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top of which is placed a seraphine. The children are permitted and encouraged to attend the services, and to join in the responses and singing, and they do so spontaneously. I accompany them upon the instrument; we chant the Magnificat, Nunc-dimittis, &c., and sing three psalms. I find the children interested in it; they love it; and, as a natural consequence, are attached to it; and through such means, to our church and her services.

I will now notice one other means of attraction, and then conclude.

It is often the case, when boys are taken from our daily schools, they think, to use their own words, they are too big to come to the Sunday schools. To remedy such a case, our excellent pastor has established an adult class in connection with the Sunday school, of which class the Rev. gentleman is the teacher. In this way a mutual feeling is ingendered between pastor and scholars; a feeling which has been hitherto productive of the most blessed results.

In our Sunday school there is a phalanx of upwards of 50 teachers, many of whom have been raised from the ranks of the scholars; some of the latter are members of our church; they hold fast the profession of their faith : and I trust and believe, adorn the doctrine of God their Saviour in all things.

Your obedient servant, Pontypool School, May 16, 1845.

Thos. GARMSON. P.S.-"R. F.” states nearly all his boys' parents are dissenters. I am in a similar situation, surrounded on all sides by schism; nay, indeed, in the very hot-bed of dissent.

It is an

Rev. SIR, Your correspondent F. has made out a strong case in reference to the defection from the service of our Church, of the children of our schools, the moment they have finished their education. evil, which, I believe, most clergymen have occasion more or less to lament; but I trust not to so wide an extent as is complained of by your correspondent. And if I am correct in identifying the initial appended to his letter, and in recognizing the sentiments contained in it, I must say, that I do not know any fellow-labourer in this portion of our blessed Lord's vineyard, who, I think, so little deserves to be exposed to the disheartening infliction of such a result of his labours. I know no one better qualified for the pastoral superintendence of the lambs of his flock, and no one, I believe, is more diligent and pains-taking in disa charging the duties demanded from him. I am fully aware that parishes are differently constituted, and that the efforts which may be crowned with abundant success in one district, may be attended by a total failure in another. As far as my own experience goes, I am bound to testify, that the greater number of children who have received their education in our schools, continue, so long as they remain in my parish, pretty constant attendants at my church. How far they persevere in this course when they are removed to other places, is a matter I have seldom the opportunity of ascertaining. To ensure this desirable consummation, I adopt no other means than frequent intercourse with them

and friendly admonition. Your correspondent appears anxious to carry out, what is called the church system; but I think the plan he recommends, will be found to defeat his intention. He proposes to dismiss the children immediately after morning prayer, and before the sermon. He says," Indeed, I cannot help thinking our sermons would be more effective, if children were not in the constant habit of hearing them till the time when they were able to profit by them. Till they are confirmed, the proper instruction of children is by means of catechising, and not by preaching; and therefore, if they were not to attend our sermons till they have been confirmed, I think it would be more correct, as well as more beneficial to them."

Has your correspondent forgotten the excellent exhortation he so frequently addresses, in the beautiful language of our Liturgy, to the godfathers and godmothers of children ? The sponsors are therein admonished" that they must remember, that it is their parts and duties to see that their infants be taught, so soon as they shall be able to learn, what a solemn vow, promise, and profession they have made by them. And that they may know these things the better, they shall call upon them to hear sermons.”

This, surely, according to the requirements of our church, is the duty of the sponsors towards their godchildren, before they are admitted to the ordinance of confirmation. To dismiss the children, therefore, before the sermon, would be compelling the sponsors to submit to a dereliction of their duty; unless, as would most probably be the case, the children called, in their way home, at some meeting house” to “ hear sermons" from unauthorised teachers.

Ithink the plan suggested by your correspondent “F." will be adopted by very few. I am anxious, however, to see the opinions of others, on this important subject, which I have no doubt will shortly appear in your columns. May 5, 1845,

P.

INSTRUCTIONS IN ARITHMETIC.

(Continued from page 137.)

ON FRACTIONS, CHAPTER III.

The Russian ball frame, which we so fully described in the last number of this Journal, affords every facility for explaining decimal fractions. This, we think, will be immediately evident to those of our readers, who have thus far given us their attention. From the diagram and accompanying explanation in page 132,* it will have been perceived

* In the note to page 132, we must point out an error of the engraver, who in drawing the spring CED, which is supposed to retain the balls in their place, has not taken care to represent the spring as pressing against the lowest ball of those on the upper part of the wire A B. It is of course intende that by means of the spring, which however the smallest effort will push aside, the balls should be prevented from sliding down by the force of gravitation when the ball frame is held in a vertical position.

in the simple apparatus we recommend, that to the left of m n, any of the balls or units on any of the wires (since they represent whole numbers) are each a tenth of any ball or unit on the wire which is next.

We have, therefore, only to show that the same holds good, though in a reverse order, with regard to those balls or units to the right of the vacant wire m n (which represents the point or division between whole numbers and decimals,) and the child will have but little difficulty to observe the analogy, and to understand how the same principle applies to the tenth, hundreth, and thousandth part of unity. When we come, however, to speak of ordinary or vulgar factions, as they are called, it is not sufficient to point out that l is the half of 2, the third of 3, &c. The question not being how we shall take the half or the third part of a number, which would be, in fact, only another name for division; but how we should divide unity itself into a certain number of equal parts for the purpose of considering any number of such equal parts.

It appears to us, that this part of arithmetic is more readily explained to the learner by means of the strait line, than by any other mode ; for this can be divided into any number of equal and similar parts, which would not be the case if we made use of surfaces in our illustrations; or, whilst the acre for instance is divisible by square measure into perches, yards, and feet, if we take any of these square

divisions to represent unity, it by no means follows that its different fractional parts should be square likewise.

With the strait line also, we shall be able to point out, that every fraction

may be viewed as the division of the number indicated by the numerator of that fraction ; for instance, that i = 3 = 4; in other words, that three times the fourth part of one, or unity, is equal to the fourth part of three. In the same way, that is by two or more strait lines, we conceive the reduction of fractions to the same denomination may be rendered a clear and distinct idea in the child's mind.

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F and B E = 1 and A E = 1; D F = ţ and C F= . It will then be readily perceived that if we divide each fourth into six equal parts, and each sixth into four equal parts, unity, represented in the one case by A B, and in the other by CD, will then be divided in both lines into 24 equal parts, or that 4 x 6 6 X 4, or again that

3 x 6

5 X 4

4 x 6

6 x 4 it will thus be easy to infer the general rule itself.

The same figure or diagram will likewise illustrate the principle upon which fractions are reduced to their lowest terms; or, in this particular case, as the denominators 4 and 6 already indicate, will show, that we may reduce both the fractions and 2, to twelfths, for that twofourths of one-sixth correspond to two-sixths of one-fourth ; or that A E = 1

L and C F=anon is. Now we assert, that all this is

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impossible when the teacher undertakes to explain fractions by taking a square to represent unity.

ON PROPORTION.

Although the rule of three or of proportion, is beyond the capacity of children who are still supposed to be receiving instruction in the intuitive method ; yet, as almost all the questions generally supposed to require some knowledge of it may be answered by a much more simple process of reasoning, it will be desirable to say something to them on the subject. We will illustrate our meaning, by taking an example of the kind from the new edition of Pestalozzi's work, published with the sanction of the Privy Council. It is there said, if 6 ells of stuff cost £3 6s. what will 20 yards of the same stuff cost? Now according to the method of Pestalozzi, the argument would run thus : 20 ells are ten times the third of 6 ells, and £3 6s. are 66s. therefore 6 ells is to ten times the third of 6 ells (or to 20 ells) as 66s. is to ten times the third of 66s. (or to 2208 £11). But according to the principles we have laid down, it would be more simply and, as we assert, more intelligibly said, 6 ells cost £3 6s. or 668.; therefore 1 ell, which is the sixth part of the price of 6 ells, or 66 will cost lls.: but 20 ells will cost twenty times as much as one ell (or 20 x Ils.; but as we can change the order of the factors, we can then say 11 x 20s., or £ll, would be the price of the stuff. If, however, as a teacher I wished to follow the course suggested by Pestalozzi, I should rather say 20 being ten times the third of six, the price of 20 ells will be ten times the third of that of 6 ells, that is of £3 6s. or 66s; now the third of 66s. is 22s. and ten times 22s. 11 x 2 x 10 11 x 20s., that is £11; and in both instances we think the chila would seize our meaning with little, if any difficulty, the language not being beyond their powers of understand ing; whereas at the best, that of the Swiss schoolmaster is unsatisfactory and incomplete, and inasmuch as it is unscientific, must subsequently be laid aside, and be exchanged for another; and though the proportions he lays down, may be in themselves correct, he adduces nothing to show that any proportion does really exist between the several terms of the question.

In concluding these preliminary remarks, we must confess that they have attained a length which we hardly anticipated in the first instance. We had before us the work to which it is intended to invite the attention of our readers and of the public; and to some persons it might have appeared a wiser course, to have given at once the first part of it in this Journal, without note or comment, leaving it for others to form their own judgment. But when we considered the high character of the works to which we venture to prefer our own, and the favour which they have generally and deservedly met with, we feared lest ours might appear rather a presumptuous undertaking, unless we in the first place pointed out in what respects we conceived the old treatises failed, and in what way they were susceptible of improvement. We trust, that whatever

may have been said by us on the subject, will have been said courteously both in spirit and in letter, and that the consequence has

been a willingness both on the part of our co-educators, and of our read. ers likewise, to give a fair amount of attention and consideration to our treatise on Elementary Arithmetic.

ELEMENTARY ARITHMETIC.

CHAPTER 1.

ON WHOLE NUMBERS AND THEIR FUNDAMENTAL COMBINATIONS.

1. Whole Numbers. 1. When we view several objects of the same kind, as children, trees, birds, houses, &c., we can either consider each separately, or we can speak of them in collections of two, or three, or more.

Thus we say two trees, five houses, &c., and these different collections are called whole numbers, one of them being what is termed a unit; so that a whole number is an unit, or a collection of two or more units of the same kind.

2. These units, however, need not be all similar one to the other, even whilst we speak of them as of the same kind, or under the same name ; ex. gr., a herd may consist of different animals, the difference not preventing us from stating the number of all of them. In this case the word animal is taken to represent unity, and not cow, or ox, or calf. 3. Whole numbers, then, consist of units, which are view

* From (Gr.) ho. ed as being, for the time at least, homogeneous,* or of the

mos, like, and same nature or description. In coins or money, the

pound sterling, is that which for the most part represents unity; in measuring length or extension, in one direction only, the foot, or yard, or mile, is generally selected for the purpose: whilst for surfaces, we take one of the same measures considered as squares, having its side a foot, or yard, or mile in length. In the case of solid bodies, by unity is commonly understood the cubic foot, each side of which consists superficially of a foot square.

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4. The process by which we learn how many pounds sterling are contained in a given number of shillings, is called reckoning (French, compter), whilst that of ascertaining how many units there are in any given straight line, is termed measuring ; so that to measure any thing is to inquire how often an unit of the same kind is contained in it. Thus, in order to measure the line A B, I apply the unit m n to A D at the point A,—then to CD,—then to D Е, and so on as far as B.

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