and much cheaper form of maps or charts. Maps are representations of the whole or parts of the earth's surface, but as it is impossible to represent correctly a curved surface on a flat or plane surface, no map is absolutely perfect. The smaller the area shown, the more faithful and accurate its delineation may be, and conversely, the larger the area the greater the amount of distortion or dissimilarity between the form of the land, etc., as shown in the map, and as it really is. To reduce this inaccuracy as far as possible, according to the purpose of the map, numerous methods of projecting a curved surface on a plane one are used. The real basis of all mapmaking being the network of parallel and meridian lines corresponding to the parallel and meridian circles of the sphere, the first thing in constructing a map is the projection of the parallels and meridians. Then only can we proceed with any certainty to mark the coast-line and rivers, and to indicate the position of towns, etc. On a map, therefore, the coast-line and other features shown occupy the same position in relation to the lines of latitude and longitude as they do to the corresponding circles on a globe. Hence A Projection is the method of representing a curved surface on a flat or plane surface. Of the many geometrical or conventional methods of projecting the whole or part of the earth's surface, the following are the most generally used: 1. The student should bear in mind that, in all projections, there is, for the reason stated, some error and consequent distortion of shape or areas. Now-a-days, the use of the globes" in enabling a student to understand clearly the principles of mathematical and astronomical geography is practically and most unwisely ignored-a glance at a globe would often clear up a point that could not be solved satisfactorily by the aid of maps alone. Globes are also useful to correct erroneous impressions of direction and distance given by maps on the best projections. Examiners frequently put the question-Through or near what places will a Orthographic Projection—a perspective projection, the point of view being supposed to be at an indefinitely great distance in space. Projected on the plane of the equator, we have the pole at the centre and the meridians diverging from it as straight lines to the circumference; while the parallels are concentric circles, which approach closer towards the circumference or the equator. Projected on a meridian, this meridian and the equator appear as straight lines, and the parallels as straight lines also, while the meridian circles are ellipses, with the polar diameter or axis of the earth as a common major axis. The distances between both parallels and meridians decrease from the centre outwards, gradually at first, and then more quickly. This projection, in every form, thus accurately represents the central portions, but towards the circumferences the distances are reduced at first gradually, then quickly, and finally to o. Countries near the outer margin are consequently much distorted and greatly reduced in breadth. Stereographic Projection-also a perspective view of the hemispheres, but from a different point of view. In this projection, the observer's eye is supposed to be at the centre of the surface of the opposite hemisphere. That is, supposing the earth to be a transparent glass-globe and to be cut in two, the cut face of each hemisphere would be the plane of projection; and, as seen through this plane from the surface of the opposite hemisphere, the equator and central meridian would appear on the plane of projection as straight lines, the other parallels and meridians as arcs, the distance between them increasing as they approach the outer margin of the map. In this projection, the reduction is towards the centre, where distances are reduced by one-half, and areas by one-fourth. Equidistant or Globular Projection: In this projection, also, the equator and central meridian are projected as straight lines, and the other meridians and parallels as curved lines. As in the stereographic projection, the parallels widen out as they approach the margin; the meridians, on the contrary, are on the equator and on every parallel at equal distances, which decrease as the meridians close together until they meet at the poles. None of these projections, however, shows the true "bearings" of places, i.e., a straight line drawn on a map between a point east and another point west of a given meridian, does not cut the meridian at the same angle as a line drawn between the same points on a globe or sphere. So that, on a map projected on any of these methods, a straight line drawn from one port to another would not, without calculation, indicate to the navigator the 'course' his vessel must take from the one in order to arrive at the other in the shortest time. This, however, is an easy matter when the map or chart is drawn on what is known as Mercator's Projection, by which we can show the whole of the world at one view, except the parts about the poles. In this projection, an upright cylinder is supposed to encompass the globe, touching it along the equator. Upon the inner surface of this cylinder the parallels and meridians, with the coast-line, rivers, &c., &c., are supposed to be projected, the point of sight being at the centre of the sphere. When opened out, the meridians appear as a series of perpendicular straight lines, parallel to and equidistant from each other, while the parallels are horizontal straight lines, also parallel to each other and cutting the meridians at right angles, with, however, this important difference, that while the meridians are at equal distances from each other, the parallels are wider and wider apart the further they are from the equator. The reason for this, and also why the Poles and very high latitudes are not shown at all on a map on this projection, will be evident when, by a drawing or experiment, it is clearly seen that, no matter how long the enclosing cylinder may be, the poles cannot be projected on it at all, and the parts near them, as seen from the centre of the sphere, also fall outside the edge of the cylinder. In consequence of this, the parts which can be projected on the cylinder must lie between the limits marked by straight lines drawn from its upper and lower edges to the centre of the sphere it encloses. Mercator's Projection has this disadvantage--that no estimates or comparisons of areas or of distances, except along the same parallel, can be based upon it. It is accurate only in that it shows the true bearings or direction of places. On a globe, the distances between the meridians decrease from the equator to the poles, while the distances between the parallels are very nearly equal. In maps on Mercator's projection, the meridians are equidistant, while the parallels are at unequal distances, which increase with the distance from the equator. There is thus a double distortion, i.e., of latitude and of longitude, or in a north-and-south, as well as in an east-to-west, direction. For example, a degree of longitude on the earth decreases from 60 geographical miles at the equator to 30 miles, or exactly one-half, at 60° N. or S. On a Mercator's map the spaces are equal, so that, at 60 N. or S., countries are drawn out to twice their actual east-and-west dimensions. At 70° N. or S., this east-and-west expansion is nearly three times the true distance. Further, the parallels which are at equal distances on the sphere, are represented by lines at unequal and constantly-increasing distances from each other. So that, on a Mercator's map, countries are drawn out or exaggerated in a north-and-south direction also. And the further they are from the equator, the greater the exaggeration becomes; and thus the area of countries in high latitudes is grossly exaggerated, as compared with that of countries of equal extent in equatorial regions. Conical Projection: If we suppose a cone of paper to be placed in contact with an artificial globe, and touching it along the central parallel of the area to be delineated, and the parallels and meridians in this area to be thrown out or projected on the cone, we get what is termed a conical projection. Now, if by some means the parallels and meridians enclosing and traversing the required area, with the coast-lines, rivers, &c., could be actually projected and marked on the paper, and the cone then opened out flat, we would have on a flat surface a representation of that part of the curved surface of the globe. Along the line where the cone touched the globe, the projection will be perfectly true, i.e., along this line the cone and sphere will correspond exactly, but north and south of this line there will be more or less dissimilarity between them. Another and more accurate form of this projection supposes the cone to be in contact with the surface of the globe along two parallels instead of one; the cone and sphere thus correspond in two places instead of one, with a corresponding reduction of the distortion. There are numerous other forms of this projection, on which maps of the continents and separate countries are usually drawn. Scale: The scale of a map is the proportion between the map and the actual extent of the corresponding portion of the earth's surface. If, for example, 1 inch on the map represents 1 mile of surface, the map is said to be drawn to a scale of one inch to a mile, or as it may be expressed 1: 63,360. This means that the map is 63,360 times less than the area it represents, for 1 mile = 63,360 inches. So that a map on a scale of 1 : 1,000,000 would have to be enlarged a million times in order to cover the area shown. Except in maps of the World in Hemispheres or on Mercator's projection, a scale of miles is usually given, and from it any distances on the map may be more or less accurately determined. Map-Making, or the construction of maps, thus requires a sound knowledge of mathematical geography, besides considerable skill in drawing, &c. In determining the projection of a map, the cartographer is guided mainly by the purpose for which the map is required; for government or administrative purposes, it is above all necessary to show correct areas; for military purposes, correct distances; and for navigation, correct "bearings." Map-Reading: A map is not a mere thing of lines and colours, but a geographical document of the highest value, and to acquire the power to read a map correctly and to understand it fully is, indeed, the main end and purpose of the study of geography. 1. That is, north is always straight up; south, straight down; an 1 cast and west, strideht across; and thas "the most ignorant sailor can lay down his course without calculation." Marine charts are, therefore, all drawn on this projection, which is also useful for physical, commercial, and other mips on which it is necessary to show nearly the whole of the earth's surface at one view. 'A map should live and glow with life and movement," and the student should, when studying a map, assiduously cultivate the habit of mentally picturing the country it represents. To most people, a map is merely a more or less irregular geometrical figure and nothing else, and it calls up no corresponding mental concept of the thing of which it is the symbol. But just as the trained musician hears the music when he sees the notes, so the student of geography should, whenever he looks at a map, mentally perceive the country it represents. Map-Drawing: As geographical knowledge, to be of practical value in life, must be definite and accurate, some proficiency in map-drawing is essential. The configuration of the coasts, the trend of mountain-ranges and the courses of rivers, the position of towns and the boundaries of countries, in short, the physical and political geography of a country, as embodied in a map, is far more vividly fixed on the mind when actually delineated than when merely studied from the printed map. The drawing of a map with some degree of accuracy, especially from memory, is, however, so difficult, that numerous plans have been put forward to assist the beginner-most of them, unfortunately, being based on the idea that the lines of latitude and longitude are not essential. Some form a series of simple geometrical figures by joining extreme or important points by straight lines, and drawing a simplified outline, &c., between and about these lines. Another method divides the map by straight lines into squares of one or more miles, &c. The coast-line, river-courses, &c., may thus be fairly well drawn, but that is all. The network of parallels and meridians is the basis of all map-making, and practice even on printed blank projections' is, after all, far more valuable than an attempt at map-drawing by any method which ignores latitude and longitude. Constant practice is absolutely necessary to sound progress, and the student should remember that it is far more useful and creditable to draw a fairly accurate map from memory than an elaborate one from copy.' III. The Earth's Surface is divided into land and water, the land Occupying little more than one-fourth, and water nearly threefourths of the whole. The total area of the globe is estimated at 197,000,000 square miles, of which Land occupies 51,500,000 square miles, and Water, 145,500,000 square miles. Natural Divisions of Land: The land consists of two large and a great number of smaller masses. In other words, the land is divided into continents and islands. A Continent is the largest division of land. An Island is a smaller portion of land surrounded by water. There are really only two great or continental land-masses-the Western Continent, embracing North and South America, and the Eastern Continent, including the so-called continents of Europe, Asia, and Africa. Australia is an Island-Continent. The Eastern Continent is often called the Old World, and the Western Continent the New World, because Europe, Asia, and Africa were known to the nations of antiquity, while America was not discovered until a comparatively modern period, towards the close of the 15th. century. Islands vary very much in size and position. Several small islands lying close to each other form a Group. Several large islands or island groups near each other form an Archipelago. An Islet is a small island in the An Eyot is an island in the channel of a river. sea. |