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TO OUR READERS.
*** have both pleasure and satisfaction in looking back upon our labours during the past year for the diffusion of real owledge among the people. We know that the POPULAR EDUCATOR has been the means of opening up a new urce of instruction and enjoyment to hundreds, nay thousands of individuals, among those classes which constitute e strength and the glory of a nation, and which but for the establishment of this JOURNAL would perhaps never ave had an opportunity of acquiring even the clements of the common branches of education. To this, we have however added instructions in those branches which were in former times deemed accomplishments, even among the middle classes; and we are happy to say that our efforts have been responded to with a degree of ardent zeal and earnest thankfulness far beyond our merits and expectations. The patronage which we have experienced from all classes fills us with the most sanguine hopes for the future, and encourages us to proceed steadily and delightfully in the path which we have marked out for the benefit of the greatest possible number of our subscribers. We may, however, remark, that in our anxiety to meet the wishes of all, we have not been able to maintain that continuity in some of our lessons which their importance would seem to require;-in the next volume this shall be more carefully kept in view; and with this consideration pressing on our minds, we must be cautious in making promises of many new additions to the subjects already in hand. Some subjects, as Phonetic Short-hand and Latin, are fast drawing to a close; others, as Drawing, French, and probably German, will be finished in the next volume. The termination of these will leave us room for the new subjects which are chiefly in demand, as Book-keeping, Greek, Hebrew, Italian, and probably Spanish; while Chemistry, Natural Philosophy, and Mechanics, will follow as close upon the heels of the Mathematics as our space will allow. Our desire is to make our work a complete Cyclopædia of all human learning; but our subscribers must be fully aware that this is a work of time, and that the elements of every branch must be taught before its grand results can be brought to bear on their minds; otherwise, our JOURNAL would very soon and justly lose its title of the POPULAR EDUCATOR.
In conclusion, we have to observe, that in consequence of numerous and pressing requests made to us, by letter and otherwise, for Lessons on Biblical and Religious Learning, on a plan similar to that which we have adopted in reference to Secular Education, Mr. Cassell has determined to issue a new Journal for the express purpose of meetEarly in May next, therefore, will appear the first Number of the POPULAR BIBLICAL ing this request. EDUCATOR, and the following Numbers will be issued regularly for the first and fifteenth day of every succeeding month. The work will be printed on fine paper, each Number containing thirty-two columns in crown quarto, price Twopence, or the Numbers for the month in a neat wrapper, price Fourpence each. The list of contributors to the Popular Wherever the subject Biblical Educator will include the names of some of the most eminent writers of the present day. The lessons will be written in a popular style, avoiding as much as possible all scholastic terms and technical phrases, so as to give to the plain English reader, not a formidable show of learning, but its intelligible results. requires Pictorial Illustrations, they will be introduced; and no expense will be spared to render the work one of the most useful of the class ever issued.
LONDON, MARCH 26, 1853.
XVII. Properties of Numbers; Different Scales of Notation
LESSONS IN FRENCH.
XXVI. The Past Anterior and the Pauperfect; Interrogative Construction..
XXVII. Idioms relating to the Verb, with particular in
XXVIII. Plural of Compound Nouns; the two Futures,
Simple and Anterior
XXIX. Irregularities of the Future; the two Conditionals; Idioms....
XXX. XXXI. Frequent Idioms; Dimension, Weight, 64, 78 XXXII. The Imperative Mood of the Regular Verbs; the Subjunctive........
XIX. Vulgar Fractions: Definitions and Principles
LESSONS IN BIOGRAPHY.
VIII. Samuel Budgett, the Successful Merchant
XV. Classes: 18. Polydelphia, Dodecandria, Icosandria,
XVI. Class 24. Cryptogamia, Lichens, Fungi, Mosses,
XXXIV. Regimen or Government of Verbs..
XXXVI. The Demonstrative Pronoun, ce; other Idioms,
XXXVIII. Idioms relating to Pronouns, Verbs, &c........ 178 XXXIX., XL. Idioms relating to Verbs.... 190 ......201, 218
XLI. Idioms relating to Nouns, Pronouns, &c. The Present Participle, the Verbal Adjective.... 236 XLII. Practical Résumé of the Rules on the Past Participle
XLIII. Examples illustrating the uses of the principal
XLIV. SECOND PART.-Parts of Speech; Nouns, Cases
XLV. Gender and Plural of Nouns...
I. Introductory Chapter: Perspective, Form, Light and
XLVI. Nouns, Plural and no Plural; Proper Names;
XLVII. Qualifying Adjectives; Formation of the Femi-
II. Angles and Geometrical Figures,
V., VI. Outline Drawing from Simple Forms; Principle
of Copying Drawings; the Pantograph........285, 317 VII., VIII. Perspective: Section I., II. Definitions, &c., 345, 377 LESSONS IN ENGLISH.
XVII. Prefixes from the Greek, the Latin, and the
'XXVIII. Greek Stems continued, &c.
XXIX. Greek Stems concluded, &c.
XLIX. Numeral Adjectives; Cardinal and Ordinal
L. Numeral Nouns; Fractional Numerals; Inde-
LI. The Personal Pronouns....
LESSONS IN GEOGRAPHY.
XXI. Explanation of the Map of Asia; Statistical Table
XIV. The Seasons; the great Circles of the Globe; the
LESSONS IN GEOLOGY.
XV. On the Action of Volcanoes on the Earth's
XVI. Extinct Volcanoes
XVII. On the Action of Rain upon Rocks
Lessons XX. to XXIII.
XXXIV. Idioms relating to Nouns, Verbs, Pronouns, &c. 278
XXXVI. to XL. Idioms relating to Prepositions, Verbs,
LESSONS IN LATIN.
XXV. to XXVIII. Deponent Verbs: First, Second, Third, and Fourth Conjugation; Exercises; .....8, 22, 37, 54 Ablative Absolute XXIX. to XXXVII. Deviations from the Model Conjugations; Deviations in the First, Second, and Third Conjugation, 70, 82, 91, 108, 123, 140, 158, 168, 183 XXXVIII. Deviational Verbs; Inchoatives; Deviations in the Fourth Conjugation; Construction, &c... XXXIX., XL. Irregular Verbs; Exercises, &c. XLI. The Defective Verbs, &c. XLII. Impersonal Verbs, &c...... XLIII. Various Kinds of Verbs; Simple, Derivative, Desiderative, Diminutive, Inchoative, and Compound; verbal stems; verbs transitive and intransitive
Lessons X, to XIII.
347, 363, 382
LESSONS IN MUSIC.
X. Revision, and Answers to Inquirers; Exercises, The
XIV. Requirements of the Tonic Sol-fa Association; Use
XV. The Scale of all Nations; Explanation of Notes;
Axioms," Nomenclature, Propositions, &c.
XIV. Intercalary Book: Book I. Prop. I. Scholia
LESSONS IN NATURAL HISTORY.
X., XI. The Bat
XII. The Common Hedgehog
XIII. The Jackal; the Foxes of Scripture
LESSONS IN GERMAN.
XVI. Adverbs, Idioms
XVII. Comparison of Adjectives; Inflection of the
XVIII. Inseparable Particles
XXI. Impersonal Verbs; Reflexive Verbs, &c.....
XIX., XX. Idioms; Verbs Active in form with Passive
XXIV. Idioms; Conditional Mood
XXVII. Verbs requiring an Accusative of a Person, and
XXVI. Adjectives requiring the Dative; Verbs requir
XXV. Idioms; Verbs governing the Genitive; Adjes-
XIV. The Walrus or Morse
XV. The Civet Cat
LESSONS IN PENMANSHIP.
I. Position of the Body, the Hand, and the Pen.... II. The Writing Alphabets; Lessons in Text, Half-Text, and Current-hand, from A to D III. Remarks on Letters and Style; Lessons in Text, Half-Text, and Current-Hand, from E to H.. IV., V., VI., VII. Lessons in Text, Half-Text, and Cur67, 95, 111, 155, 171 rent-Hand, from I to Z
LESSONS IN PHYSIOLOGY.
XI. Concluding Lesson: Glossary of Physiological Terms
XXVIII. Verbs requiring two Accusatives; also those
II. Variable and Compound Articulations; Double
IV. Affixes or Terminations; Recapitulation of Prefixes and Affixes; Key to Exercises
V. Abbreviations of various kinds, List of Subordinate
VI. List of Subordinate Words represented by a Simplification of their Alphabetic form; Illustration with Ky
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. Fig. 1. Thus, in fig. 1, if you fix two pins on a board, at the points and ', and fasten a string FMF, 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 м, 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 AC 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 P 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 and rare 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 ' 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 compre hend the fundamental principles of Astronomy,-viz. Kepler's
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 r' 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, 4 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