culties, our feelings would be more excited, our energies more developed, and our meetings would therefore be more interesting; the speakers would have something more to do, and the people something more exciting to listen to. But, we must accept our condition as it is, and be thankful that we have so few difficulties to contend with--that so many avow now that popular education is not only a necessity by reason of the ignorance that prevails, but a solemn duty, binding on all who would have any regard for the welfare of their species. That popular ignorance prevails to a very great extent has been shown in the statistics brought before you in the Report. There is one thing, however, which no statistics can very well bring out; and that is, the very imperfect education of those who are educated. The fact is, numbers are on the books during the course of the year who perhaps do not receive more than a month's education out of the twelve. That should be borne in mind when considering the necessity for education. But, among all the institutions for promoting popular education, the question naturally arises, “ Why should I attach myself to this or that?" And I have had some difficulty, I confess, in answering that question. Three things, however, have been very palpable to my mind. The first is,-all admit that the people must be educated; with the most dissimilar aims, and principles, and expectations, in connexion with education, we come to that conclusion. I am right sure that the people will be educated. There is an influence in the people of this country which is far beyond their specific aims and even desires, which will compel them to that issue; and God, wiser and better than man, has outstripped the expectations and desires of the best, and, in His own way, will secure that which we have not had the wisdom rightly to seek. There is such an endless diversity of opinion, that it is utterly impossible to reconcile all. I am driven to this conclusion,--education, to be conducted at all effectually, must be conducted by the combination of numbers. Hence it strikes me that there is an absolute necessity for compromise. My question is, "Where must I compromise the least?" I feel that I compromise the least here, and therefore attach myself to this Society. Then I perceive that sectarianism is universally denounced. Our secular friends denounce all religious people as the sects, and those who take the most denominational grounds are as firm as all the rest in denouncing sectarianism. I think that after all one finds less sectarianism here than anywhere else. What all the world condemns as a bad thing must be a bad thing, and I go, therefore, where there is the least of it. And, last of all, I think there is more liberty of conscience here than anywhere else. In one point, I disagree with the Committee as a matter of theory; and that is, about receiving Government help. I do not say it is wrong, I do not say it must be harmful; I am not convinced on that point; all I say is, I would not take it. But I find there is perfect liberty of action. The Society has no agency to denounce other people; it does not employ itself directly or indirectly in frustrating the efforts of others; and in the schools that are severally connected with this Institution, people may take or refuse Government help just as they will; and, as I do not like to be dictated to, and do not like to see dictation, I feel necessitated to come to this conclusion, that here and here only can I find any sphere of general co-operation for the purpose of accomplishing this object. There is an old adage, "In essentials unity, in non-essentials liberty, in all things charity;" I find the largest amount of all three here, and, therefore, I beg leave to move this resolution. The Rev. WM. GILL, from Raratonga, in seconding the resolution, expressed his gratitude for the Society's labours.

The more he contemplated the blessings of Christianity to the heathen world, the more deeply he felt interested in the general education of the great masses of this country. He then referred to the great advance in education which had taken place in the islands of the South Sea, and the difficulty experienced by the

missionary in first forming a written language. It would, he said, perfectly confound the advocates of secular without religious knowledge, if they attempted to impart their secular education to the natives of those islands. It would be quite impossible to teach the people, if they did not believe that the teacher had a religious object in view. They were essentially a religious people; all their ceremonies were bound up with religion. The missionary had not to teach them there was a God, or that there was such a thing as sin, or that sin caused convictions and apprehensions as to its consequences. So also they needed not to be told that there was a futurity: he had never found, in all those heathen tribes, a man who, in his natural condition, would say that his life was the same as that of the beast; in fact, they never used the word "dead" in reference to man; they spoke of him as fallen, or as asleep, or as gone. The Bible was the only instrumentality that could meet the depth of the necessities of the heathen world, and raise them to the position which God would have them occupy in this life and the next; and in going to heathen countries with the Bible in their hands, the missionaries were as much interested in the civilisation, and advancement, and dignity of their fellow-creatures, as those who would have the Bible excluded from the school. In the South Seas there were 400 native teachers who had been instructed in the missionary schools; and he should be glad to see such institutions more encouraged, as the normal schools invariably turned out the best men for the mission field. The resolution was put by the Chairman, and unanimously carried.

The Very Rev. the DEAN OF HEREFORD moved :—

"That the most respectful thanks of the meeting be offered to Her Majesty the Queen, and to His Royal Highness Prince Albert, for the continuance of the Royal patronage and support."

He said, they were all well aware of the very great interest taken by Her Majesty and Prince Albert in the cause of education, and of their anxiety to promote also the religious education of the people; therefore, he need say nothing about the resolution. He was much gratified at being present at the examination, and per. fectly concurred with the observations which fell from his lordship. He also claimed to be a worker in the cause of education, and not a man of crotchets and theories merely, for he had been for some years endeavouring to work it out, by making it as practical as he could in those neighbourhoods and districts in which he had been placed, insisting upon promoting practical education, whether in the schools of the British and Foreign School Society, or in any others. He had been very successful in his exertions, and did not recollect hearing of an objection on the part of a parent, although it was the rule that any objection should be at once attended to. He did not quite concur in one objection which fell from a preceding speaker, with regard to placing schools in connexion with the Committee of Council. During the last ten years, he had been convinced of the advantages of placing as many schools in connexion with it as possible, and his conviction had also been shared by the managers of both British and Foreign, and National Schools, who had seen the good effects arising, in the way of teachers and school apparatus, and many other things. In fact, the inspection itself, so far as he was aware, did not interfere with the liberty of the managers; the inspectors merely ascertained whether the education was such as was deserving of the support of the Committee of Council, which assurance those who gave support had a perfect right to expect. The working of the scheme had been in every respect good; indeed, he believed the present public feeling in regard to education to be attributable to that more than to any other cause; and, although he was quite aware of the deficiency of education among the labouring classes, both in the rural districts and in the towns, he was perfectly convinced that greater progress had been made during the last ten years than in any other similar period. There were, it was true, hundreds of schools that had not done the amount of good that might have been expected, and he could himself,

by going to them, give an examination which would show the schools up; but he was certain that a greater amount of good had followed the working of the system than many gave it credit for. He attended lately some schools conducted on this principle, with which he was himself connected; they were schools for the labouring classes, and were carried on in such a way as to show that they were effective for the purposes for which they were established. The boys from nine years of age he considered should have a kind of practical education which would be useful to them in life; but that was the time when their labour was becoming valuable, and, therefore, the time when they would be likely to be leaving school. He classified the boys according to age, and tested all those between nine and eleven by a very simple test on practical things, such as reading, arithmetic, and dictation of common sentences; but when he came to inquire into the time in which those children had been to school, he was astonished to find that numbers of them had been to scarcely any school previously. He was certainly surprised at the high per centage of children above the age of nine years. In two schools he once examined in a rural town there were 110 children present in one, and 109 in the other; in one of them 86 per cent. and in the other 79 per cent. were above that age. This per centage he ascribed entirely to the idea they had of the education being useful to them. One observation he would make upon the scheme of the Committee of Council with regard to teachers, a feature which had been used in Parliament against the scheme. It was stated by Sir John Pakington that a very large number of pupil-teachers who were trained in the schools, as soon as their apprenticeship expired, went to other occupations, and, therefore, the money spent on them was in some measure wasted. He believed, that the numbers who left were not by any means so great as they were said to be, and that it would turn out, upon inquiry, that the numbers who left were very small indeed; but supposing them even to be great, it was one of those things. that he would rather encourage than the contrary, for they became afterwards little centres of civilisation among those with whom they were placed, and, instead of doing harm, did a vast amount of good. He had always been anxious, as far as possible, that the recipients of education should be made to pay for it; and his own experience convinced him, that where the education was good, and came home to the practical wants of the people, they would do all in their power to get it; and that they would also take a greater interest in it by having to pay for it than they would otherwise. Besides, in making education free, you were in some measure relieving the parent from the responsibility which it is by no means desirable to relieve him from. He would rather impress upon the parents the necessity of doing all they could to educate their children.

RICHARD SLANEY, Esq., late M.P. for Shrewsbury, in seconding the resolution, said:

Thanks to our graciousTM

It was one that must meet the approval of every heart. Queen and her Consort, for the approval and assistance which they gave to the schools. He need scarcely say, that it was by their example, the example of their domestic virtues, which they so constantly gave, in going about with their children, and showing an example of those domestic virtues to their people, that they best supported schools like those of the Society; and he rejoiced to think that the noble Duke who presided was following the same example, in bringing those who were dearest to him to countenance such a noble Institution. Upon the general measures of the Society he would say but a very few words. It was his lot, a few years ago, in Parliament to move for a Committee, the last, he thought, upon the education of the people, and the evidence that was given before the Committee distinctly proved, that in all the large towns of the realm there was the greatest possible deficiency. In round numbers the proportions were, that while one in

eight ought, after all allowance, to be educated in schools of this nature, there were in Manchester, and Birmingham, and Leeds, three of the greatest towns of the realm, about one in twenty-nine; that in all the eastern parishes of this vast metropolis, the numbers were very little more; and that in many of the neglected large towns of the country the deficiency was still greater. Although great efforts had been made, thank God, since that time, he doubted much whether great improvement in proportion to numbers had taken place in those districts, because the Census showed that the increase of population every ten years, since the beginning of the century, had been, in those populous districts, about 30 per cent. But there was another point to be considered,--the quality of the education given. He feared that many were contented with a numerical attendance, as his excellent and reverend friend had mentioned; but when they came to examine the quality of that education, it was found to be frequently extremely evanescent, and to pass away as something that the children did not understand. He hoped to see the day when we should have such an education as was introduced into some schools in a distant county, by the rev. gentleman who had just addressed them; such an industrial and intelligent education, that not merely did all the children of the district attend willingly to pay for it, but numbers of persons came from a distance to take lodgings for their children within the parish, that they might receive the benefit of that education which they knew would be beneficial to them in after-life. Some years ago he was travelling in Perthshire, and was struck by the beauty and height of the mountains. He remembered going into the abode of a poor shoemaker, and asking him what was the height of the mountains, but had little expectation of an answer. What was his astonishment to find the shoemaker bring out to him a scale of the heights, not only of his native mountains, but of all the mountains in the world. In the country in which he dwelt, looking on the beautiful mountains of Wales, he believed that he should seldom find a person in the valleys who could give him such an answer as that. The difference was owing to the spread of education, because they were intelligent and regular in their habits. So that from merely worldly motives there was a great advantage in the acquirement of a good education. There was only one other point that he would refer to, and that was, the good effects of encouraging the most active and energetic in the schools; but he should like to see also that there were great pains taken to encourage those who were perhaps the most diffident, the most gentle, the most kind-hearted and benevolent among them, but to draw forth whose benevolent feelings was of greater consequence to their after-happiness than anything that could be done for their intelligence. It was in this way not merely the happiness of those who came in contact with them, but their own well-being, would be best consulted; and this more particularly as regarded the gentler sex, who, as mothers, as daughters, as sisters, as wives, by a smile, or a gentle word, could so often turn what was calamitous into what was happy and smooth, and give a serenity to the home when the husband or the father returned.

SAMUEL GURNEY, Esq., moved the following resolution, which was unanimously adopted :

"That the best thanks of the meeting be presented to His Grace the Duke of Bedford, the President, for his munificent subscription, and to His Grace the Duke of Argyll, for kindly taking the chair on the present occasion."

The Noble CHAIRMAN briefly returned thanks, expressing his regret at the absence of Lord John Russell, who had always manifested so much interest in the welfare of the Society.

A Gentleman stepped forward at the close of the meeting, and, addressing the Chairman, said it might interest him to know that the Duke of Bedford was about to lay out from £1,500 to £2,000, in building British and Foreign Schools at Tavistock.

ON TEACHING DUODECIMALS.

Very little observation will show that in the progress of the educational movement, not only in relation to the subjects taught to our scholars, but to the teachers themselves, we are coming nearer to the practical and useful; while those matters which, but two or three years since, were considered of primary importance, are now taking their proper place, and are looked upon rather as disciplinary, than as bearing on the practical working of our schools. Looking at the subject from this point, it is proposed to give two or three papers on the proofs of the rules in arithmetic, which, until the recent curriculum of study for training colleges was prepared by Mr. Moseley, were generally looked upon as unimportant; for, as far as it is known to the writer, no English arithmetic, except the excellent one recently published by Cornwell and Fitch, notices the proofs to which these papers will be devoted. The American reprint, edited by Mr. Wallace, and known as "Cassell's Arithmetic," gives some little attention to the subject.

In this number, the proof of the rule for finding areas by duodecimals will be taken up, leaving others, as those for rods of brickwork, &c., to a future time.

In duodecimals, the sub-divisions of areas are by twelfths, and hence differ from all other superficial measurements; they are square feet, twelfths of square feet, (called primes)*, twelfths of primes (or 144ths of square feet, called seconds), twelfths of seconds (or 1728ths of square feet, called thirds), and twelfths of thirds, &c., (called fourths.) The following table will be necessary :—

Y

n

D

Suppose the following question to be proposed.† Find by duodecimals the superficial content of a board, 5 feet 7 inches long, and 4 feet 3 inches wide, and prove the rule you use. Let the annexed diagram represent the board; from F to C being 5 feet 7 inches, and from C to H, 4 feet 3 inches (or 5 and 4) and at each foot, and inch (or 12th), make marks, and draw lines across at right angles to each other; the board will then be divided into square feet, twelfths of square feet (or primes) and twelfths of primes (or seconds.)

Since F to W is 1 foot, and F to Y is foot, .. F, Y, S, W,

is a square foot;

R

A

and since it is divided into twelve parts by the vertical lines, each of these parts is th of a square foot or a prime (being 1 inch one way and 12 inches the other). But each of the spaces in D, N, K, C, is a prime, being 1 inch by 12, and there are seven of them in D, N, K, C; but from C to B is 4 feet, .. the number of primes in D, A, B, C, will be expressed by 7 x 4 28 primes; but 12 primes = a square foot,.. 28 primes 2 square feet and 4 primes, the area of D, A, B, C.

=

These are generally, but erroneously, called inches.

+ This kind of question was proposed at the last examination for certificates.