MATHEMATICAL GEOGRAPHY. 17 Fig. 18, The Conical Projection. in most maps both parallels and meridians are curved lines. Therefore, in most maps due north and south and due east and west will lie along the meridians and parallels, and not directly toward the top and bottom, or the right- and left-hand side. . 21, The Hemispheres.—The equator divides the earth into a Northern and a Southern Hemisphere. The meridian of long. 20° W. from Greenwich is generally taken as the dividing-line between the Eastern and Western Hemispheres. 22. The Movements of the Earth; Rotation.— The earth turns around from west to east on its diameter or axis. This motion is called its ro- tation. That the earth rotates from west to east the following consideration will show: To a person in a steam-car mov- ing rapidly in any direction, the fences and other objects along the road will appear to be moving in the opposite direction: their motion is of course apparent, and is caused by the real motion of the car. Now, the motion of the sun and the other heavenly bodies, by which they appear to rise in the east and set in the west, is apparent, and is caused by the real motion of the earth on its axis; this motion must therefore be from west to east. The sun, the planets, and their satellites, so far as is known, also turn on their axes from west to east. The earth makes one complete rotation in about every twenty-four howrs—accurately, 23 hours 56 minutes 4.09 seconds. The velocity of its rota- tion is such that any point on the equator will travel about 1042 miles every hour. The veloci- ty of course diminishes at points distant from the equator, until at the poles it becomes nothing. 23. Change of Day and Night—tThe earth re- ceives its light and heat from the sun, and, being an opaque sphere, only one-half of its surface can be lighted at one time. The other half is in dark- ness, since it is turned from the sun toward por- tions of space where it only receives:the dim light ° of the fixed stars. The boundary-line between the light and dark parts forms approximately a great circle called the Great Circle of Illumination. Had 3 the earth no motion either on its axis or in its orbit, that part of its surface turned toward the sun would have perpetual day, and the other part perpetual night ; but by rotation different portions of the surface are turned successively toward and away from the sun, and thus is occasioned the change of day and night. 24, The Revolution of the Earth —The earth has also a motion around the sun, called its revolution. The revolution of the earth is from west to east; this is also true of all the planets and asteroids, and of all their satellites, except those of Uranus, and probably of Neptune. The phrases “rotation of the earth on its axis” and “yevolution in its orbit” are often used in reference to the earth’s motion; but the simple words “rotation” and “yvevolution” are sufficient, since the first refers only to the motion on its axis, and the second only to the motion in its orbit. The earth makes a complete revolution in 365 days 6 hours 9 minutes 9.6 seconds.. This time forms what is called a sidereal year. The tropical year, or the time from one March equinox to the next, is somewhat shorter, or 865 days 5 hours 48 minutes 49.7 seconds. The latter value is the one generally given for the length of the year. It is nearly 3653 days. It will be found that the sum of the days in all the months of an ordinary year is only equal to 365, while the true length is approximately one-quarter of a day greater. This deficiency, which in every four years amounts to an entire day, is met by adding one day to February in every fourth or leap year. The exact time of one revolution, however, is some 11 minutes less than 6 hours. These eleven extra minutes are taken from the future, and are paid by omitting leap year every hundredth year, except that every 400 years leap year is counted. In other words, 1900 will not be a leap year, since it is not divisible by 400, but the year 2000 will be a leap year. The length of the orbit of the earth is about 577,000,000 miles. Its shape is that of an el- lipse which differs but little from a circle. The sun is placed at one focus of the ellipse, and, as this. is not in the centre of the orbit, the earth must be nearer the sun at some parts of its revo- lution than at others. When the earth is in that part of its orbit which is near- est to the sun, it is said to be at its perihelion; when in that part farthest from the sun, at its aphelion. The peri- helion distance is about 90,259,000 miles; the aphelion dis- tance, 93,750,000 miles. The earth reaches its perihelion about January Ist. The earth does not move with the same rapidity through all parts of its orbit, but travels more rapidly in perihelion than in aphelion. Its mean velocity is about 19 miles a second, which is nearly sixty times faster than the speed of a cannon-ball.