OPTICAL ILLUSIONS
No. I.—SWALLOWED!
Take a small card and place it on its longer edge upon the dotted line. Now set the picture in a good light on the table, and let your head drop gradually towards the card until you almost touch it with your nose. You will see the bird fly into the jaws of the snake!
AMUSING PROBLEMS
THE CARPENTER’S PUZZLE
1. A carpenter was called in to mend a hole in a wooden floor. The gap was two feet wide, and twelve feet long, while the only board at hand was three feet wide, and eight feet long.
This had been put aside as useless, but, on catching sight of it, the carpenter ran his rule over it and said that he could make a perfect fit, and cover all the hole by cutting the board into two pieces. How did he do this?
No. II.—AN ILLUSION OF ROTATION
This most interesting optical illusion was devised by Professor Thompson some years ago:—
If the illustration is moved by hand in a small circle on the level, with such motion as is given in rinsing out a bowl, the circles of the larger diagram will seem to revolve in the direction in which the paper is moved, while the cogs of the smaller diagram will apparently turn slowly in the opposite direction.
No. III.—WHIRLING WHEELS
Here is another combination of the clever illusion of the whirling wheels.
If a rapid rotating motion is given to the diagram, each circle will seem to revolve, and the cog wheel in the centre will appear to move slowly round in the opposite direction.
GOLDEN PIPPINS
2. A man leaves an orchard of forty choice apple trees to his ten sons. On the first tree is one apple, on the second there are two, on the third three, and so on to the fortieth, on which there are forty.
Each son is to have four of the trees, and on them an equal number of the apples. How can they thus apportion the trees, and how many apples will each son have? Here is one way:—
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 20 | 19 | 18 | 17 | 16 | 15 | 14 | 13 | 12 | 11 |
| 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
| 40 | 39 | 38 | 37 | 36 | 35 | 34 | 33 | 32 | 31 |
| 82 | 82 | 82 | 82 | 82 | 82 | 82 | 82 | 82 | 82 |
Can you find another perfect solution?
No. IV.—AN ILLUSION OF MOTION
We call very particular attention to this fascinating illustration of the fact that the mind and eye may receive and register false impressions under quite simple conditions:—
Hold this at rather more than reading distance, upright, and move it steadily up and down. The dark line will soon seem to slide up and down upon the perpendicular line. It will be better seen if drawn to pattern on a card.
No. V.—ARE THEY PARALLEL?
As the eye falls upon the principal lines of this interesting diagram, an immediate impression is formed that they are not parallel.
This, however, is a most curious illusion, created in the mind entirely by the short sloping lines, as is found at once by the simple test of measurement.
AN AWKWARD FIX
3. With no knowledge of the surrounding district, I was making my way to a distant town through country roads, guided by the successive sign-posts that were provided.
Coming presently to four cross-roads I found to my dismay that some one had in mischief uprooted the sign-post and thrown it into the ditch. In this perplexing fix how could I find my way? A bright thought struck me. What was it?
LINKED SWEETNESS LONG DRAWN OUT
4. As I stood on the platform at a quiet country station, an engine, coming along from my left at thirty miles an hour, began to whistle when still a mile away from me. The shrill sound continued until the engine had passed a mile and a half to my right. For how long was I hearing its whistle?
No. VI.—ILLUSION OF LENGTH
In this curious optical illusion the lines are exactly equal in length.
The eye is misled by the effect which the lines drawn outward and inward at their ends produce upon the mind and sight.
ELASTIC QUARTERS
5.
In room marked A two men were placed,
A third he lodged in B;
The fourth to C was next assigned,
The fifth was sent to D.
In E the sixth was tucked away,
F held the seventh man;
For eighth and ninth were G and H,
Then back to A he ran.
Thence taking one, the tenth and last,
He lodged him safe in I;
Thus in nine rooms ten men found place,
Now can you tell me why?
EXCLUDED DAYS
6. Are there any particular days of the week with which no new century can begin?
No. VII.—ILLUSION OF HEIGHT
These straight lines, at right angles to each other, are, though they do not seem to be, exactly equal in length.
This and similar illusions are probably due to the variation of the vague mental standard which we unconsciously employ, and to the fact that the mind cannot form and adhere to a definite scale of measurement.
DRIVING POWER
7. Why has a spliced cricket bat such good driving power? and why is the “follow through” of the head of a golf club so telling in a driving stroke?
THE BUSY BOOKWORM
8. On my bookshelf in proper order stand two volumes. Each is two inches thick over all, and each cover is an eighth of an inch in thickness. How far would a bookworm have to bore in order to penetrate from the first page of Vol. I. to the last page of Vol. II.?
No. VIII.—ILLUSION OF DIRECTION
Can you decide at a glance which of the two lines below the thick band is a continuation of the line above it?
Make up your mind quickly, and then test your decision with a straight edge.
A TERRIBLE TUMBLE
9. From what height must a man fall out of an airship—screaming as he goes overboard—so as to reach the earth before the sound of his cry?
N.B.—Resistance of the air, and the acoustical fact that sound will not travel from a rare to a dense atmosphere, are to be disregarded.
IN A PREDICAMENT
10. Imagine a man on a perfectly smooth table surface of considerable size, in a vacuum, where there is no outside force to move him, and there is no friction. He may raise himself up and down, slide his feet about, double himself up, wave his arms, but his centre of gravity will be always vertically above the same point of the surface.
How could he escape from this predicament, if it was a possible one?
No. IX.—THINGS ARE NOT WHAT THEY SEEM
It is difficult, even after measurement, to believe that these figures are of the same size.
But they will stand the test of measurement.
A CLIMBING MONKEY
11. A rope passes over a single fixed pulley. A monkey clings to one end of the rope, and on the other end hangs a weight exactly as heavy as the monkey. The monkey presently starts to climb up the rope. Will he succeed?
GAINING GROUND
12. Seeing that the tension on a pair of traces tends as much to pull the horse backward as it does to pull the carriage forward, why do the traces move on at all?
No. X.—THE SHIFTING BRICK
A very curious and interesting form of optical illusion is well illustrated by what may be called “the shifting brick.”
The central brick, drawn to show all its edges, as though it were made of glass, will assume the form indicated by one or other of the smaller bricks at its right and left, according to the way in which the eyes accommodate themselves for the moment to one pattern or to the other. If you do not see this at first, look steadily for awhile at the pattern you desire.
ASK A CYCLIST
13. Why does a rubber tyre leave a double rut in dust, and a single one in mud?
TODHUNTER’S UNIQUE PUZZLE PROBLEM
14. If two cats, on opposite sides of a sharply sloping roof, are on the point of slipping off, which will hold on the longest?
No. XI.—AN ILLUSION WITH COINS
If you place four coins in the positions shown at the top of this diagram, and attempt, or challenge some one to attempt, without any measuring, to move the single coin down in a straight line until the spaces from C to D on either side exactly equal the distance from A to B—
It must drop as far as is shown here, which seems to the unaided eye to be too far.
This excellent illusion can be shown as an after-dinner trick with four napkin-rings.
No. XII.—THE FICKLE BARREL
Here is another excellent optical illusion. Look attentively at the diagram below, and notice in which direction you apparently look into it, as though it were an open cask.
Now shake the paper, or move it slightly, and you will find, more often than not, that you seem to see into it in quite the opposite direction.
HEADS I WIN!
15. I hold a penny level between my finger and thumb, and presently let it fall from the thumb by withdrawing my finger. It makes exactly a half-turn in falling through the first foot. If it starts “heads,” how far must it fall to bring it “heads” to the floor?
HE DID IT!
16. “They call these safety matches,” said Funnyboy at his club one day, “and say that they strike only on the box. Don’t believe it! I can strike them quite easily on my boot.”
No sooner said than done. He took out a match, struck it on his boot, and—phiz!—it was instantly alight. The box was handed round, and match after match was struck by the bystanders on their boots, but not one of them could succeed.
“You don’t give the magic touch,” said Funnyboy, as he gaily struck another. How did he do it?
No. XIII.—A STRANGE OPTICAL ILLUSION
How many cubes can you see as you look at the large diagram? The two smaller ones should be looked at first alternately, and they will assist the eye to see at one time six, and at another time seven, very distinct cubes.
No. XIV.—A CIRCULAR ILLUSION
This curious optical illusion is not easily followed by eye to the finish of the several lines.
Each short line is, in fact, part of the circumference of a circle, and the circles when completed will be found to be accurately concentric. It would seem at first sight that the lines are taking courses which would eventually meet at some point common to them all.
A CYCLE SURPRISE
17. We commend this curious point to the special attention of cyclists:—
A bicycle is stationary, with one pedal at its lowest point. If this bicycle is lightly supported, and the bottom pedal is pulled backward, what will happen?
No. XV.—THE GHOST OF A COIN
A most remarkable optical illusion is produced by the blending of the dark and light converging rays of this diagram. Stand with your back to the light, hold the page, or better still, the diagram copied on a card, by the lower right-hand corner, give it a continuous revolving movement in either direction, and the visible ghost of a silver coin, sometimes as large as sixpence, sometimes as large as a shilling, will appear! Where can it come from?
ROUGH AND READY
18. A merchant has a large pair of scales, but he has lost his weights, and cannot at the moment replace them. A neighbour sends him six rough stones, assuring him that with them he can weigh any number of pounds, from 1 to 364. What did each stone weigh?
No. XVI.—A TAME GOOSE
Here is a pretty form of our first illusion:—
Place the edge of a card on the dotted line, look down upon it in a good light, and, as you drop your face till it almost touches the card, you will see the goose move towards the sugar in the little maiden’s hand.
REJECTED ADDRESSES
19. A wheel is running along a level road, and a small clot of mud is thrown from the hindermost part of the rim. What happens to it? Does it ever renew its acquaintance with the wheel that has thus rejected it?
No. XVII.—ILLUSION OF LENGTH
Here is another method by which an optical illusion of length is very plainly shown:—
Judged by appearances, the line A B in the larger figure is considerably longer than the line A B below it, but tested by measurement they are exactly equal.
THE CARELESS CARPENTER
20. A village carpenter undertook to make a cupboard door. When he began to put it in its place it was too big, so he took it back to his workshop to alter it. Unfortunately he now cut it too little. What could he do? He determined to cut it again, and it at once became a good fit. How was this done?
No. XVIII.—PERPENDICULAR LINES
Here is another excellent illustration that seeing is not always believing.
No one could suppose at first sight that these four lines are perfectly straight and parallel, but they will stand the test of a straight edge. The divergent rays distract the vision.
BY THE COMPASS
21. If from the North Pole you start sailing in a south-westerly direction, and keep a straight course for twenty miles, to what point of the compass must you steer to get back as quickly as possible to the Pole?
No. XIX.—ILLUSION OF PERSPECTIVE
The optical illusion in the picture which we reproduce is due to the defective drawing of the two men on the platform. In actual size upon the paper the further man looks much taller than the other.
Measurement, however, shows the figures to be exactly of a height. This illusion is due to the fact that the head of the further man is quite out of perspective. If he is about as tall as the other, and on level ground, both heads should be about on the same line. As drawn, he is, in fact, a monster more than eight feet high.
DICK IN A SWING
22. If Dick, who is five feet in height, stands bolt-upright in a swing, the ropes of which are twenty feet long, how much further in round numbers do his feet travel than his head in describing a semi-circle?
No. XX.—OUR BLIND SPOT
Here is an excellent and very simple illustration of a well-known optical curiosity:—
Hold this picture at arm’s length in the right hand, hold the left hand over the left eye, and draw the picture towards you gradually, looking always at the black cross with the right eye. The black disc will presently disappear, and then come into sight again as you continue to advance the paper.
A POSER
23. Can you name nine countries in Europe of which the initial letters are the same as the finals?