SIR,

HOLLY BANK'S PROBLEM.

(1.)

TO THE EDITOR OF THE ENGLISH JOURNAL OF EDUCATION.

I send you the answer to the problem proposed by "Holly Bank" in your number of the present month, page 281.

Let x-length; y=breadth.

We have the first equation xy+3=(x−3) (y+3)=xy+3x-3y-9; subtracting xy on each side, we have 3-3x-3y-9; transposing-9 we have 12-3x-3y; dividing by 3, we have 4=x—y.

The second equation is xy-5-(x-5) (y+5)=xy+5x—5y—25, which, worked as the first is finally reduced to 4-x-y; thus for two unknown quantities we have only one equation; therefore the problem is undeterminate, and the number of solutions unlimited, the only condition being that the length be 4 yards more than the breadth, as may be seen by the final equation to which the two primitive ones have been reduced 4-x-y. Thus the problem is susceptible of solution by the method of x and y, since by that method we find that any two numbers whose difference is 4 will

answer.

For instance let us suppose the length to be 56 yards, and the breadth 52; adding and subtracting at first 3, and then 5 we have

Again let us suppose the length to be 39 and the breadth 35, we shall find the three following products

All which products evidently fulfil all the conditions of the problem.

Generally let a,b be two unequal factors, d their difference, so that a=b+d; then ab—(b+d) b—b2+bd.

Then, let us subtract from a, d-1, that is, a number equal to the difference of the two given factors, diminished by 1, and let us add to b the same d-1, and multiply the two new factors; we have a=b+d; then, a-(d-1)=b+1 therefore (b+1) (b+d-1)=b2+bd+d-1; this product is greater than the first b2+bd by a-1.

Now let us subtract from a and add to b, this quantity d+1; we have a-(d+) ; then multiplying the two new factors we have (b—1) (b+d+1)=b2+bd—d—1.

This product is evidently smaller than the first one b2+bd by d+1. Therefore any two given numbers being multiplied together, if we subtract from the greater, and add to the smaller their difference diminished by one, and then multiply, the new product will surpass the first by that same difference minus 1; but if we subtract from the greater factor, and add to the smaller their difference +1, and then multiply, the new product will be smaller than the first by that same difference +1.

SIR,

TO THE EDITOR OF THE ENGLISH JOURNAL OF EDUCATION.

August 11th, 1857. I enclose the following solution of Holly Bank's "anomalous problem" involving a "peculiar property of numbers" and "which could not be solved in the ordinary x y manner."

Hoping it will satisfy him as to the possibility of solving it by the ordinary method.

I remain, yours obediently,

Therefore, it is evident that if we can find values of x and y which will hold good in one case, they will hold good in the other.

Accordingly (6-3) (2+3) must equal 6×2+3 or 15=15

and (6-5) (2+5)

... Values required are 2=6

y=2

6x2-5 or 7=7

SIR,

MISS SMITH.

TO THE EDITOR OF THE ENGLISH JOURNAL OF EDUCATION.

Dundee, 14th August, 1857.

I see a paper in your journal, reflecting on a sermon by me, which appeared in the "Christian World." That Journal I have not seen, but, the extracts you comment on were never uttered or spoken by me. The thing is a flagrant hoax. I never uttered one of the sentiments or sentences that are put into my mouth. As a matter of mere justice I claim the publication of this letter. I should take it kind too, if you could send me a copy of the "Christian World," as I don't know where to procure one.

Yours truly,

GEORGE GILFILLAN.

[We never dreamed of imputing the sermon in question to Dr. Gilfillan, a gentleman for whom we have the highest possible respect. We did not know who wrote the sermon, nor did the "Christian World" give the name of the writer. Ed. E. J. E.]

WHAT WILL BE THE FUTURE EARTHLY LIFE OF A SCHOOL CHILD -Few sights are more significant and touching to a teacher's heart than the group of girls gathered out of many homes around her table. What is to be the earthly future of these youthful beings? That little sunburned honest face may be a wife in whom the heart of her husband shall trust, whose clothing shall be strength and honour; that other childish form may yet be a mother whose children shall rise up and call her blessed; that little one with the fair rosy cheek, may, alas, turn into one laden with many lusts, whose ways are the ways of death. Another may be the good and faithful servant, so rare and so precious in the sight of the Master in heaven, as well as the master on earth; another yet may be the brawling woman, who bringeth woe on all around her, or a tattler and busybody, spreading mischief from house to house. But how solemn the question, though largely depending on the other, what will the everlasting future of these children be? Fearful is the responsibility, deep the anxiety of those who feel how much of those two futures depend on their faithful use and application of God's Word, and on their earnest prayer for that Holy Spirit who can alone teach successfully all things, from the things that are of Jesus to the performance of the commonest duty. But go on in the blessing of God's grace-go on, and be of good cheer; go on to counteract the evil tendency-to pluck out the weed-to sow the good seed-to foster the springing grain-the blessing is promised, and will come, and will not tarry.

Notes of Books.

Mensuration, Plane and Solid. By the Rev. J. Sidney Boucher, M.A. London: Longman and Co. 1857.

HIS book gives very clear and familiar explanations of the most important practical truths established by Geometry. It grapples with the simplest things, such as the quantity of yards of given breadth required to cover a given area of floor up to the measurement of water pressure. It is one of the best, simplest, and most intelligible books of the kind we ever saw.

Haydn's Oratorio-The Seasons. Arranged by V. Novello. Pp. 176. London: Novello, Dean Street, Soho.

WE hail with delight these volumes of Novello's arrangement. Some of the airs and choruses are beautiful. The type and execution are both good, and the binding elegant. We are glad to perceive that Mr. Novello intends to compile some of Mozart's splendid masses. We recommend all parents whose children sing, to purchase these volumes.

A New and Complete Course of the French Language. By Auguste Aigre De Charente, French Master in the Royal Military Academy, Woolwich. Pp. 836. London: Longman and Co. 1857.

THIS is an entirely new method of teaching French, and we think it seems a very good one. It is divided into four parts, the first of which treats of French Pronunciation and Accidence; part the second, of French and English Syntax compared; part three, of Gallicisms and Anglicisms; and part four

"Forms a resumé of the three preceeding, and comprises the difficulty of construction and agreement."

Part three treats of the "idiotisms "* of both languages.

This work is intended for the use of young students as well as for those of an older growth, and we wish it every success.

LITTLE BOOKS.

A Short French Grammar. This book is edited by the Rev. J. D. Collis, Head Master of the Grammar School, Bromsgrove, and like all works by that gentleman, deserves commendation. We are glad to see that it has gone through a second edition.

Manual of Scripture History. By the Rev. J. E. Riddle. This is a very valuable work, comprising the whole of Scripture History, including the History of the Jews between the periods of the Old and New Testaments. There are questions for examination at the end of each chapter, and it contains notices of biblical antiquities and geography, oriental manners and customs, &c. &c. We recommend this book to all families, even where there are not children to educate, as the information it contains is most useful.

SERIALS RECEIVED.

Fraser's Magazine.-Sunday School Teacher's Magazine.-Penny Post.

*The author says "An idiom is a peculiar tongue or dialect; an idiotism is a locution peculiar to a certain idiom."

Intelligence.

CARLISLE DIOCESAN EDUCATION SOCIETY.-At the annual meeting of the subscribers to this institution the Lord Bishop of Carlisle (President) gave from the Report the following deplorable account of education in common schools in that Diocese. To the first point, then, as to the condition of the buildings, Mr. Hodgson reports that as a general rule the school houses are totally unfit for the purposes to which they are applied. The children in some of them learn writing whilst standing up and holding the copy-book in their hands; so that you may easily imagine the sort of instruction they are likely to receive. The furniture in most of the schools is extremely deficient, especially in one point, which was a most important one to every school-house or office -important to moral training and most useful to the man of business in whatever position he may be placed-they have not a clock! And, as a natural consequence of this deficiency, there was no greater irregularity to be found than the hours at which the various schools were called together, some assembling at the moment others are learning; in fact, to follow out the idea of the clock, though they are not certainly guided by its movements, they are all at sixes and sevens. With regard to the accommodation out of doors there is positively none at all, and the consequence was the practice and encouragement of everything indecent. In two places the children and fowls occupy the school-room in common, and in one place the master's head was comfortably ensconced beneath the turkey's tail. Then comes the question of the masters. In many cases the masters are entirely self-appointed, no one else taking any interest in the school whatever. They come there and assume the duties of schoolmaster solely as a speculation, which, if not found to answer, will be thrown up and the school abandoned. Next, as to the attainments of the scholars. I have classed them in this way,-reading, writing, and spelling fair, but-and it is very important but-thought, reflection, and application very deficient; so that, though they possess the knowledge as a mere machine, they have no power of applying that knowledge. This was proved by the answers to the questions they gave from their books, and also from their utter incapability of writing from dictation. It was also proved from practical questions put to them in arithmetic, so simple that they might occur in every-day transactions, and yet they could not be answered. In grammar their answers proved that they knew their lessons only by rote; in geography they were very deficient, and throughout the whole of the schools, maps and geographical books are exceedingly few and are very much wanted. That meets the points mooted by some gentlemen in this room as to whether any grant from the Council of Education could be obtained to meet the local grants, so as to completely furnish these schools with books and maps, and not suffer them to go on in the old hum-drum way, but provide them with such instruments as would fit them more for the pursuits of every day life, and make them a blessing to their generation. Then again, as to the scholars, we have the same thing which I have already noticed only in a different form. I mentioned the irregularity consequent upon the want of a clock; that referred to the hours of assembling the schools, but there are also great irregularities in the attendance. There seems to be a want of hold upon the children and their parents to induce them to persevere week after week in their education. The amount of religious knowledge Mr. Hodgson declares to be very low, except where there are Sunday-schools; and where there are, there is a marked difference, the children exhibiting great readiness and pleasure in answering the religious questions put to them. Then comes the question of the masters. There is a total want of method in the teaching of the masters, and the consequence is double difficulty to both master and scholar; for instance, having the children up one by one to read, and carrying out their examinations without method. In one point the masters seem admirable, as to their average age-nearly 38. Unfortunately, however, the profession of schoolmaster is constantly assumed because of the want of bodily health, or from physical deformity; so that an office that requires great courage, both physical and moral, health and strength, and unwearied attention, is undertaken by those who are wanting in all these qualities. Now, as to the means of maintenance. The sum from endowments amounts to £527 18.; from subscriptions, £252 2s.; giving an average for each school, without the quarter