Stewart's guide-book to the queen's scholarship and certificate examinations, and to public elementary schools and training schools

of the questions, by which the children are bewildered. (b) Treatment of the subject in a manner unsuitable to their age, either so that the teacher's language is above their comprehension, or so that they feel that they are being treated as babies, and become sulky. (c) Want of animation, which causes the children to catch the teacher's manner and become drowsy.

Want of interest in work may be caused (as far as the teacher is concerned) by :-(a) Want of geniality and enthusiasm. Children are exceedingly sympathetic, and will catch the spirit of their teacher. (b) Want of decision and clearness. Children feel by instinct the need of a firm guide in their work, and failing to find one, lose heart and hope. (c) Insufficient use of anecdote, illustration, &c. Children cannot grasp abstract ideas without the help of illustration and analogy, but are quick to do so with their assistance.

SECTION VII.

Write full notes of a lesson on one of the following subjects: (u) Some useful trade.

(6) The railway that passes through or near your own neighbourhood.

(d) The manufacture of a horse-shoe, or a teacup, or a needle, or thread.

THE MANUFACTURE OF A NEEDLE.

Class. Standard II.-Time allowed: half an hour.

Objects required for illustration: pieces of fine steel wire, a common needle for each child in the class, a few darning or worsted needles, map of England.

(1.) Call upon the children to say of what material needles are generally made. Show the steel wire, and let class compare it with the needle, to find the differences, and thus to infer that the wire must be cut and pointed, the eye must be made, and the needle polished.

(2.) Propose to imagine a visit to a needle factory. Tell name of town or district (Redditch and neighbourhood) to which we should go. Let a child find on the map the place where the school is situated; point out Redditch and call on the class (a) to say in what direction we must travel to reach it; (b) then to point in that direction, and say by what road or railway we must go. Note on board, "needles are manu

factured chiefly at Redditch and the places near it." Call attention to the word "chiefly ;" ask what it means, what it implies here. If necessary, tell that needles are made in other places, but not to so great an extent.

(3.) Imagine the factory reached; describe it, the class helping, where possible. A large building with many rooms, many people in it at work, and a steam engine to do all the hard work that wants only strength and regularity. (If time allows, let children suggest some of this work, such as turning wheels, lifting weights, &c.)

(4.) Tell that we should not see the steel made into wire ; that is done at other places. Infer that in the first room we shall find quantities of wire to be manufactured. Note, "they. are made from steel wire." Describe the large heavy coils, with many yards of wire in each, of different thicknesses. Class say why this is so.

(5.) From this, lead the children to see that the first thing done will be to cut a piece of the wire. Tell them that the pieces cut are long enough to make two needles. From their

experience of dropping needles, frequently because they are so small, they can judge one reason for this; convenience of handling. Note, "the wire is cut into lengths, each enough for two needles." Describe the cutting-work for machine.

(6.) Tell that in the next room we should find men with bundles of cut wire standing before grinding-wheels. Ask what they will be doing; what will turn the wheel for them. Show how the grinder rolls the wire between his hands; the children, by experience in sharpening pencils, can judge the reason (to make the point central). Tell briefly how these men cover the nose and mouth; how much suffering they sometimes undergo from the unhealthiness of their work; tell also that many plans are tried to alter this, but none are quite effectual. Thus lead children to see our obligation to those who labour that we may enjoy comforts and conveniences-what our duty is in return. Note, "these are sharpened at each end."

(7.) Tell that the wire is next heated, in order to soften it, that it may not snap, but yield, and then rolled to straighten it. Note, "softened and straightened" as next processes.

(8.) Describe the wire, quite straight, laid under a very small hammer, which comes down just in the middle of it. Class infer that the wire will be flattened (why not broken?) Tell that then two sharp steel points are forced through this

flattened part; draw a rough diagram, and let class say what this process will be called. Note, "eyed." Tell and note that the wire is then broken into two needles, and the broken parts smoothed down.

(9.) Recall that the wire is now soft; must be hard, but not too brittle to be useful for needles: so the next thing is to harden it again. Explain that this is done by heating the needles and plunging them into cold water or oil. Note, "hardened." But they would be too brittle after this, so they are again heated, and allowed to cool gradually. Tell and note that this is called " tempering."

(10.) Picture the needle now, black and rough. Class infer that polishing will be needed. Note this. Class say what will be probably used-emery and oil. Describe the working about of a mass of needles in a woollen cloth saturated with this mixture-picture result.

(11.) Recapitulate the information, first with the aid of the black board, then without it. Call on individuals to tell the heads of the lesson; on others to correct any errors or omissions that may occur.

ALGEBRA.

SECTION V.

(a) Find the difference in value between the arithmetical expression 57 and the algebraical expression ab when a=5,

b=7.

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(6) Simplify the expression:

(2a- {3b-a-c} + {46-3a—c})

Clearing vinculum = (2a - {33 - a+c} + {4b-3a+c})
Clearing{}=(2a-3b+a-c+4b-3a +c)
()=2a-3b+a-c+4b-3a+c

= b. Answer.

(c) Reduce (1 − a) + (a − 1 ) b + (1 − a) (b − 1) c + (1 − a) (1 – b) (c-1)d to one expression consisting of factors of the form (1-a)

− ( − a) + (a − 1 ) b + (1 − a) bc − (1 − a) c + (1 − a) cd − (1 − a) bd--(1-a) d+ (1 - a) bd

From the first we get by rearranging and altering signs:

− (1 − a) − (1 − a) b − (1 − a) (1 − b)c − (1 − a) (1 — b) (1 – c)d − (1 − a) (1—b) − (1 − a) (1—b)c − (1 − a) (1 − b) (1 — c)d -(1-a) (1-b) (1−c) -(1-a) (1-6) (1-c)d

= (1 − a) (1 − b) (1−c) (1 - d).