fronted with the pre-existing fact that the bases are the same. But this difficulty has been met in figures (3) and (4).1

9. In giving these ample details of the Author's experiences in teaching these early propositions, it is not meant that other teachers. should reproduce these explanations verbatim. The object is rather to show how important it is that the teacher, in the earliest lessons of geometry, should "keep touch" with the pupil. Where the learner can readily accept the proof without these or similar explanations, the teacher may safely pass on without them,

But the teacher must be quick to perceive the least symptoms of bewilderment, and must never allow the pupil to lose coolness and confidence, or to guess and "plunge," like a bad swimmer, out of his depth. Children differ greatly in the habit and manner of assenting. Some, out of a desire to please, will say "Yes," in answer to the question, "Do you understand this?" when, in reality, they do not understand it, but only remember it. Therefore, when a child says he understands any statement in geometry, he should be immediately confronted with several exemplifications of that statement in different shapes angles of different sizes, triangles upside down, X and Y instead of A and B, Arabic numbers instead of letters, and so on; and not till he has passed these tests must the teacher be satisfied that the pupil really understands.

Also, in repeating Euclid, the child must not only be compelled to draw his own figures (or to dictate to the teacher how to draw them), but also when he makes a statement he must be constantly called by the teacher's "Why?" to give a reason for it. "Therefore the base AB is equal to the base CD." Why? "By the Fourth Proposition." "Therefore the remainder AB is equal to the remainder CD." Why? "Because if equals be taken from equals, the remainders are equal." "And AE is equal to AD." Why? "By construction," or "Because we made it so." "Now AB is equal to AC." Why?"By hypothesis," or "Because we supposed it to be so from the beginning."

After the Fifth Proposition has been intelligently and thoroughly mastered, Euclid should present little difficulty till the pupil reaches the Sixth Book, which belongs to a stage of instruction beyond the scope of these pages.

But still, up to the Fifteenth Proposition, or further, the teacher will do well to rely mainly on oral instruction, and—particularly if his pupils have good memories-to beware of the book.

Deductions, of a very simple sort, should be in use from the start.

1 A shorter method would be, after the figure has been constructed, to say, “Now we are going to use the Fourth Proposition. Enunciate it. What triangles do you see that look equal? (Ans., ABE, ACD.) "Then we shall try to prove that these two have two sides and the included angle of the one equal to two sides of the included angle of the other." This done, you say, "Now what other triangles look equal?" (Ans. BCD, CBE.) "Then we shall prove the same thing in these triangles." If the boy can readily pick out the two pairs of equal triangles for himself, it may be unnecessary to use the longer method of instruction.

VI. RELIGIOUS INSTRUCTION AND HOME INFLUENCE.

57. RELIGIOUS INSTRUCTION.

1. It is now generally admitted that, in all subjects of education, it is an injury for the young to be taught to repeat language to which they attach no meaning.

Teachers who believe this, and who believe further that Religious Instruction is the most important of all educational subjects, ought to be especially on their guard here lest the desire to train children in this subject early should result in their being trained prematurely, and consequently inefficiently.

2. But the presence of children at short religious acts, such as "saying grace," singing hymns, and other short expressions of devotion, is a very different thing from making them learn and repeat long and (to them) unintelligible formularies of religion.

Silence and attention during "grace" afford one of the earliest and most impressive indirect means of helping a child to realize that there is a Power in the Family, never approached but with reverence; unseen and unheard, yet addressed in words; One who is present not only on Sundays, but on all days, and who, though He is far above us, is nevertheless not so high but that we may ask Him to bless our daily bread. 3. The Lord's Prayer-much though we may desire it to be the first prayer because it is the best prayer-ought, in the Author's judgment, to be deferred till the child has been accustomed to the usual simple petition for "father, mother, brothers, and sisters." No words can well be more powerful than these in introducing the child to the conception of One who must be above all things in greatness and goodness, because he is even greater and better than the child's parents.

As to the importance of the circumstances of prayer, enough has been said above (see § 32).

4. Not till after a child has thus realized in some faint degree the human revelation of God, revealing Him as One who can bless and help, should he be introduced to that other revelation through Nature, which reveals Him as the Maker and Sustainer of all things. Suffer the child first to exult a little in the beauty, and to admire the glory and order, of the visible world, before leading his thoughts up from the things made, to Him who made them.

And when the attempt is made, it is best made by the father or mother, not by nurses or servants. "I remember," writes Preceptor, "that on one occasion, during a walk in the country, when I noticed that my son—a child of four or five years old-seemed more than usually impressed with the beauty of what he saw around him, I thought the time might now have come to lead him from things visible to the invisible Maker, and I asked him who, he thought, had made all

this beautiful world. He at once replied 'God;' but his emotions of joy were at once checked, and his countenance became blank and inexpressive, as if he were passing from a state of genuine feeling into mere unmeaning speech. It was obvious to me that he did not realize, in any sense whatever, the meaning of what he uttered; and I guessed at once (what I afterward ascertained upon inquiry) that he had been trained to say it by his nurse, and was merely answering by rote.

"I felt that this teaching, however well intended, had been premature. Wesley records it as one of the critical moments of his life, when his mother took him into a room by himself, and there for the first time spoke to him of the Being above, to whom alone worship is due. Not to all parents assuredly is it given so to impress their children as the young Wesley was then impressed by his mother; and very probably I might have failed as the nurse failed. But I felt that I had been deprived of even the chance of succeeding. No great harm had been done; but an opportunity of good-which I might possibly have utilized, and should have liked at least to have tried to utilize-had been irrevocably lost."

5. The name of God ought by no means to be introduced lightly, or on every occasion, to enforce duty. The consciousness of right and wrong in the first place, and where this is insufficient the will of the parents, ought to suffice for the most part without appeal to religion.

Above all things, teachers should avoid accustoming or encouraging children to talk much about religious matters. Such talk, even when accompanied with right action, cannot be wholesome, for it must always express more than the child really feels. Besides, in most cases, it will not be accompanied with right action: it will be a mere safety-valve for unnatural excitement, letting off steam which ought to have been utilized for something better than words. A child who gushes generally turns out badly; and it is this type of gushing creature which goes far to justify the proverb, "The greater the saint, the greater the sinner." 6. Yet it should always be tacitly assumed that God is the Author of all duties, the Maker of the ties that bind a household together, that he sees right and wrong, even though unwrought and unuttered, and existent only in the mind; and that He is pleased with what is right, and displeased with what is wrong.

The best time for impressing this upon the child is before his evening prayer. Most children are apt to be more open and disposed to reveal their thoughts at this time; and it therefore affords the best opportunity for the parent or trainers to review the events of the day. "Now have we anything to think of before prayers? Is there anything done amiss to-day which you must try to do better to-morrow?" Many a child who would have resented a sudden scolding, especially before strangers, will be much more open to genuine conviction and contrition if his fault is thus for the first time pointed out; and a resolution thus made, and followed by the usual evening prayer, is more likely to be adhered to than if made at any other time.

7. By this habit of practically reviewing the day-not, however, to be mechanically or invariably adopted-an additional force and meaning will be given to prayer. Acknowledgment of fault and weakness naturally leads the mother to speak of God as the Forgiver and Helper, to whom prayer must be addressed for forgiveness of the past and strength for the future.

8. As regards church-going, it is obvious that what are called children's services must be less tedious and more intelligible for them than the ordinary services; and with discreet management-so conducted in the church, and with the results so moderated at home, as not to produce any unwholesome excitement-they are probably of advantage.

9. But on the other side much is to be said for the presence of children at the religious observances of their elders. In the Law of Moses it is assumed that the child is present at the celebration of the Passover before he is aware of its meaning; and part of the celebration consists of the child's inquiry and the father's reply, thus traditionally handing down the meaning of the institution from one generation to

another.

In the same way the presence of a child with his parents at the services of the church (where they are not so long or so dull as to be absolutely intolerable, probably conveys more indirect benefit than is commonly supposed, giving him an early conception of religion as a social and not merely individual influence, and quickening his apprehension of the Being to whom not only his parents but the whole neighborhood unite in all solemnity to pay homage.

10. If a child is fond of reading, and chooses to read the Bible for himself, his instinct will probably guide him to those parts which are most intelligible, or from which he can at least extract a meaning, and there is no sufficient reason for preventing him from this desultory perusal. But it would be a very sad mistake for a teacher to cause children to read through the Bible consecutively as a religious task. Not to speak of the genealogies, there are obviously many portions of the books of the Law and the Prophets which should be passed over in teaching children, and there are other portions in the historical books treated with a fullness of detail which does not fit them to be reading lessons for the young. Yet, on the other hand, the summaries of the Bible frequently employed by those who have to “get for examination," for the most part, omit everything that constitutes the life of the Biblical narrative, so that they cannot be accepted as substitutes for the original.

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11. The best course seems to be that a child should receive, as an introduction to the reading of the Bible, one or two oral lessons about the early history of religion, illustrated perhaps by a visit (if in London) to the Egyptian and Assyrian rooms in the British Museum, showing how the great nations of antiquity, groping after the great God who

made heaven and earth, typified Him in various imperfect forms, representing His power and wisdom, and how they fell short of the conception of the Eternal Righteousness and the worship due to Him.

12. After this, they may be taught how God in the darkness sent down a ray of light to Abraham the Father of the Faithful, and to his children and descendants, guiding and chastening them, and revealing Himself to them not only as Powerful, but as being One, Eternal, Righteous, Just, Forgiving; and with this introduction the child may read the lives of the Patriarchs and of the deliverers of Israel, understanding (though, of course, very imperfectly as yet) that the great merit of all these heroes was their faith or trust in Right against Might.

13. Not till a later period must the story of Christ be introduced. In prayers and hymns the child will be already familiar with parts of it. But now these parts are to be combined for him into a brief whole; and he is to be introduced to the Incarnation as being the central event in the world's history, wherein God, who had previously revealed Himself through servants, at last revealed Himself through His Son as being our Father in Heaven.

14. Some people maintain that the conception of God as "our Father" is not in itself sufficient, being compatible with self-conceit, foolish hopes for oneself, contempt for others, and an insensibility to justice; and doubtless if a child is taught to realize God as "my Father," these objections are well founded. But they disappear if he recognizes the full force of "our," namely, that God is the Father of our enemies as well as our friends, of those whom we are disposed to dislike or neglect as being offensive or common-place, no less than of those whom we admire as exceptionally good and great; and that He cannot be supposed to fall below Plato's standard of justice, which consisted in "giving to all what is best for them."

15. It is thought by many in these days an old-fashioned and exploded doctrine to teach that there is an Evil Being in the world resisting the Good. Yet without believing in the existence of the weaker Evil it is scarcely possible to believe in the existence of the stronger Good.

Even to a child the question must suggest itself in his very earliest years, How can the world-being, in part, evil-have been created by a perfectly good God?

Admit at once that the origin and existence of Evil are past all explanation, and constitute a logical difficulty. The reply is obvious, that any theory whatever of the existence or non-existence of a God involves a logical difficulty. It is therefore the right course to adopt that theory which, though logically inexplicable, does least violence to reason and best approves itself to the instinct of Faith.

Not for nothing therefore does the Bible put at the very fore-front of its teaching the doctrine that there is Evil contending against Good; and to suppress this doctrine, even for children, is, in the Author's judgment, to do great harm.