') POPULAR EDUCATOR: COMPRISING LESSONS IN ENGLISH GRAMMAR AND COMPOSITION; FRENCH, GERMAN, ITALIAN, AND SPANISH; CASSELL, PETTER, AND GALPIN, LA BELLE SAUVAGE YARD, LUDGATE HILL, E.C. INDEX. X. Gothic Architecture; with Illustrations LESSONS IN ARITHMETIC. XXXII. to XXXV. Latin Stems: Explanations and Ex- ercises; Conversations on English Grammar, XXXVI. to XXXVIII. Latin Stems: Explanations and XIX. Vulgar Fractions: Definitions and Principles .... VIII. Samuel Budgett, the Successful Merchant XV. Classes: 18. Polydelphia, Dodecandria, Icosandria, . XVI. Class 24. Cryptogamia, Lichens, Fungi, Mosses, ..... V., VI. Outline Drawing from Simple Forms; Principle VII., VIII. Perspective: Section I., II. Definitions, &c., 345, 377 XVII. Prefixes from the Greek, the Latin, and the Saxon; Origin of Numerals and some Com- XVIII., XIX., XX., XXI. Suffixes: List of English Suffixes, Able to Ly: Conversations on English Grammar and Composition, No. 1., 26, 33, 59, 74 XXII. Suffixes continued; Ment to Y; Summary of XXIII. Uncombined Suffixes: Adverbs, Prepositions 102 XXV. to XXVII. The Greek Element: Greek Stems, &c., Conversations on English Grammar, No XXVIII. Greek Stems continued, &c. 34 PAGE New Planets, Additional Table of the Solar 61 89 XV. Explanation of Latitude and Longitude by Rectan- gular Axes; First Meridian; East Longitude, XVI. Latitudes and Longitudes; to make a Circle pass through any three points; Construction of the Map of the World; small Circles of the Globe; the Arctic and Antarctic Circles; the Tropics of Cancer and Capricorn; the Five Zones of the Earth, its surface and solid content XVII. Explanation of the Map of the World; Natural Divisions on the Earth's Surface XVIII. Explanation of the Map of Europe: Table of the XXV. to XXVIII. Deponent Verbs: First, Second, Third, and Fourth Conjugation; Exercises; XXIX. to XXXVII. Deviations from the Model Con- jugations; Deviations in the First, Second, and Third Conjugation, 70, 82, 91, 108, 123, 140, 158, XXXVIII. Deviational Verbs; Inchoatives; Deviations in the Fourth Conjugation; Construction, &c... 199 XLIII. Various Kinds of Verbs; Simple, Derivative, Desiderative, Diminutive, Inchoative, and XVII. On the Action of Rain upon Rocks XVIII. On the Origin of Springs of Water.. XIX. On the Phenomena of Artesian Wells XX. On the Chemical Action of Water; Calcareous, X. Revision, and Answers to Inquirers; Exercises, The XI. Mental effect of the Notes of the Scale XII. Mental effect of Notes; Exercises, The_Norwich Chant, White Sand and Grey Sand, If Happiness 114 XIII. Rules for performing the Exercises; Exercises, Old XIV. Requirements of the Tonic Sol-fa Association; Use of the Black Board; Dictation; Exercises, Full XV. The Scale of all Nations; Explanation of Notes; Exercises, The Man's the Gold for all that, Nare's Chaunt, Delightful Sounds, The "Merry I. Position of the Body, the Hand, and the Pen.... II. The Writing Alphabets; Lessons in Text, Half-Text, III. Remarks on Letters and Style; Lessons in Text, Half-Text, and Current-Hand, from E to H..... XXVIII. Verbs requiring two Accusatives; also those governing the Accusative with the Dative; Prepositions requiring the Dative ..... XXIX. Prepositions requiring the Accusative, and the Dative or Accusative; Examples of the use XXX. Examples of the use of Prepositions; Idioms relating to Verbs, Nouns, &c.... XXXI. Idioms relating to Conjunctions; Words relating to Number, Quantity, Weight, and Measure 234 A CM SUPPOSE that you were elevated in the heavens, or in the vast space in which roll all the stars, to a point millions of miles above the sun; and that you were furnished with a telescopic eye so powerful, that from that point you could observe the magnitudes, motions, and distances of all the bodies in the Solar System; that is, the bodies or planets which revolve round the sun in consequence of the laws of attraction and tangential impulse; you would perceive among them a highly-favoured planet called the Earth, accompanied by a satellite (an attendant) in its course, called the Moon. This Earth and her satellite, like all the other planets and their satellites which you would behold in this bird's-eye view, receive both their light and their heat from the sun; and the influences of these imponderable bodies are distributed to all the planets in the same ratio as the power of attraction which keeps them revolving in their orbits (tracks or paths); that is, in the inverse ratio of the squares of their distances; or, to express it more clearly, the power of the attraction, the light and the heat of the sun on one planet, is to that on another planet, as the square of the distance of the latter, is to the square of the distance of the former. In your elevated position, you would next perceive that the planets in their various revolutions, would at some times be nearer to the sun than at other times; and that if the orbit of each were traced by a white line in space, it would appear to your eye, if rightly placed, to have the form of an oval nearly, being in fact, what is called in the language of mathematics, an ellipse. In order that you may understand the nature of this curve, we shall explain it by means of a diagram. Thus, in fig. 1, if you fix two pins on a board, Fig. 1. at the points F and r', and fasten a string F MF, of any convenient length, but greater than the distance between the two points, by its extremities, at these points; and if you take a crayon or chalk pencil, and press it on the string horizontally at M, so as to keep it always tense (i. e. stretched), and parallel to the board, moving the pencil round and round at the same time, from one side to the other; you will describe the curve A C BD, which is called the ellipse. It is evident that the limits of the form of this curve are the circle and the straight line. If the two points F and F are brought close together, the curve will be a circle; if they be separated as much as the string will allow, the curve will become a straight line. The two points F and are called the foci (the plural of focus) of the curve; the straight line AB drawn through them, and terminated both ways by the curve, is called the major axis; and the straight line c D drawn at right angles to this axis from its middle point o, and terminated both ways by the curve, is called its minor axis. If a straight line be drawn from F' to c, it will be equal to the straight line A o, or half the major axis. The point o is called the centre of the ellipse, and the ratio of Fo to Ao, that is, of the distance between the centre and the focus to half the major axis, is called the eccentricity of the ellipse. The distance from the focus to any point м in the curve is called the radius vector of the ellipse; it is least at A, and greatest at B. With these explanations, while you are supposed to be looking at the orbit of a planet from your elevated position in space, you will now be able to comprehend the fundamental principles of Astronomy,-viz. Kepler's Laws. D B the sun to the centre of the planet passes over equal areas in equal times in every part of the orbit; that is, whether the planet be in its aphelion, or farthest from the sun, in its perihelion, or nearest to the sun, or at its mean distance from the sun. And 3. That the squares of the periodic times of the planets, that is, of the times of a complete revolution in their orbits, are proportional to the cubes of their mean distances from the sun; in other words, that the square of the periodic time of one planet is to the square of the periodic time of another planet, as the cube of the mean distance of the former from the sun is to the cube of the mean distance of the latter from it. Into the full explanation of these laws we cannot enter until we treat of astronomy; in the meantime it is necessary to give some explanation of the law which we have marked first, though it is generally accounted the second, in order to clear up some points connected with phenomena relating to the earth, and the circles drawn on the globe, which is the only true representation of the earth's surface. Supposing then the ellipse in fig. 1 to represent the earth's annual orbit round the sun, and the focus F' the place of the sun's centre; then the point a will represent the position of the earth's centre at mid-winter, when it is nearest the sun, or in its perihelion ; B will represent its position at mid-summer when it is farthest from the sun, or in its aphelion ; c will represent its position at the spring or vernal equinox, when it is at its mean distance from the sun; and D its position at the harvest or autumnal equinox, when it is also at its mean distance from the sun. We think we hear some of our readers exclaiming, notwithstanding the elevated position in which we have supposed them to be placed, What! will you tell us that the sun is the cause of light and heat on the earth's surface, and yet you assert that the earth is nearer to the sun in winter than in summer? How can this be? Paradoxical as this may seem, it is nevertheless true; and the reason we shall now give. As you are supposed to be looking from a great distance, and to be able to discern all the motions of the planets, if you look narrowly at the earth, you will perceive that besides its orbitual motion round the sun, it has a revolving or journal motion on its own axis. By aris here is meant that imaginary straight line passing through the globe of the earth, on which its rotation is supposed to take place, and which is aptly represented in artificial globes by the strong wire passing from one side to the other, at the points called the poles (that is, pivots), which are the extremities of the axis. This motion may be likened to the spinning of a top, a motion which continues while the top is driven forward in any direction from one place to another. In fact, the analogy would be so far complete, independently of the causes of the motion, if the top, while it is spinning or revolving as it were on its own axis, were made to run regularly round in an oval ring on the ground, under the lash of the whip. Thus, the earth has two motions; one on its own axis, performed once every twenty-four hours; and one in its orbit, performed once every 365 days 6 hours; we have stated these periods in round numbers, in order that they may be easily remembered; but the exact period of the earth's daily revolution on its axis, is 23 hours, 56 minutes, seconds, and 9 hundredth parts of a second; and the exact period of the earth's annual revolution in its orbit is 365 days, 5 hours, 48 minutes, 49 seconds. The analogy of the motions of the top, however, to the motions of the earth, as thus described, is incomplete in respect of the position of their axes. The axis of the spinning top is in general upright or perpendicular to the oval ring in which it is supposed to move; but the axis of the earth in its daily motion is not perpendicular to the plane of its orbit, or the ellipse in which its annual motion is performed. In speaking of the plane of the earth's orbit our analogy fails, for there is nothing to represent the ground on which the motion of the 27 The eminent German astronomer just mentioned, who flourished at the close of the 16th century and the beginning of the 17th, discovered, by laborious observations and calculations, the follow-ground, which may be called the plane of its orbit, that is, of the ing remarkable laws, which were afterwards mathematically demonstrated by Sir Isaac Newton:-1. That the planets all revolve in elliptic orbits, situated in planes passing through the centre of the sun; the sun itself being placed in one of the foci of the ellipse. 2. That the radius vector or straight line drawn from the centre of VOL. II. |