CHAPTER LXIII.—MECHANICAL AND OTHER PUZZLES.
I.—Some Mechanical Puzzles.—By F. Chasemore.
(1) The Balance Puzzle.—Cut a piece of cardboard four inches square. In the middle punch two holes, and punch a hole also in each corner. Take four pieces of thread eight inches long and knot the ends together; then pass one thread through each corner hole of the card and fasten them there by tying a bead to each. Now take another piece of thread eighteen inches long and double it in the middle, then pass the loop down through one of the holes in the middle of the card and up through the other hole, and pass the loop through a small ring. Next pass the ends of the thread through the loop and draw it tight, and fasten the ends to the knot joining the four other threads ([Fig. 1]). The puzzle is to get the ring off the threads without cutting them.
Fig. 1.
Take the loop and pass it down through one of the corner holes under the thread, and pull the bead down through the loop. Do this to each corner, and the loop will now be seen to surround the whole of the threads: pass the loop down over the cardboard, when the ring will come off. To replace the ring reverse the movement.
Fig. 2.
(2) The Card Bridge.—Take a visiting-card and bend it as in [Fig. 2], so that the parts bent up are half an inch high. Now place this card on a table, resting on the two bent parts. The puzzle is to blow the card bridge right over on to its back. This will not be so easy a job as it appears. The secret is in blowing on the table about six inches in front of the bridge.
(3) The Triangle Puzzle.—Take six pieces of stick about three inches long, and with them form four equilateral triangles, each triangle to have one stick for the side. This is done by placing three sticks in a triangle on the table, and placing a stick at each corner and letting these three sticks come together at the other ends.
Fig. 3.
(4) The Six Squares Puzzle.—Take seventeen pieces of stick three inches long and arrange them as in [Fig. 3]. The puzzle is, by taking away five sticks, to leave three perfect squares, and three only, these three squares to be three of those originally formed, and all the same size. To do this take the two sticks from the two top corners and the middle stick at the bottom.
Fig. 4.
(5) The Puzzle Box.—Take six visiting-cards and bend them as in [Fig. 4]. The puzzle is to put them together in the form of a box, making them fasten each other. The box will bear rough usage. This is done by fitting the cards together as in [Fig. 4], when they will be found to fasten each other.
If you make a small hole in one of the sides and get one of your smoking friends to fill the box with smoke, on tapping gently the side opposite to the hole a beautifully perfect ring of smoke will issue from the hole, and you can produce any number you like.
II.—Thought-guessing.
This game is not the same played by Irving Bishop a few years ago when he pretended to read the number of a bank-note held by a gentleman, but is quite as easy. This game was shown me by a friend home from Penang, where it is played a great deal, although not of foreign origin. It is played as follows:—One of the company goes out of the room while those remaining decide on something to be thought of; it may be something in the room or some idea suggested by something in the room. When this is decided upon, the absentee is admitted, and he has to guess what was thought of by asking questions, to which he only receives answer ‘Yes’ or ‘No.’ He may ask any question that will help him. The first question should be, ‘Is it a substance?’ ‘No.’ ‘Is it an abstract idea?’ ‘Yes.’ ‘Is the thing that suggested the idea in the room?’ ‘Yes.’ He should first localise the thing suggesting the idea by dividing the room by imaginary lines in all directions, and asking first if it is on one side, and then if it is on the other, always framing the question in such a manner that it can be answered by ‘Yes’ or ‘No’ as otherwise no answer will be given. The game allows of great ingenuity in selecting the idea and also in working up to it in finding it out. One of the ideas I had to guess once was this—the quantity of silex or flint in the cane of a chair on which I was sitting. And another was this—the curve formed by the head of the hammer when giving the last stroke to a particular nail in the wall. These look difficult, but if properly managed will be found to be guessable. The game improves by practice, as after two or three times you will be able to find out ideas that would at first have appeared impossible.
III.—An Improved Ring Puzzle.—By Herr Meyer.
Among the many wire puzzles which I have seen at different times, I was pleased with one which had two loops. I therefore added a third and subsequently a fourth, and was successful in making the puzzle more interesting. Any boy can easily construct the toy of iron-wire with a pair of pliers from the accompanying [illustration].
The large ring is 3 inches in diameter, and the bar is 4 inches long. The object is to remove the large ring by pushing it through the smaller ones. The movements are explained by means of the figures and letters written in the diagram. The ring of the bar is called B, the ring of the first loop is 1, that of the second loop is 2, and so on.
The large ring is folded by moving D upwards, so that it falls on C. Then A is pushed from the left to the right through 1, moved over B (that is, B is pushed through between the two wires), and drawn back through 1. Then the ring is folded the other way and pushed through 2 and 1, over B, back through 1, over 1 and B, and back through 2. Then all through 3. Then through 1, over B, back through 1; folded the other way; all through 2; then through 1, over B, and back; and the ring is off.
The ring is put on thus: Fold it, push it half length through 1, over B, back through 1; fold; all through 2; through 1, over B, back; fold all through 3; through 2, over B and 1, through 1, over B, back through 1 and 2, through 1, over B, back, and it is on.
When there is a fourth loop, then the ring is removed thus: Push it through 1, over B, back, fold, through 2 and 1, over B, back over 1 and B, back through 2, through 3 and 2, over B and 1, through 1, over B, back through 1 and 2, through 1, over B, back, over 2 and 1 and B, back through 3, all through 4, through 2, over B and 1, through 1, over B, back through 1 and 2, through 1, over B, back, fold, all through 3, through 1, over B, back, fold, all through 2, through 1, over B, back, off.
The ring is placed on the fourth loop thus: Fold it, push it half-way through 1, over B, back, fold, all through 2, through 1, over B, back, fold, all through 3, through 2, over B and 1, through 1, over B, back through 1 and 2, through 1, over B, back, fold, all through 4, through 3, over B and 1, through 1, over B, back, over 2, through 2 and 1, over B, back, over 1 and B, back through 2 and 3, through 2, over B and 1, through 1, over B, back through 1 and 2, through 1, over B, back, open the ring.
IV.—Aërial Rings.
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| Fig. 2. | |
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| Fig. 1. | Fig. 3. |
A few very pretty experiments can be made with smoke rings, and as the apparatus is cheap and easily procurable it may be worth while to say a few words about them. The best arrangement for producing satisfactory results is that shown in [Fig. 1], where a glass jar with a tap at the base is resting on a stand. Into the jar and through the cork a small tube is fixed and the whole sealed down, so that all air passing into the jar must come through the tube. The finer the tube the better; the material is of no consequence—it may be of metal, glass, or clay—so long as the passage down it is kept clear. To it, as shown in the [cut], a holder is fixed, to which the candle or what not is attached, so that the centre of the tube points fairly into the smoke. The jar is filled with water, the cork fixed down tightly, and the candle lighted. The tap is then turned, and as the water runs out it sucks down the smoke, and the rings will be seen rising through the water and forming on its surface, as shown in [Fig. 2]. These rings will soon disappear and gradually merge into a sort of collar, shown in [Fig. 3], where the central bar is the tube leading up to the source of smoke.
Fig. 4.
Fig. 5.
There are other ways of producing smoke rings. For instance, rings such as shown in [Fig. 4] are produced during the combustion of phosphuretted hydrogen, the white vapours of the phosphoric acid rolling up into the air in apparently whirling crowns. From guns and field-pieces the smoke often emerges in rings, and steam out of a small vertical jet is often shot forth in small circles, such as shown in [Fig. 5].
There is, however, a far simpler way of making smoke rings than any we have described, and that is by procuring a cubical cardboard box with a small round opening in two of its opposite faces, filling it with smoke from burning brown paper, and sending the ring into the air by hitting the palm of the hand against one hole so as to eject the smoke wreath at the other. In this way most excellent rings are formed, and if received on a piece of damp glass the rings can be caught and held for a few moments for examination. In a quiet room free from draughts the regularity and duration of the rings will provide a surprise for those who have not tried the experiment.
V.—Bubble Blowing.
We are all of us familiar with the ordinary bubble, and we have probably all had a try with a long clay pipe and a basin of suds, and succeeded more or less, principally less, in setting 4-inch balloons afloat over some quiet neighbourhood. It is possible that a few of us have filled such soap balloons with hydrogen, and by applying a light to them have caused an explosion in mid air. But how many of us have tried to attach a car to our bubbles?
This can be done easily after a little practice, and the sketches herewith make clear how to set about it. Get an ounce of glass tube from the nearest druggist, and cut out of thin paper whatever your fancy leads you to fix to the balloon. As something out of the ordinary lines, we give the exact size of an aëronaut we recently despatched on a cruise ([Fig. 1]). D is a small disc of paper—proper size; F is a fine thread—proper length below it is the paper figure, cut out of the orange wrapper of one of the Boy’s Own Paper monthly parts, and it is traced from the figure we used.
Fig. 1.
Fig. 2.
To make the experiment a success it is as well to remember the conditions. The bubble rises because the air it contains is lighter than that which surrounds it; it floats when the air is of the same temperature, it falls when the air within is colder than the air without. The air in the bubble comes hot from the lungs, and the greater the difference in heat between that air and the air you breathe the higher will the bubble go. In short, to have bubbles in perfection you should blow them in an ice room! As it is not every one that can obtain the use of a meat storage safe for bubble blowing, let us make our first experiment in a cool room. Begin with working up a good stiff lather; and the better the soap the better the suds for our purposes. Use your tube as you would your pipe, and blow downwards into the basin steadily and strongly. Take a good breath of air to begin with, and hold it for a second or two. Keep the point of the tube downwards until you have fixed on the disc in the way shown in the sketch. No gum or stickiness is required: all you have to do is to let the dry disc drop lightly on the wall of the balloon; the moisture will keep it in its place provided the knot of the cotton is small enough. If you pass the cotton through with a needle and have the same sort of single knot as if sewing, the disc will answer all your requirements.
Fig. 3.
As soon as the disc is firmly fixed, turn the tube gently upwards, and away will go the bubble, aëronaut and all. It will not cross the Atlantic, but it will at least reach the ceiling; and if on a cold day you try it out of doors, you may get it to travel unchecked for several hundred yards.
VI.—Marionettes,
or Fantoccini, are very entertaining when dexterously worked, as they may be by a little practice. Say you have a table with drapery arranged round it to form a little platform, and drapery also at the back. Let the latter be dark in colour, so that the string, thread, or silk, with which you work the dolls, may be less distinguishable if they are so at all.
Fig. 1.
The human performer (out of sight) works the figures over the back drapery, moving every joint, and throwing balls about gaily, as in [Fig. 1].
When Living Marionettes are introduced—as they sometimes are at public exhibitions—the effects are most comical. On a small stage an ordinary man’s head is apparently attached to a miniature body, and this latter walks, dances, and goes through many antics. The head, too, has eyes ‘in a fine frenzy rolling,’ and is gifted vocally, being able to talk and sing as well as many persons who fill a much larger space in the world.
Fig. 2.
This is managed by having two backgrounds, one the height of the performer’s chin, the other—a little farther back—extending to the top of the scene. Both of these are black, and at a little distance the break in them is not distinguishable. The performers walk on a platform at a lower level than the stage, the doll-bodies being fastened beneath their chins, hanging over the front drapery, and the doll’s feet resting on the platform in view of the audience. The performers also carry black curtains attached to them (not perceptible against the similar background), and through these wires, fixed to the arms and legs of the manikins, are pulled to give them motion. (See [Fig. 2].) We have also described ‘[Living Marionettes]’ in another part of this volume.
VII.—Model Wrestlers.
A good deal of amusement can be had out of a pair of model wrestlers. The way in which the dolls are fitted and worked is sufficiently shown in the accompanying [illustration]. The legs are in one piece, and the arms are joined so that each doll has only four working parts. The feet are loaded to keep the figures upright on the string, but it is not necessary that this should be done, as they can be kept firmly on the table without. The device is a very old one. Curiously enough, in the Hortus Deliciarum of Herrade de Lansberg, Abbess of Hohenburg—a manuscript over seven hundred years old, now in the Paris Library—a man and woman are represented playing with a couple of figures arranged very much on the same principle, the only difference being that the dolls are separate, and worked with two strings instead of one. The figures are knights in complete armour, with swords and shields. They are hung close together, so that the swords are crossed, and the heels are loaded to keep them upright. The strings are crossed, and held one in each hand by the man and woman. The cross comes between the figures, so that the string that is attached to the waist of one figure is fastened to the knee of the other, and any motion forward is balanced by one backward, and a most realistic encounter can be fought out almost automatically.
THE WRESTLING DOLLS
With the substitution of thin cap wire for the thread an excellent marionette or shadow show could be easily arranged, it being much easier to work horizontally than vertically in all cases where vigorous action is required to be simulated.
CHAPTER LXIV.—KEEPING THE BALANCE.
By the Rev. T. S. Millington, M.A.
In Greece there lived a man—
(Old Ælian tells the tale,
Believe it if you can)—
So light and thin and frail,
He could not go about
Upon a windy day
For fear of being blown out
Or carried clean away.
Therefore, so it is said,
To keep him on the ground,
Two plates of solid lead
Under his feet were bound.
Yet still he was so light,
That when the wind did blow
He could not stand upright,
But wavered to and fro.
To sit upon a chair
Was equally in vain;
The slightest breath of air
Would lift him up again.
And when, upon his bed,
He sought a brief repose,
Down went his heels; his head
Immediately uprose.
No man was ever known
So empty and so weak
(By every zephyr blown)
As this unhappy Greek.
‘The unstable man here commemorated was a native of Cos. I have enlarged a little upon the description in order to introduce to you a figure which, in some respects, resembles him. Here it is. You may easily make one like it. Get a leaden bullet and cut it through the middle with an old knife and a hammer. Then cut out a light figure of cork or pith, and fasten its feet to the flat part of the bullet. Now if you try to make him lie down, you will not succeed. The moment you let go of him he springs up again and remains in an erect position. Why is this?’
‘His heels are heavier than his head.’
‘Yes. The man himself is so light, that nearly all the weight is in the lead; and this being round or half-spherical, when you lay the figure down you set the half-bullet on its edge. By so doing, you raise the centre of gravity; and it will not rest until it has fallen again and is supported.’
‘What is the centre of gravity?’
‘The centre of weight; that point in a body round where all the other parts balance each other. It is not necessarily the centre of the figure, because one part of a figure may be denser and heavier than another; but it is the centre of its weight.’
‘Now take the other half of your bullet, and use it for the head of another figure. This man will be still more eccentric than the Greek, for he will persist in standing upon his head. His brains are evidently the heaviest part of him. The centre of gravity is in his skull, and therefore it will seek the lowest place, and keep it too. So you see what inconveniences a thick-brained, heavy-headed fellow is exposed to.’
‘He is not much worse off, though, than the light-headed Greek.’
‘I suspect Ælian was quizzing some one who had no force of character, and was easily turned this way or that by anybody who would take the trouble to persuade him: like St. James’s double-minded man, unstable in all his ways, driven by the wind and tossed.’
‘Whereabouts is the centre of gravity in a man?’
‘That would be difficult to say. Somewhere in his body or trunk; for that is, of course, the heaviest part of him.’
‘How could you find it out?’
‘You might get near it by hanging him up in two different positions. Hang him first by his head, and by means of a plumb-line draw a perpendicular from the point of suspension. Then hang him by the shoulder or side, and draw another perpendicular, which, this time, will fall across him. Where these two lines cross each other will be the centre of gravity; and on that point you might balance him, if you were strong enough. I dare say you have seen it done in the streets or at a circus—a man balanced at the end of a long pole.’
‘Yes. And I once saw a donkey balanced at the top of a ladder. It was a very small donkey; but the ladder was rather a long one, and rested on the man’s chin.’
‘The longer the ladder the easier the feat would be; I’ll tell you why presently.’
‘If the centre of gravity is in our body or chest, how do we manage so easily to stand upright? My sister has a wooden doll which won’t stand up at all.’
‘That doll has no muscles in her feet. You have; and even when you are standing still those muscles are constantly at work, controlling the body so as to keep the centre of weight directly above the feet.’
‘I don’t feel them working.’
‘No; you are so used to it. But balance yourself on one foot. Do you feel the muscles now?’
‘Yes; they are constantly at work. Try it, all you boys.’
All the boys tried it; and very comical they looked standing in a row on one leg and swaying about in their efforts to keep the balance. The centre of gravity was in each case supported, though there was not much gravity in their faces. That is not the right place for ‘gravity’ at playtime.
‘Steady!’ cried their teacher, ‘you are swaying about like the unhappy Greek! Why do you throw out your arms, first to one side and then to the other?’
‘To keep the balance, sir.’
‘In other words, that you may bring the centre of gravity over the foot on which you are standing. The centre of gravity moves as your arms move. If you feeling yourself falling towards the left, you throw out your right arm, and that brings the centre of weight more towards the right side. The centre of gravity is but a point; and while you keep that point supported, you may stand upon a point, or upon a rope, or upon anything else. That is how the rope-dancers manage. They usually have a pole, weighted at each end with lead. The man and the pole form, practically, but one body, and have but one centre of gravity; therefore, by moving the pole a very little the performer can easily throw more weight to one side or the other as required, and so bring the centre of gravity directly over the rope.
‘It requires time and practice to become a good rope-dancer; more than it is worth, perhaps. But you can make a good balancer with very little trouble.
‘Take a common wine-bottle; fit a short cork to it, and stick a needle through the cork, so that the point may project upwards. That must be done before you put the cork into the bottle; otherwise you would have to get into the bottle to do it. The use of the bottle is merely as a stand. I wish the bottle were never put to any worse use than that.
‘Take another cork and stick a long pin through it, so that the point may project half an inch or so downwards, into the sides of this second cork stick two forks in a slanting direction, handles downwards. Now with a little patience you will be able to place the point of the pin upon the point of the needle; and once there, there it will remain balanced, swaying about and perhaps turning round a little, but without falling off. The weight is here in the forks, and the centre of gravity low down, between the two handles. The handles, therefore, being free to move, adjust themselves, so that the centre of gravity is supported, and that is all that is required.’
‘Our Jack was carrying a bucket of water the other day, and the handle came off. The bucket dropped down on one side, and he fell over on the other. What made him fall, sir, when the bucket fell?’
‘Jack was carrying the bucket in his left hand, I suppose, and leaning over to the right, stretching out the right arm to keep the balance. When the weight of the bucket was suddenly removed, the centre of gravity was raised, and thrown at the same time to the opposite side. As long as the heavy bucket formed part of him (as I may say), the centre of gravity was nearer the ground; but when it fell, Jack’s centre was raised, and he overbalanced. The lower the centre of gravity is in any body, the more firmly that body will stand; and the higher it is up, the more likely it will be to topple over. I saw some of you walking on the top of a wall the other day, and you had some difficulty in balancing yourselves. Others crept on their hands and knees; they required no balancing, because their centre of gravity was lowered, and their base of support extended.’
‘Yes, I understand that. But you said just now that a man could be more easily balanced at the top of a long pole than on a short one; or a donkey (with four legs) upon a high ladder more easily than on a lower one. How can that be?’
‘It sounds like a contradiction, but it is true, nevertheless. Try it. Not with a donkey, but with this stick, which has a heavy knob at one end. With the knob downwards, resting on the palm of your hand, you can scarcely balance the stick for a moment; but with the knob upwards there is comparatively little difficulty.’
‘It is so, certainly; but I don’t understand why.’
‘Because in this case the centre of gravity is supported by keeping the hand in a proper position under it. When the weight is at the top of the stick, it has a larger arc to traverse in falling from the perpendicular than if it were lower down, and the person who balances it has a proportionately longer time to move his hand so as to give it the necessary support. In other words, the higher the centre of gravity is, the farther it has to fall, and the more time there is to check it while falling.
‘Do you ever walk on stilts? If so, you will know that it is much easier to keep the balance upon high stilts than on low ones. In some parts of France the people are in the constant habit of walking about on stilts. The elevation enables them to see farther across the level plains, and to observe where their flocks are feeding. If they were to fall they would describe a large arc, and come down with great force, but they do not fall. A very slight movement of the stilt is sufficient to keep it under their centre of gravity. If they were lower down, greater exertion and a swifter movement would be necessary to correct every unsteadiness. Men cannot stand still upon stilts, because there are no muscles at the foot of the stilt to play upon the ground and react upon the body. Observe, then, that when the base is movable, as in balancing a ladder with a donkey on it, or in walking upon stilts, the higher up the weight is the better. But when the base is not movable, the lower down the centre of gravity is, the less risk there will be of an upset. Boats have often been capsized by timid people standing up in a moment of alarm, and so raising the centre of gravity, and coaches by having too great a load of passengers and luggage on the roof, with no “insides.” The great thing is to keep the centre of gravity supported, and then, though it be but a pin’s point resting upon that of a needle, there can be no fall.’
‘Yes; but one can’t always be thinking about one’s centre of gravity.’
‘It is not necessary. Habit or instinct supplies all that is wanted. You balance yourselves from the time you get out of bed in the morning till you go to bed again at night, without ever thinking about it. Only when you stand on one leg, or go into dangerous places, are you conscious of the effort you are making. Your Maker has ordered it thus, that you may guard against accidents, and yet be free from constant care and trouble in doing so. Even the birds are taught to place their heads under their wings when sleeping, so as to render their form more compact and their balance more perfect.
‘Walking has to be acquired in infancy, and until the foot has learnt to use its muscles unconsciously and rightly, the child has many a fall. There are also two ways of walking, a right and a wrong way. Some men sway from side to side as they walk, altering the centre of gravity at every step, and being obliged to straggle their feet accordingly to support it. A well-drilled soldier, on the contrary, keeps his body steady, and uses his legs for the forward movement only. Of course he gets over the ground much faster and with less exertion than the sloucher. Balancing, like everything else, has to be learnt, and, when learnt, is practised without any trouble. There was a man once who had been a cripple from his mother’s womb, and who never had walked. Suddenly the use of his limbs was given him—“his feet and ankle bones received strength.” If that had been all, it might have taken him days or weeks to learn the right use of his muscles; he would not have been able, without much practice, even to stand upright. But the miracle was carried beyond this. St. Peter’s words to the cripple were, “In the name of Jesus Christ of Nazareth, rise up and walk. And he leaping up stood, and entered with them into the temple, walking, and leaping, and praising God.” Not only was strength given him, but skill to use it; he was to “rise and walk,” and was enabled to do so at once.
‘That completeness of cure was intended to teach what the power of the Saviour can do for the soul in all ages, as then for the body. Our strength, and the instinct by which we apply it, come to us gradually, and not by a miracle: but let us think about it sometimes, and be thankful for it all the same.’
