Republic; senate and assembly, *Mecklenb'g-Schwer. Gr'd Duchy, Limited monarchy; one chamber, 66 Ionian Isles, *Liechtenstein, *Lippe Detmold, 66 66 " 66 66 *Lubeck, Free City. *Mecklenb'g-Strelitz, Duchy, Principality, Duchy, Gr'd Duchy, Duchy, Absolute monarchy, 66 66 Limited monarchy; two chambers, 66 Absolute monarchy, 66 66 Pontifical States, or Popedom, States of the Church, Portugal, Kingdom, Limited monarchy; two chambers, 66 *Prussia, 66 66 66 66 *Reuss-Greitz, *Reuss-Schleitz, 66 66 66 66 Russia, Empire, San Marino, Republic, Sardinia, Kingdom, Absolute monarchy, Republic; senate and counc. of ancients, Evangelical. 66 Greek Church. 66 66 66 *Saxony, 66 66 66 66 66 *Saxe Altenburg, *Saxe Weimar, 66 66 *Saxe Coburg Gotha, 66 *Saxe Meiningen, *Schwarzb'g-Rudolst. Principality, *Schwarz'g Sonder'n, Sicilies (The Two), Kingdom, 60 Sweden & Norway, Switzerland, Republic, Empire, *Waldeck, *Wirtemburg, 66 one cham. for ea. duchy, Absolute monarchy, one chamber, Limited monarchy; with a legislature, Principality, Limited monarchy; one chamber, 66 66 two chambers, *Forming part of the Germanic Confederation. The King of Belgium is a Protestant, though his subjects are mostly Catholics; the King of Greece is a Catholic, though most of his subjects are of the Greek Church; the King of Saxony is a Catholic, though the majority of his subjects are Protestants; and about one-fourth of the European sublects of the Sultan of Turkey are Mohammedane, the remainder are chiefly of the Greek Church. Algiers, TITLE FORM OF GOVERNMENT. Empire, Despotic, PREVAILING Mohammedan. French Col., Ruled by a governor-general appointed Mohammedan. Tripoli,. Pashawlic, 66 Egypt, Kingdom, Nubia, Abyssinia, Under the dominion of Egypt, and R. Cathol. Mohammedan. 66 66 66 Somauli Territory, A part of this territory is ruled by a A corrupt Christianity. Pagan and Mo hammedan. Pagan and Mo hammedan. Governed by various kings and chiefs, British Col., Partly under the control of Great Britain, 66 66 66 66 66 66 66 bebas, Guinea, PART II. MATHEMATICAL GEOGRAPHY. CHAPTER I. DEFINITIONS-MOTIONS OF THE EARTH. MATHEMATICAL GEOGRAPHY is that branch of science which it cludes a description of the earth as a planet, treating of its form, its magnitude, its motion, and of the various imaginary lines upon its surface. REMARK TO THE PUPIL.-We here introduce for your study the definition of certain geometrical figures with which you should be acquainted, in order to enable you fully to comprehend what is said respecting the form and motions of the earth. Definition of a Circle.-A Circle is a plane figure bounded by one continuous line, called its circumference; all the points of which are equally distant from a point within called the centre of the circle. Thus, in the adjoining figure, if the points A, D, E, and B are equally disE tant from the point C, they will be situated in the circumference of a circle, whose centre is at C. B The equal lines drawn from the centre of a circle to its circumference are each called a radius. Thus, each of the lines C A, C D, C E, and C B, is a radius. A line such as A B, passing through the centre and terminating in each direction in the circumference, is called a diameter of the circle. All diameters of the same circle are equal, each being the sum of two opposite radii. Definition of an Ellipse.-An Ellipse is a plane figure bounded by one continuous line called its circumference, which, like the circle, In an ellipse there are always two points, E and F, in the transverse diameter, so situated that the sum of any two lines such as E G, F G, drawn from them to the same point in the circumference, is always equal to the transverse diameter. Each of these points is called a focus of the ellipse. An Angle and its Measure.-The difference in direction of two lines proceeding from the same point is called an angle. If the circumference of a circle be described having for its centre the angular point, the arc comprised between the two points forming the angle may be taken as the measure of the angle. If the entire circumference of a circle be divided into 360 equal portions, each one of these portions or arcs may be regarded as measuring an angle of one degree. Thus, for example, if the arc B E (see first diagram) contains 20 of these equal divisions, the angle BCE is called an angle of twenty degrees, usually written 20°. The sixtieth part of a degree is called a minute, and the sixtieth part of a minute is called a second. The mark for minutes is (), that for seconds is ("). Thus, twentythree degrees, twenty-seven minutes, and thirty seconds is usually written 23° 27′ 30′′. If radii be drawn dividing the circumference into four equal portions, each angle thus formed will be an angle of 90°, and the diameters thus formed will be perpendicular to each other. Since an angle of one degree is measured by the 360th part of the circumference of a circle, having its centre at the angular point, it follows that the circumference of any circle, whether great or small, may be regarded as the measure of 360 degrees. Consequently, the length of the arc measuring any given angle must vary with the magnitude of the radius. Definition of a Sphere.-A Sphere is a body bounded by one continuous surface, every point of which is equally distant from a point within called its centre. Any line drawn from the centre to the surface is called a radius. A line passing through the centre and terminating in each direction at the surface is called a diameter. All diameters of the same sphere are equal, being the sum of two opposite radii. If a sphere be divided by a plane, the section will be a circle. The circular section thus formed will be the greatest when the dividing plane passes through the centre of the sphere, in which case it is called a great circle of the sphere. In all other cases the radius of the circular section will be less than the radius of the sphere, and such sections are called lesser circles of the sphere. The two halves into which a sphere is divided by a great circle are called hemispheres. MOTIONS OF THE EARTH. From astronomical observations aided by mathematical investigations, we learn that the Earth moves in a plane about the Sun in an elliptical orbit, having the sun in one of its foci; that its mean distance from the sun is about 95,000,000 of miles; that it is nearest the sun about the 31st of December, or the 1st of January, and furthest from the sun about the 30th of June or the 1st of July, and that the difference between these extreme distances is about 3,000,000 of miles. The Earth's Annual Revolution.-This revolution about the sun is called the earth's annual revolution. The Earth's Orbit, etc.-The length of the earth's orbit, or path, is estimated at 600,000,000 miles. As the earth travels this distance in about 365 days, its annual motion must exceed 68,000 miles an hour. In consequence of the earth's annual motion, the sun seems in the course of a year to describe a circuit in the heavens called the ecliptic, and in the same direction as the earth actually describes it. The Earth's Axis of Revolution.-While the earth is performing its annual revolution, it is constantly and uniformly revolving about one |