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434

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XXXI.

453

XXIV. Reduction of Equations by Involution; Reduc tion of Equations by Evolution; Adfected Quadratic Equations

XXXII.

513

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XXV. Method for Completing the Square; Second Method for Completing the Square; Demonstration; Other Methods of Completing the Square, General Rule

XXXIII. XXXIV.

XXVIII. La vierge aux ruines. Sections I., II., III., IV., V., with exercises, etc......... XXIX. L'enfance du poète, with exercises, etc. L'emploi du temps, with exercises, etc. XXX. Les hirondelles, with exercises, etc. Le vieux roi et la jeune fille; Sections I., II., with exercises, etc. Sections III., IV., with exercises etc. La charité; Section I., with exercises, etc. Section II., with exercises. Eudoxie; Sections I. II., with exercises, etc................................... Section III., with exercises, etc. Section IV., with exercises, etc. Le vaisseau en péril, with exercises, etc.

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551

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533

599

615

632

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XXVIII. Geometrical Proportion and Progression.... XXIX. Problems in Geometrical Progression; Evolution of Compound Quantities

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587

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on the Coal Measures

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...... 617

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656

XXX. Application of Algebra to Geometry.

719

LESSONS IN ARITHMETIC.

XXX. Decimal Fractions; Decimal Table; Exercises; Addition of Decimal Fractions

Old Red Sandstone, or the Devonian Formation; Lithological Character of the Devonian; Organic Remains of the Devonian; Some Geological Phenomena of the Devonian Period ..........

LESSONS IN GREEK.

716

464

XXXI. Subtraction of Decimal Fractions: Multiplica-
tion of Decimals; Contractions in Multiplica-
tion of Decimals; Division of Decimal Frac-
tions; Contractions in Division of Decimals 486
XXXII. Periodical, or Circulating Decimal; Reduction
of Circulating Decimals; Addition of Circu-
lating Decimals, etc. etc.

XXXIII. Percentage; Commission; Brokerage; and
Stocks

XXXIV. Interest; Compound Interest.

XXXV. Discount; Bank Discount; Insurance;

XXXVI. Life Insurance; Profit and Loss ................................
XXXVII. Analysis

BIOGRAPHY.

XV. William Pitt

XVI. James Thomson

XVII. David Hume

XVIII. Samuel Johnson..

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510

rately; their Agreement.

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LI.

Voices of the Verb...

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544

LII.

Tenses of the Verb.....

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574

LIII.

Moods

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.....

606

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546

640

673

the Article

LVI.

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LV. Attributives; the Demonstrative Pronouns;

Attributive Words with Substantive Import;
Enlargement of the Predicate..

.......

the Single Accusative LVIII. The Predicate with a Double Accusative

LIX. Import and Use of the Dative......
LX. Import and Use of the Genitive..
LXI. Syntax of the Prepositions

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Interrogative and Imperative Sentences

LESSONS IN ITALIAN.

XXXIV. Irregular Verbs ending in ére long (continued) 419 XXXV., XXXVI.

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XXXVII.' Irregular Verbs ending in 'ere short; "Verbs 448, 467

ending in cere .......

576

609

641

674

701

736

764

.798

CONTENTS.

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

II. Whether Conscience is the same as the Understanding, or a Faculty different from and independent of it; Moral Sense compared with the Taste; Moral Obligation; Supremacy of Conscience

PAGE

III. 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 connected with the Operation of Conscience .... IV. Moral Agency, and what is necessary to it; Man a Moral Agent; Man not under a Fatal Necessity V. Man's Direction and Government of his Actions, and his consequent Responsibility; Objec tions to the Uniform Influence of Motives; Summary View of Liberty

VI. The kind of Indifference which has been considered essential to Free Agency; Whether Men are Accountable for their Motives, or whether Desires and Affections which precede 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 ?.. VII. Moral Habits; Nature of Virtue VIII. Different Hypotheses...

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IX. Whether Virtue and Vice belong only to Actions?

541

572

X. Author of our Being, considered in Relation to Moral Science

603

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XVI. List of Irregular, Defective, and Impersonal Verbs....

IX., X., XI., XII. Conjugation .... 596, 611, 629, 644 XIII. Reflective Verbs; Passive Verbs XIV, XV. Irregular Verbs

570

661

677, 691

409

LIV. Circular Polarisation....

425

XVIII. XIX. XX.

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List of Numerals, of Pronouns, of Verbs Use of the Moods and Tenses of Verbs........ Of the Passive Verb, the Regimen of Verbs, Verbs followed by certain Prepositions, the Use of the Verbs Ser and Estur XXI. Idiomatic Use of certain Verbs; of the Adverb 789 XXII. Of the Conjunction

List of Verbs with Irregular Past-Participles; Of the Adverb, the Conjunction, the Preposi tion, the Interjection, the Article, the Noun, the Adjective

708

725

740

751

768

$3

.......... $15

489

THEORY AND PRACTICE OF TEACHING.

505

LX. Various Effects of Statical Electricity; Dynamical Electricity; Voltaic Pile

521

LXI. Dynamic Electricity; Chemical Theory of the Pile: Constant Current Piles

I. Spirit of the Teacher; Responsibility of the Teacher....

685

II.

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LXII. Constant Current Piles.......

553

IV.

LXIII. Physiological, I'hysical, Magnetic and Chemical

Effects of the Galvanic Pile or Battery.....

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LXIV. Magnetic Effects; Galvanometer

555

LXV. Chemical Effects of the Galvanic Pile or

VI.

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Personal Habits of the Teacher
Literary Qualifications of the Teacher
Right Views of Education; Right Modes of
Teaching; Pouring-in Process
Drawing-out Process; the more Excellent Way;
Waking-up Mind; Conducting Recitations.. 773
Exciting Interes in Study; Incentives to Study;
Emulation; Prizes

710

731

760

780

620

LXVII., LXVIII.

tion; Apparatus founded upon Curren's of Induction ......

VII.

LXIX Dynamical Elce'icity; Phenomena of Induc

633, 619

VIII.

Proper Incentives; School Government Requisites in the Teacher for Good Government S14

804

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LXX. Phenomena of Induction; Practical Applications of the Galvanic Battery

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LXXI. Dynamical Electricity; Practical Application

Plane Trigonometry; Solutions of Right-Angled Triangles

II.

of the Galvanic Battery...

Solutions of Oblique-Angled Triangles

751

697

III.

LXXII. Thermo-Electrical Currents..

Trigonometrical Formulæ...

713

LXXIII. General Laws and Velocity of Electrical Currents; Animal Electricity....

IV.

Spherical Trigonometry; Right-Angled Sphe

rical Triangles.....

729

LXXIV. Application of Electricity to Medical Purposes 745
XXV. Meorology; Acris1 Meteos, Aqueous Meteors
VI. LXXVil.
111.

V.

Oblique-Angled Spherical Trangles

VI.

Trigonometrical Formule..

Lummous Meteors

761 777, 793

MISCELLANEA.

809

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POETRY

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ON PHYSICS, OR NATURAL PHILOSOPHY.

No. LIII.

(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 happen if the right spot is looked at with the left eye. Mariotte has 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 cæcum, or the blind point. Continuance of the Impression on the Retina.-On whirling round a lighted coal with rapidity, we perceive a sort 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.

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.

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 vice versa; if the object is yellow, the image is violet. These Muller found that, on looking with a single eye at a white disc coloured appearances were remarked by Buffon, who gave on a black ground, the image is clear when the eye is adapted them the name of accidental images or colours. Accidental to the distance of the disc, that is to say, when the image is colours continue for a length of time, proportioned to that formed on the retina. But he observed, that if the eye is not during which the object was observed, and to the intensity of adapted to this distance, that is to say, if the image is formed the light upon it. Generally speaking, they do not disappear at a distance either in front or at the back of the retina, the gradually and without interruption, but present alternate disc appears to be surrounded with a very narrow blue band. disappearances and reappearances. It is well known also that He concluded from this and other experiments that the eye is if, after having looked attentively at a coloured object, we achromatic as long as the image is received from the focal close the eyes rapidly, and as firmly as possible, so as to distance, or as long as the eye is adapted to the distance of exclude the light, and even screen them from the light by the object. It is not yet known what is the precise cause of means of a thick piece of cloth over them, the accidental images this apparent achromatism of the eye, but it is generally still appear. attributed to the delicacy of the pencils of light which pass Various theories have been proposed to account for the through the aperture of the pupil, and to the fact that the rays phenomenon of accidental colours. That of Darwin is deser-being of various refrangibility, and meeting the media of the ving of mention. He thinks that the part of the retina which eye almost perpendicularly, are very little refracted, and hence is wearied by one colour, becomes insensible to the rays of the dispersion is not perceptible. As to spherical aberration, that colour, and is only capable of impressions of the com- we have already seen how that is corrected by the iris, plementary colour; also, that this part of the retina spon- which is a real partition, arresting the marginal rays that taneously assumes an opposite mode of action, which produces have a tendency to go beyond the crystalline, and only sufferthe sensation of the complementary colour. The first part of ing those to pass which are nearest the axis. 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 accidental images,

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, Fraunhofer and Muller. Fraunhofer 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.

VOL. V.

Short 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 of being 131

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fraction in Crystals with two Axes.-Crystals very numerous. Of this class are the sulmagnesia, barites, potash, and iron, with the topaz of Brazil. In these different 'es of the two axes assume very different rom three to ninety degrees. Fresnel distheory and demonstrated by experiment, that in ith two axes, neither of the refracted rays follows of simple refraction, but calling the line which bisects between the two axes the middle line, and that which Lhe supplement of this angle the supplementary line, he that in every section perpendicular to the middle line, the refracted rays follows the ordinary laws of refracand in every section perpendicular to the supplementary , it is the other ray which follows these laws.

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POLARISATION.

Polarisation by Reflection.--Polarisation is a particular modification of the luminous rays, by virtue of which, when once they have been reflected or refracted, they become incapable of further reflection or refraction in certain directions. Polarisation was first discovered in 1810 by Malus, a French philosopher, who died only a few years since. Light is polarised by reflection or refraction. If reflected on a surface of black glass, light is polarised when the reflection takes place at an angle of 35° 25' with the glass. The following are some of the properties of the polarised ray.

1. This ray undergoes no reflection on falling upon a second plate of glass at the same angle of 35° 25', if the plane of incidence on this second plate is perpendicular to the plane of incidence on the former, but it is more or less reflected if incident at other angles.

2. When transmitted through a double refracting prism it only gives one image, if the principal section is parallel or perpendicular to the plane of incidence, while in every other position with respect to this plane, it gives two images more or less bright.

3. It cannot be transmitted through a plate of turmalin whose axis of crystallisation is parallel to the plane of incidence, but on the contrary is more and more easily transmitted, as the axis of the turmalin becomes more and more perpendicular to that plane.

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