depreciate in value. I might with as much propriety assert of the system of which your Correspondent is the exponent, that its adoption as a purely decimal system involves the depreciation of the gold money 91 per cent. This result must surely appear ridiculous; and yet if the calculation is made upon the principle applied to the “copper money," such it really is. If this notion of the depreciation then be acknowledged, how vastly superior must the pound and mil system, with its four per cent. of loss, be to the twenty. penny system, with its loss of ninety-one and one-third per cent.

But again let us confine our consideration to the copper coins, and compare our friend's new piece, the fifth of a penny, with its corresponding coin, the farthing. Here, upon his depreciatory principle, the extent of loss would amount to twenty per cent.

Here then again is a preference in favour of the pound and mil system, and that to the extent of sixteen per cent.

Now, Sir, having put the “two matters of fact” before your readers in a proper light, I may further be allowed to make a few remarks upon the contemptuous manner in which your correspondent dismisses the subject. Declining further controversy seems to imply that my attempt to put the subject before the public in its true form and in opposition to the views of the writer in question was a gratuitous undertaking as far as that public was concerned, and a vexatious intermeddling with the plans of the twentypenny advocates. But, Sir, the real position of the matter is just the reverse of this. Your number for February contained a very sensible article on the subject, in which the following sentence occurs,—“Nine-tenths of all who have given a thought to the subject concur in the opinion that the pound and mil system is the only one possible, and if the Government would only announce that they have decided on that system, though the immediate carrying it out be postponed, no small step in advance would be made.” This article, the aim of which was rather to present the importance of the subject to teachers, than to oppose the views of those who advocated particular and peculiar schemes, was followed in the succeeding number by the article on the twenty-penny system. Although, it is true, this exposition was subscribed with the writer's name, it held so prominent a place in the pages of the Journal that it was only natural its fallacies would be pointed out. Thus, Sir, arose the discussion the result of which has been so precipitately declared by your correspondent.

I will only add, for his satisfaction, that I have perused the Report of the Decimal Coinage Commissioners; and not only Lord Overstone's questions, but Professor De Morgan's answers to them. When writing to one of our educational periodicals, published on the 1st of July, I stated “Perhaps Professor De Morgan never appeared to greater advantage than in the complete answers he has given to the sixty-five questions proposed by the noble banker, which, from his lordship’s position as one of the three Royal Commissioners appointed to inquire into the desirability of introducing the decimal system into our currency, might, without being so ably answered, have not only influenced the question in the minds of the public, but might have retarded the introduction for a generation, or till schoolmasters set earnestly about teaching the simple beauties of the system, and spreading an acquaintance with the advantages which it possesses over the present ugly, cumbersome, and unscientific scheme.”

I am, Sir,

Yours very truly, August 30th, 1857.


CONNECTION OF SCHOOL WITH HOME FEELINGS. --The more we can engraft and connect the school with home feelings the better; and I trust the time will come when the poor man will look upon a provision for his child's instruction as a part of his own household expenditure-just as much so as of food and clothing. The wages of the labouring man ought to be equal to all his decent wants-food, clothing, shelter, and education; and the less which is required from others in order to help him to accomplish this, the more independent and happy he will be. That state of a community is the most healthy, in which the wages of labour of the honest and industrious working man are equal to all his wants, and where he thinks it his Christian duty to provide for, and make them a part of, his family expenditure.--Effective Primary Instruction.



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=(3-3) (y+3)=xy+32—379; subtracting wy on each side, we have 3=3.3--3-9; transposing-9 we have 12=3x3y; dividing by 3, we have 4=-y.

The second equation is xy5—(245) (y+5)=xy+5x—5425, which, worked as the first is finally reduced to 452-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--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




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


34=39_5 35

38=35+3 40=35+5

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1365 1368 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=16+d) b=b+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 samed-1, and multiply the two new factors; we have a=b+d; then, a d i)=+1 therefore (6+1) (6+d-1)=+d+d-1; this product is greater than the first b2 + bd by d-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 (6-1) (6+1+1)=62+621.

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.

50=37+13 38=50-(13-1) 36=50-(13+1)

49=37+(13—1) 51=37+(13+1)

1862=1850+13—1 1836=1850—(13+1)

Yours respectfully
Manor House Academy, Leamington Spa.


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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,

D. I. D.
Let x=length of the original rectangle-


and xy=area 1st Case.

2—3=length of second rectangle.
y+3=breadth ,

and (2-3) (y+3)=xy+3
or xy+32—37—9=xy +3


x- y= 4 2nd. Case.

-5=length of third rectangle.
y-5=breadth 2
(345) (75)=area ,
and (x–5) (y+5)=xy-5
or xy+5x454—2 5=xy5


x- y=4. 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.

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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,

GÉORGE 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.7

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.

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Mensuration, Plane and Solid. By the Rev. J. Sidney Boucher, M.A.

London: Longman and Co. 1857. A HIS book gives very clear and familiar explanations of the most 19 important practical truths established by Geometry. It grapples 10 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.

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."

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