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greatest truth it may be affirmed, that if we desire to pass through this life in peace and comfort, we must rely on God, who will give us those consolations, which are so requisite to human happiness; but, as the immortal Dryden very justly observes,

“ Look 'round the habitable world, how few
Know their own good, and knowing, it pursue !"

Treme II. “On Cowardice,” by Miss Dawson, aged 12, Spalding Seminary.

Those are cowards only who, when involved in misfortunes and distress, seek an end to their afflictions in death. It is the part of a brave man, when involved in unavoidable distress, to rise superior to every trouble, to set at defiance the insults of the world, and to place a proper confidence in his own endeavours.

For while the coward sinks beneath the weight of his afflictions, the brave inan, instead of giving way to the impulse of despair and passion, instead of impeaching the goodness of the Divine Being, cheerfully places a firm reliance upon his own wisdom. Cowardice may be compared to the fighting bulls, which fled from the field of battle just at the moment of victory. Cato, when he found himself conquered by Cæsar, in a fit of despair slew bimself; how much more heroic would he have appeared, if he had braved his misfortunes with real courage and fortitude, instead of giving himself up a prey to passion! Rochefoucault observes, “ that intrepidity is an extraordinary strength of mind, which prevents the emotion and disorder which the view of great dangers usually excites; it is by this means heroes preserve the use of reason in the most surprising and terrible situations." Whatever misfortunes may befal us, let us never sink under them, but, instead of murmuring at the dispensation of the Supreme Being, let us reflect how many there are placed in worse situations than ourselves; and instead of giving way to despair, let us use our utmost endeavours to extricate ourselves from any

difficulties in which we may be involved. Attested by Miss S. and I. Hebard, Spalding Serninary. Theme III. “ No bad man can be happy," by Miss Aon Ayre, aged 114, Spalding Seminary.

It is utterly impossible for the man who practises evil things to be happy in himself, nor can he contribute to the happiness of those around him ; for his evil deeds must be uppermost in his thoughts, and, consequently, he must be miserable. Like as the animal wounded by the arrows of the hunter, tries to fly from its pain, but cannot, so does the wicked man endeavour to fly from the reproaches of his own conscience; but it is impossible. We have a striking instance in King Pygmalion, who had a very bad conscience; and, to contribute to his safety, he had fifty persons to guard his body; but this would not procure him happie ness. A contented mind, and a good conscience, will make a man happy in all conditions. To conclude, if we wish to attain happiness, we must act uprightly.

Another good Theme,“ On Order," was sent by Miss E. Willerton, aged 144, Spalding Seminary.

Attested by Miss S. and I. Hebard.

ARTICLE XVII.

QUESTION 1. Answered by Master H. Cotton, Reading Mathematical School.

The amount of il. for 1 year, at 5 per cent. is 105, whose logarithm is .021189, which multiplied by 60 gives 1.27134, to which add the log. of 6 = 0.778151, we have their sum= 2.049491, the number answering to which is 112.07 pence = 9s. 4d. nearly.

Again, by Master T. Stiles, Surfleet Academy. First 60 x log. 1.05 = 60 x .0211893 = 1.271358, the number answering to which is 18.6791, and 18.6791 X .025 = .56697751.

= 9s. 4d. the amount required. Again, by Master W. Harrison, Burton, and Master Winterbotham, Rochdale.

By the tables, 18.6791 is the amount of 11. at 5 per cent. for 60 years; which mult. by .0251. gives Os. 4d. as before.

This question was answered also by Masters W. Clark, Reading; H. Atkin, Sheffield; J. Macann, Long Sutton; R. Nicholson, Horsforth; J. Aíkinson, T. H. Hopkinson, and J. Goring, Attercliffe Academy; R. Partington, Rochdale ; B. Burnell, W. Nicholson, J. Wheatley, and B. Burnley, Wortley Academy; J. Bramall, Lingardswood; F. Charlton, T. Charlton, and T. Bell, Hexham Grammar School.

QUESTION 2. Answered by all the above young gentlemen, their answers being all very nearly the same.

First, 9 x 9 x.7854 x 210 = 13359 654 feet, is the solidity of the earth dug out; which at 1 d. per foot, comes to 691. 11s. 7.d.

QUESTION 3. Answered by Master F. Charlton, Hexham Grammar School.

Since all regular polygons of the same number of sides, are similar to each other, and similar figures being squares

of their like sides, we have 387.107325 (area of a pentagon whose side is 15): 152 :: 16940 (yards in 3 acres) : 984,6106632; the square root = 99.227549 yards is the length of one side, as required. Again, by Master J. Wheatly, Wortley Academy.

16940 Here, ✓ 3-5 *.4840)

✓ 1.720471 v (9846.106632) = 99.2275 yards. Again, by Master J. Atkinson, Attercliffe.

16940 First, 31 acres = 16940 yards, then V (1.720471) 99.2275 yards.

Again, by Master R. Nicholson, Horsforth. The area = 3 acres is = 16940 yards, hence the side will be = 16940 * .76238 = 99% yards, nearly,

Again, by Master T. Stiles, Surfleet Academy. Here 34 acres = 16940 yards, then, by mensuration, 16940 • 172047 (the area when the side is 19) = 9846.106632 is the square of one side, and

as the

1.720471.)

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G

C с

V(9846.106632) = 99.2275

yards, is the length of each side as before.

This question was answered by Master W. Scofield, Farnley, near Huddersfield, and by all those young gena tlemen who answered the first question:

QUESTION 4. Answered by Master J. Brumall, Lingardswood..., Construction. With A Fas radius = 25, describe the circle ABCD, erect C G perpendicular.to AC,= 24, draw G D parallel to A C, meet

F E ing the circle in D; join A D, CD, make A B=DC, and B C = AD, and join A B, BC, and ABCD

B will evidently be the rectangle required.

Calculation. Let fall the perpendicular D Е, and joia DF; then, in the right-angled triangle, D E F, we have D E = 24, and D F = 25, therefore, F E =

(25? — 242)=7; consequently A E = 25 + 7 = 32 and EC = 25—7 = 18. Hence ADEN (322 + 24?). = 40 and DÇ=(18+ 24%) = 30, and the perimeter = 140 chains; which at 111d. per rod comes to 271. 85. 4d.

In nearly the same manner it was answered by
Masters T. Stiles, J. Macann, R. Partington, F. Charlton,
T. Charlton, and T. Bell.
Again, by Master Winterbotham.
1200

1440000 Put x = one side, then is the other, and

x? + x = 2500 by the question. Put x = y, and, by redụction, we shall have ya.

2500 y

1440000, from whence y = 1600, and x = 40; therefore the other side is 30, and the perimeter 140, &c.

Again, by Master W. Harrison, Burton Pidsea. Put 1200 chains the content of the field = a, x = its breadth, and 50 the diagonal =d; then,

isits length, but v" (4***) is its length also, therefore

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a

016 ), dx =

x also the length

) = 40, as before.

as obia In this manner it was answered by Masters Atkin' R. Nicholson, J. Atkinson, J. Going, B. Burnell, Wr Nicholson, J. Wheatley, and B. Brumley.

Master R. Nicholson, and Master W. Harrison, each of them requested to send for any book, the price of which does not exceed five shillings.

90911

are

On the comparative Strengths of Planks when whole, and

when slit into Boards. SEEING two persons carrying planks the other day, one at each end, some of which were whole and some sliti into boards, I observed that those which were slit, bents much more than those which were not. This circumstance led me to consider their comparative strengths, as in the following

QUESTION.

What will be the comparative strength of a plank 3 inches thick, supported at each end, with its flat side downwards when whole, and also when slit into three boards, one of į an inch thick, another 1 inch, and the other i, inches, when lying on each other; supposing no waste in slitting?

ANSWER.

By Emerson's Mechanics, "the strength is as the .square of the depth;" therefore, when the plank is whole, we shall have 32 = 9 for its comparative strength ; also, I +1+%= 31 is the comparative strength of the boards, or of the plank when slit; whence the strength of the whole, is to the same when slit, as 9 to 3, or as 18 to 7. By inserting the above, you will greatly oblige,

Your very humble Seryant, Lingardstood.

This paper, by Master Bramall, will show our juvenile friends how very easy it is to find the comparative strengths of pieces of timber of different dimensions. Many similar examples are given in Marrat's Mechan

JOHN BRAMALL.

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