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VOLUME THE SIXTH.

Biasing furnishes the mind only with materials of knowledge; it is thinking makes what we read ours. We are of the
ruminating kind, and it is not enough to cram ourselves with a great load of collections; unless we chew them over
and over again, they will not give us strength and nourishment. There are, indeed, in some writers, visible instances
of deep thought, close and acute reasoning, and ideas well pursued. The light these would give would be of great use,
if their readers would observe and imitate them: all the rest at best are but particulars fit to be turned into knowledge;
but that can-only be done by our own meditation, and examining the reach, force, and coherence of what is said; and
then, as far as we apprehend and see the connection of ideas, so far is it ours; without that, it is but so much loose
matter floating in our brain.—Lodu.

LONDON:

JOHN CASSELL, LA BELLE SAUVAGE YARD, LUDQATE HILU

MDCCCLT.

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The Present Series of the Popular Educator is now completed. It was our intention to have closed it with a Supplement to Volume V., consisting of some 2U0 pages. But the difficulty of completing so many subjects in that limited space, together with urgent appeals from numerous Headers and Correspondents, induced us to postpone its termination till the completion of another Volume, uniform with the five preceding. This will explain the continuity of the paging from the commencement of the Fifth Volume to the close of the work. The appearance of uniformity will be greatly preserved by having the entire Series bound in three double volumes.

In presenting these Six Volumes to the public, we may confidently call them an EDUCATIONAL Cvclopedia; comprising a vast amount of solid and useful information in a popular form, and at a price unprecedented even in the present age of Cheap Literature. The highest encomiums have been bestowed upon our labours by a large portion oj the Public Press, by learned Professoi-s, by Teachers of Youth, and by a host ol Students who have profited by out publication. Every post has brought us numerous expressions of gratitude for the seasonable and valuable aid we have rendered, and of deep regret that we have brought our labours to a close. We take our respectful leave cf Ji^r friends, thanking them sincerely for the assurances they have given us that we have not laboured in vain.

CONTENTS.

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XXI.

XXII.

XXIII.

XXIV.

XXV.

XXVI.

XXVII.

XXVIII.
XXIX.

XXX.

XXX.
XXXI.

XXXII.

XXXIII.

XXXIV.

XXXV.

XXXVI.
XXXVII.

Powers of Hoots; Evolution; General Rule for

Evolution; Redaction of Radical Quantities 416

Addition of Radical Quantities; Subtraction of

Radical Quantities; Multiplication of Radical

Quantities 434

Division of Radical Quantities; Involution of

Radical Quantities; Evolution of Radical

Quantities 453

Reduction of Equations by Involution; Reduc-

tion of Equations by Evolution; Adfected

Quadratic Equations 613

Method for Completing the Square j Second

Method for Completing the Square; Demon-

stration; Other Methods of Completing the

Square, General Rule' 527

Problems in Adfected Quadratic Equations;
Ratio and Proportion 566

Compound Ratio: Proportion; Arithmetical
Proportion and Progression 691

Geometrical Proportion and Progression G24

Problems in Geometrical Progression; Evolu-
tion of Compound Quantities • 656

Application of Algebra to Geometry 719

LESSONS IN ARITHMETIC.

Decimal Fractions; Decimal Table; Exercises;

Addition of Decimal Fractions 404

Subtraction of Decimal Fractions: Multiplica-
tion of Decimals; Contractions iu Multiplica-
tion of Decimals; Division of Decimal Frac-
tions; Contractions in Division of Decimals
Periodical, or Circulating Decimal; Reduction
of Circulating Decimals; Addition of Circu-
lating Decimals, etc. etc

Percentage; Commission; Brokerage; and

Stocks •-' *1

Interest; Compound Interest 674

Discount; Bank Discount; Insurance; 606

Life Insurance; Profit and Loss 640

Analysis 673

BIOGRAPHY.

William Pitt

James Thomson

David Hume

Samuel Johnson

William Robertson

Edward Gibbon

Oliver Goldsmith

William Cowper

Felicia Dorothea Hematis

Sarah Margaret Fuller

Laura Bridgman

Catharine Maria S. dgwick

Mrs. Troll..; e

Mary Russell Mitford

Lydia Humley Sigourcey

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La vierge auxruinei. Sections L, IL, III., IV.,

V., with exercises, etc • 633

L'enfance du poete, with exercises, etc.

L'emploi du temps, with exercises, etc 551

Les hirondelles, with exercises, etc. Le vieux

roi et la jeuue fille; Sections I., IL, with ex-

ercises, etc. 583

Sections III., IV., with exercises etc. La

charite; Section I., with exercises etc 599

Section H., with exercises. Eudoxie; Sections

I. H., with exercises, etc 615

Section III., with exercises, etc 632

Section IV., with exercises, etc. Le vaisseau
en peril, with exercises, etc 647

LESSONS IN GEOLOGY.

Classification of Rocks; Permian Formation 555

_ „ Lithological Character of the

Coal Rocks 587

„ ,, on the Coal Measures 617

.. „ ... 651

Old Red Sandstone, or the Devoman Forma-

tion; Lithological Characterof the Devonian;

Organic Remains of the Devonian; Some

Geological Phenomena of the Devonian

Period 716

LESSONS IN GREEK.

Formation cf Words; Verbs; Compounds;

Recapitulation 421

Invariable Words 437

Syntax; Preliminary Explanations; Subject;

Predicate; Agreement; Government 450

The Parts of a Simple Sentence considered sepa-
rately; their Agreement 465

Voices of the Verb 479

Tenses of the Verb 499

Moods 515

Enlargement of Simple Sentences 546

Attributives; the Demonstrative Pronouns;

the Article 676

Attributive Words with Substantive Import;

Enlargement of the Predicate 609

,, „ the Single Accusative 641

The Predicate with a Double Accusative 674

Import and Use of the Dative 701

Import and Use of the Genitive 736

Syntax of the Prepositions 764

Interrogative and Imperative Sentences 798

LESSONS IN ITALIAN.

Irregular Verbs ending in ere long (continued) 419

XXXVI „ 448, 467

Irregular Verbs ending in ere short; Verbs

ending in cere 481

„ ,. » „ 501

Verbs ending in dere 530

Verbs ending in urre, contracted from cere; Verbs

ending in gen 561

Verbs ending in ggere; Verbs ending in gliere;

Verbs ending iu guere 593

Verbs ending in lore; Verbs ending in mere;

Verbs ending in pert 627

Verbs ending in orre; Verbs ending in rere;

Verbs ending in tere; Verbs ending in arre;

Verbs ending in rere 659

Table of Terminations of the Verbs in rice .... 676

XLVI. „ „ „ „ •.... 688, 703

Impersonal Verbs; Participle; Adverb 722

Preposition ; Conjunction; Interjection 739

Syntax: Of Article 762

„ Of Nouns, Adjectives, Comparative,

and Superlatives, Numeral! 766

„ Of Personal, Possessive, Demonstra-

tive, Relative, and Interrogative Pronouns, . 786

„ Of Indefinite Pronouns; of Verbs .. 801

Of Participles, Adverbs, and Conj unctions.... 813

TiQB

LESSONS IN MORAL SCIENCE.
I. Conscience, or the Moral Faculty; The Moral
Faculty, Original and Universal; A Moral
Faculty bciri,' supposed, whether its Dictates
are Uniform? How far all Men are agreed in

their Moral Judgments 411

IL Whether Conscience is the same as the Under-
standing, or a Faculty different from and
independent of it; Moral Sense compared
with the Taste; Moral Obligation; Supre-
macy of Conscience 129

HI. Whether we always do right by obeying the
Dictates of Conscience? Whether there is
in the mind a Law or Rule, by which Man
judges of the Morality of particular Actions?
The Moral Feeling which accompanies every
Moral Judgment; Belief in God, as con-
nected with the Operation of Conscience .... 444

IV. Moral Agency, and what is necessary to it;
Man a Moral Agent; Man not under a Fatal
Necessity 4S0

V. Man's Direction an il Government of his Actions,
and his consequent Responsibility; Objec-
tions to the Uniform Influence of Motives;
Summary View of Liberty 476

VI. The kind of Indifference which has been con-
sidered essential to Free Agency; Whether
Men arc Accountable for their Motives, or
whether Desires and Affections which pre-
cede Volition have a Moral Character? The
Division of Motives into Rational and Animal;
Whether Morality belongs to Principles as
well as Acts, or is confined to Acts alone •.. 491

VII. Moral Habits; Nature of Virtue 609

VIII. Different Hypotheses 541

IX. Whether V irtue and Vice belong only to

Actions? 572

X. Author of our Being, considered in Relatien to

Moral Science 603

XI. Phenomena of the Universe 635

XII. Duties of Man to the Creator as thus manifested 668

LESSONS IN PHYSICS, OR NATURAL PHILOSOPHY.
LI1I. The Eye considered as an Optical Instrument;
Sources of Light, and the Action of Light on
Plants; Double Refraction; Folarisauoo .. 409

Circular Polarisation 425

Magnetism; Properties of the Magnet; Terres-
trial Magnetism: the Compass 441

Magnetisation and Laws of Magnetic Action •. 4-57

Electricity; Measure of Electric Forces 473

Action of Electrised Bodies on Bodies in their

Natural State: Electrical Machines 489

LIX. Effects produced by the Accumulation of both

Electricities... 505

Various Effects of Statical Electricity; Dyna-
mical Electricity; Voltaic Pile 521

Dynamic Electricity; Chemical Theory of the

Pile: Constant Current Files 537

Constant Current Piles 553

Phvsiological, Physical, Magnetic and Chemical

Effects of the Galvanic Pile or Battery 669

Magnetic Effects; Galvanometer 585

Chemical Effects of the Galvanic Pile or

Bart try 601

Electro-Dynamics; Electro-Magnetism ...... 620>

v.. LXVIII. , „ 633, 613

LXIX Dynamical Electricity; Phenomena of Induc-
tion; Apparatus founded upon Currents of

Induction 665

Phenomena of Induction; Practical Applica-
tions of the Galvanic Battery 631

Dynamical Electricity; Practical Application

of the Galvanic Battery 697

Thermo-Electrical Currents 713

General Laws and Velocity of Electrical Cur-
rents; Animal Electricity 729

Application of Electricity to Medical Purposes 715

Meteorology ; Aerial Meteors, Aqueous Meteors 761

x' "Luminous Meteors 777, 793-

„ 809

POETRY.

The Rich Man's Son and the Poor Man's Son 436

Elijah's Interview 741

After the Battle 744

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LESSONS IN READING AND ELOCUTION.

XXIII. Religion the Guardian of the Soul; Study of

Human Nature essential to a Teacher; The
Stasre; Education 543

XXIV. The Press; Greece in 1820; Trving to Please;

The Wild Bay; The Mockiqg'Bird 531

XXV. Character of Julius Caesar; Scrooge and

Marley 613

XXVI. Our Control over our Physical Well-being;

Classical Learning: Dame Nature's Charms 695

XXVII. The Lyre: Edmund Burke; Truth 711

XXVIII. God, the Creator; The"Ursa Major 791

XXIX. Excellence of the Holy Scriptures: Crescentius;

Rectitude of Character; Address to the
Ocean; the Bible; the Downfall of Poland;

the Love of Truth 80S

XXX. The Scholar's Mission; the Treasure t'aat
waxeth not Old; the Young Mariner's Dream;
the V.cior Angels 820

LESSONS IN SPANISH.

L Orthography and Pronunciation; Different
Methodsof Spelling; Sound of Diphthongs and
Triphthongs; Syllabication; Accent; Punc-
tuation .469

II. Of the Article and the Noun 481

III. Of the Adiective 503

IV. Degrees of Comparison of tue Pronoun 517

V. Possessive Pronouns 532

VI. Relative Pronouns; Interrogative Pronouns .. 519

VII. Demonstrative Pronouns; L.definite Pronouns 563
VIII. The Verb 679

IX., X., XI., XII. Coniugat.on 596, 611, 6it9, 614

XIII. Reflective Verbs: Passive Verbs 661

XIV. , XV. Irregular Verbs 677, 691

XVI. List of Irregular, Defective, and Impersonal

Verbs 703

XVII. List of Verbs with Irregular Past-Participles;

Of the Adverb, the Conjunction, the Preposi-
tion, the Interjection, the Article, the Noun,

the Adjective 725

XVIII. List of Numerals, of Pronouns, of Verbs 740

XIX. Use of the Mood* and Tense* of Verbs .754

XX. Of the Passive Verb, the Reaimen of Verbs,
Verbs followed by certain Prepositions, the

Use of the Verbs Her and Estar 7C8

XXI. Idiomatic Use of certain Verbs; of the Adverb 783

XXII. Of the Conjunction 803

XXIII. Of the Preposition and Interjection 815

THEORY AND PRACTICE OF TEACHING.

I. Spirit of the Teacher; Responsibility of the

Teacher 6S5

II. Personal Habits of the Teacher 710

III. Literary Qualifications of the Teacher 731

IV. Right Views of Education; Right Modes of

Teaching; Pouring-in Process 769

. V. Drawing-out Process; the more Excellent Way;

Waking-up Mind; Conducting Recitations.. 773

VI. Exciting Interest in Study; Incentives to Study;

Emulation; Prizes 789

VII. Proper Incentives; School Government 804

VIII. Requisites in the Teacher for Good Government 812

LESSONS IN TRIGONOMETRY.

I. Plane Trigonometry; Solutions of Right-Angled

Triangles 734

II. Solutions of Oblique-Angled Triangles 751

III. Trigonometrical Formulae 771

IV. Spherical Trigonometry; Right-Angled Sphe-

rical Triangles.. 7S4

V. Oblique-Angled Spherical Triangles 796

VI. Trigonometrical Formuta) 817

MISCELLANEA.

Address to the Readers of the Popular Educator 620

Correspondence.

Answers to Correspondents.

Literary Notices, etc. etc.

ON PHYSICS, OR NATURAL PHILOSOPHY.
No. LIU.
(Continued from page 396.)

THE EYE CONSIDERED AS AN OPTICAL
INSTRUMENT.

Insensible part of the Retina.—The retina is not equally sensitive in every part, as is proved by the following experiment of Mariotte. Let two black spots be made on white paper, at a distance of from half an inch to an inch from each other. Then, when the paper is brought very near the eye, let the right eye be fixed upon the left spot without preventing it from seeing the other. If the paper be now slowly withdrawn, the right spot will disappear for a time, but reappear soon afterwards if the paper is still further removed. The same thing will hap

fen if the right spot is looked at with the left eye. Mariotte as remarked that at the moment when the spot ceases to be visible, its image is projected upon the insertion of the optic nerve in the interior and lower part of the eye. This insensible part of the eye is called punctum ccecum, or the blind point.

Continuance of the Impression on the Retina.—On whirling round a lighted coal with rapidity, we perceive a Bort of band of continuous fire. Similarly, the rain which falls in drops, appears like liquid threads in the air. These appearances are owing to the fact that the impression produced by objects on the retina remains after the object is removed or replaced by another. The duration of this continuance varies according to the sensibility of the retina and the intensity of the light. M. Plateau of Brussels has discovered, by various methods, that it is on the average about half a second.

The impressions of colours as well as forms remain after the removal of the objects that produce them, for if we divide a circle into sectors and paint them different colours, on turning it round, the colours mix and produce the sensation of the colour which would be formed by their mixture. Thus blue and green produce the sensation of green; yellow and red that of orange, blue and red that of violet; and the seven colours of the spectrum that of white, as is shown by Newton's disc. There are several curious apparatus, the effects of which are explained by the continuance of the impressions upon the retina. Such are the thaumatrope, the phenakisticope, the kaleidophone, and Farraday's wheel.

Accidental Images.—If a coloured object be placed upon a dark ground and looked at attentively for some time, the eye soon becomes wearied and the intensity of the colour 'grows feeble. On directing the eyes to a white piece of paper or on the ground, we perceive an image of the same form as the object, but of a complementary colour; that is to say, a colour which would form white if it were combined with that of the object. In the case of a green object, the image is red, and rice versa; if the object is yellow, the image is violet. These coloured appearances were remarked by Buffon, who gave them the name of accidental images or colours. Accidental colours continue for a length of time, proportioned to that during which the object was observea, and to the intensity of the light upon it. Generally speaking, they do not disappear gradually and without interruption, but present alternate disappearances and reappearances. It is well known also that if, after having looked attentively at a coloured object, we close the eyes rapidly, and as firmly as possible, so as to exclude the light, and even screen them from the light by means of a thick piece of cloth over them, the accidental images still appear.

Various theories have been proposed to account for the phenomenon of accidental colours. That of Darwin is deserving of mention. He thinks that the part of the retina which is wearied by one colour, becomes insensible to the rays of that colour, and is only capable of impressions of the complementary colour; also, that this part of the retina spontaneously assumes an opposite mode of action, which produces the sensation of the complementary colour. The first part of this theory does not explain the appearance of accidental colours even in darkness, and the second part is merely a statement of the phenomenon of accidtntal images.

VOL. T.

Irradiation is a phenomenon in which white objects, or those of a bright colour, when seen on a dark ground, appear larger than they really are. The reverse takes place with a black object on a white ground. It is thought that irradiation arises from the circumstance that the impression on the retina extends more or less beyond the outline of the image. The effect of irradiation upon the apparent magnitude of the stars is very perceptible, and they may thus appear several times larger than they really are.

According to the researches of M. Plateau, irradiation varies considerably in different persons, and even in the same person on different days. This philosopher has also shown that irradiation increases with the brightness of the object and the length of time it is observed. It is perceptible at all distances, is increased by divergent lenses and diminished by convergent ones.

Accidental Halo. Contrast of Colours.—Colours which instead of following the impression of an object like accidental colours, appear round the object itself when attentively looked at for some time, are called accidental halos. The impression of the halo is the reverse of that of the object; that is to say, if the object is distinct, the halo is obscure, and vice versa.

Contrast of colours is a reciprocal action which takes place between two colours nearly allied, and by virtue of which each of them assumes the complementary colour of the other. This contrast was observed by M. Chevreul, who profoundly investigated the subject, with a view to ascertain the laws of the phenomenon. It is attributable to the reciprocal action of the accidental halos above mentioned. M. Chevreul found that on red and orange being placed side by side, the red inclined to violet and the orange to yellow. If the experiment be made upon red and blue, the red inclines to yellow and the blue to green. With yellow and blue, the yellow passes into orange and the blue to indigo, and similarly with many other combinations. It is needless to remark how important is the bearing of this subject upon the manufacture of cloth, carpets and other coloured articles. Those who would wish to be successful in combining colours must understand the principles of the effect of contrast.

The Eye not Achromatic.—It was long the custom of philosophers to attribute to the human eye the property of perfect achromatism, but this notion cannot be admitted without qualification after the various experiments of Wollaston, Young, Fraiinhofer and Muller. Fraiinhofer observed that in a telescope with two glasses a very fine thread placed inside the instrument is distinctly seen through the eye-piece when the telescope is illuminated with red light only, but ceases to be visible, if, without altering the position of the eye-piece, the telescope is illuminated with light of a violet colour. To see the thread again, it is necessary to diminish the distance between the two glasses, much more than is required by the refrangibility of violet light. Hence it is evident that part of the effect is due to the aberration caused by the refrangibility of the eye.

Muller found that, on looking with a single eye at a white disc on a black ground, the image is clear when the eye is adapted to the distance of the disc, that is to say, when the image is formed on the retina. But he observed, that if the eye is not adapted to this distance, that is to say, if the image is formed at a distance either in front or at the back of the retina, the disc appears to be surrounded with a very narrow blue band. He concluded from this and other experiments that the eye is achromatic as long as the image is received from the focal distance, or as long as the eye is adapted to the distance of the object. It is not yet known what is the precise cause of this apparent achromatism of the eye, but it is generally attributed to the delicacy of the pencils of light which pass through the aperture of the pupil, and to the fact that the rays being of various refrangibility, and meeting the media of the eye almost perpendicularly, are very little refracted, and hence the dispersion is not perceptible. As to spherical aberration, we have already seen how that is corrected by the iris, which is a real partition, arresting the marginal rays that have a tendency to go beyond the crystalline, and only suffering those to pass which are nearest the axis.

Sliort Sight and Long Sight.—The usual cause of short-sightedness is a too great convexity of the cornea or crystalline. The eye being then too convergent, the focus instead cf being

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