Chapter X: Conclusion (2)

This is one of the newest and most interesting optical surprises invented, but, like many other instruments, it is indulged with a very hard name, which means, "Solids I see." For mere amusement, the instrument supplied with the necessary pictures may suffice, and they are now sold like the kaleidoscope at all optical instrument makers, toyshops, &c. The effect consists in obtaining the perfect solidity of a geometric object from two ordinary drawings, pictures of columns, statuary, figures, flowers, &c., &c., having a rounded appearance, "breadth," and keeping, which induce the spectator to believe he is gazing at the natural figure. Our limits preclude a lengthened description of the philosophy of this instrument, the invention of Professor Wheatstone. We may, however, first recommend our readers to study the structure of the eye, in Brewster's Treatise on Optics, which may be thoroughly impressed on the mind by dissecting carefully the eye of a sheep or bullock. Now, if we cut open a portion of the eye of a recently killed animal, and look in upon the retina, which is a delicate network of nerves, and is considered the "mind of the eye," we shall behold all images inverted. How then, do we see them upright? Again, as we have two eyes at a distance from each other, the images formed on the two retinæ cannot be precisely alike: how is it that confusion is not the result, instead of perfect images, in which we can appreciate the geometric niceties of length, breadth, and thickness? Now the stereoscope assists us in understanding these difficult questions; and, quoting Professor Wheatstone, we find he states "that the theory which has obtained the greatest currency is that which assumes that an object is seen single because its pictures fall on corresponding points of the two retinæ; that is, on points which are similarly situated with respect to the two centers, both in distance and position. This theory supposes that the pictures projected on the retinæ, are exactly similar to each other corresponding points of the two pictures falling on corresponding points of the two retinæ."

Now, the fact is, that an object presents an entirely different appearance to each eye. Sir D. Brewster remarks, "That were a painter called upon to take drawings of a statue, as seen by each eye, he would fix at the height of his eyes a metallic plate, with two small holes in it, and he would then draw the statue as seen through the holes by each eye." With the utmost care, however, he could not reproduce the statue by their union. In order to do this, a camera with _two lenses_ of the same aperture and focal length, placed at the same distance as the _two eyes_, must be constructed and used.

The stereoscope is, consequently, an imitation of the powers of the eyes, giving solidity and a perfect relievo appearance to any two pictures which might be drawn separately from the two lenses in the camera obscura mentioned. That is to say, if it were possible to be behind the retina of each eye, and draw the two pictures of any object seen by our eyes, those pictures put into the stereoscope, would reproduce the solidity from which they were drawn.

Two instruments are sold, and may be obtained with the photographic pictures, almost at any optician's, viz.: the reflecting and the refracting stereoscope, of which we give drawings.

THE REFLECTING STEREOSCOPE.]

REFRACTING STEREOSCOPE.]

_a_ _a_, the two pictures, B B, the two mirrors, so adjusted that their backs form an angle of ninety degrees with each other, i. e., the quarter of a circle.

OCULAR SPECTRA.

One of the most curious affections of the eye is that in virtue of which it sees what are called _ocular spectra_, or accidental colors. If we place a red wafer on a sheet of white paper, and, closing one eye, keep the other directed for some time to the center of the wafer, then, if we turn the same eye to another part of the paper, we shall see a green wafer, the color of which will continue to grow fainter and fainter, as we continue to look at it.

By using differently-colored wafers, we obtain the following results:

WAFER. SPECIMEN.
Black, White.
White, Black.
Red, Bluish Green.
Orange, Blue.
Yellow, Indigo.
Green, Violet, with a little Red.
Blue, Orange Red.
Indigo, Orange Yellow.
Violet, Bluish Green.

BRILLIANT WATER MIRROR.

Nearly fill a glass tumbler with water, and hold it, with your back to the window, above the level of the eye, as in the engraving. Then look obliquely, as in the direction E, _a_, _c_, and you will see the whole surface shining like burnished silver, with a strong metallic reflection; and any object, as a spoon, A, C, B, immersed in the water, will have its immersed part, C B, reflected on the surface, as in a mirror, but with a brilliancy far surpassing that which can be obtained from quicksilver, or from the most highly-polished metals, by any means whatever.

OPTICS OF A SOAP BUBBLE.

If a soap-bubble be blown up, and set under a glass, so that the motion of air may not affect it, as the water glides down the sides and the top grows thinner, several colors will successively appear at the top, and spread themselves from thence down the sides of the bubble, till they vanish in the same order in which they appear. At length, a black spot appears at the top, and spreads till the bubble bursts.[7]

THE KALEIDOSCOPE.

If any object be placed between two plane mirrors, inclined towards each other at an angle of thirty degrees, three several images will be perceived in the circumference of a circle. On this principle is formed the kaleidoscope, invented by Sir David Brewster, and by means of which the reflected images viewed from a particular point exhibit symmetrical figures, under an infinite arrangement of beautiful forms and colors. The kaleidoscope may be bought at any toy-shop, but it is requisite that every young person should be able to construct one for himself. He must, therefore, procure a tube of tin or paper, of about ten inches in length, and two and a half or three inches in diameter. One end of this should be stopped up with tin or paper, securely fastened, in which is to be made a hole, about the size of a small pea, for the eye to look through. Two pieces of well-silvered looking-glass, B B, are now to be procured; they must be not quite so long as the tube, and they should be placed in the tube lengthwise, at an angle of 60 degrees, meeting together in a point at A, and separating to the points C C, the polished surfaces looking inwards. A circular piece of glass is now to be laid on the top of the edges of the reflectors, B B; which, by their not being quite so long as the tube, will allow room for its falling in, and it will be supported by the edges of the tube, which may be slightly bent over, to prevent the glass from falling out. This having been done, now proceed to make the "cap" of the instrument. A rim of tin or pasteboard must be cut, so as to fit over the glass end of the tube; and in this, on the outer side, a piece of ground glass must be fastened, so that the whole may fit on the tube like the lid of a pill-box. Then, before putting it on, obtain some small pieces of broken glass of various colors, beads, little strips of wire, or any other object, and place them in the cap; and by passing it over the end, so that the broken glass, &c. has free motion, the instrument is complete. To use it, apply the eye to the small hole, and, on turning it, the most beautiful forms will appear, in the most wonderful combinations.

The following curious calculation has been made of the number of changes this instrument will admit of. Supposing it to contain 20 small pieces of glass, and that you make 10 changes in a minute, it will take an inconceivable space of time, _i. e._ 462,880,899,576 years, and 360 days, to go through the immense number of changes of which it is capable.

SIMPLE SOLAR MICROSCOPE.

Having made a circular hole in a window-shutter, about three inches in diameter, place in it a glass lens of about twelve inches focal distance. To the inside of the hole adapt a tube, having at a small distance from the lens a slit, capable of receiving one or two very thin plates of glass, to which the object to be viewed must be affixed by means of a little gum water exceedingly transparent. Into this tube fit another, furnished at its extremity with a lens of half an inch focal distance. Place a mirror before the hole of the window-shutter on the outside, in such a manner as to throw the light of the sun into the tube, and you will have a solar magic lantern.

The method of employing this arrangement of lenses for microscopic purposes is as follows: Having darkened the room, and by means of the mirror reflected the sun's rays on the glasses in a direction parallel to the axis, place some small object between the two moveable plates of glass, or affix it to one of them with very transparent gum water, and bring it exactly into the axis of the tube; if the moveable tube be then pushed out or drawn in, till the object be a little beyond the focus, it will be seen painted very distinctly on a card, or piece of white paper, held at a proper distance, and will appear to be greatly magnified. A small insect will appear as a large animal, a hair as big as a walking-stick, and the almost invisible eels in paste or vinegar as large as common eels.

ANAMORPHOSES.

This is a very curious optical effect, producing a distorted and grotesque figure from a regular one. The term is derived from two Greek words, signifying a distortion of figure, and by its means many optical puzzles may be produced geometrically.

Take any subject, such as the portrait of a head; divide it vertically and horizontally with parallel lines, of which the outer sides shall form the boundary, A, B, C, D, and the whole shall be equi-distant. Then, on a separate piece of paper, or cardboard, prepare a drawing similar to Fig. 2 by the following means:

1. Draw a horizontal line, _a b_, equal to A B, and divide it into as many equal parts as the latter is divided.

2. Let fall a perpendicular line, _e v_, from the middle of _a b_, and then draw _s v_ parallel to _a b_.

3. Both _e v_ and _s v_ may be any length at pleasure, but the longer the first is, and the shorter the other, so will the anamorphoses be more and more deformed. The proportions in our figures are sufficiently different.

4. After having drawn from the point _v_ right lines, _v_ 1, _v_ 2, _v_ 3, _v_ 4, to the divisions of _a b_, draw the line _s b_, and through each point where _s b_ intersects the divergent lines, draw other horizontal lines parallel to _a b_. We now have a _trapezium_, _a b c d_, divided into as many cells as the square in Fig. 1.

The next step is to fill up all the cells of Fig. 2 with portions of the device, proportionate to their position in Fig. 1. For instance, in Fig. 1 the nose is in the second vertical division from the left, and in the third and fourth horizontal divisions from the top, and that portion of the face must accordingly be placed in a corresponding part of Fig. 2.

By these means we procure the anamorphosis seen in Fig. 2, which, when viewed from a particular position, will lose all its distortion, and assume an appearance resembling that in Fig. 1. This position lies immediately over the point _v_, and at a height above it equal to the length of the line _s v_; and the means of determining it are as follow:

Place the drawing horizontally before a window; take a slip of card, and rest its lower edge on the line _s v_, the card being accurately vertical; pierce a small hole in the card vertically over the point _v_, and at a height from it equal to the length of the line _s v_, then, with the eye placed immediately behind the card, look through the orifice at the anamorphosis, and it will be found that as soon as the eye has become accustomed to the novelty of the experiment the anamorphosis will lose its distortion, and appear almost exactly like the symmetrical figure.

It would be very difficult, and would require geometrical reasoning of a lengthened kind, to show why this particular form of construction should lead to such results.

THE COSMORAMA.

The principle upon which the cosmorama is formed is so simple, that any person may easily fit up one in a small summer house, &c. Nothing more is necessary than to fix in a hole a double convex lens of about three feet focus, A, and at rather less than this distance a picture, B, is to be hung. To absorb all the rays of light but those necessary for seeing the picture, a squared frame of wood blackened on the inside is placed between the lens and the picture. The picture may be hung in a large box having a light coming in upon it from above, or in a small closet illuminated in the same manner. Should it be wished to show the picture by candle-light, a lamp, _c_, may be placed on the top of the wooden frame, and if the light of this be converged by a lens to a moderate radius, it will be more effective.

DISTORTED LANDSCAPES.

Landscapes or other matters may be drawn so as to produce curious optical illusions by the following method. Take a piece of smooth white pasteboard, and sketch the design upon it. Prick the outlines in every part with a fine pin or needle, then place the pricked drawing in a perpendicular position, and put a lighted candle behind it. Place before it another piece of pasteboard, and follow with a pencil the lines given by the light, and you have produced a distorted landscape. Now take away the candle and the pricked drawing, and place your eye where the light was, and the drawing will assume the regular form. To get your eye in the proper position, it will be advisable to cut out a piece of card according to the preceding pattern, and raising it on its base, B, look through the hole at A, when the object will appear in its proper proportions.

THE MAGIC COIN.

Among the numerous experiments with which science astonishes and sometimes even strikes terror into the ignorant, there is none more calculated to produce this effect than that of displaying to the eye in absolute darkness the legend or inscription upon a coin. To do this, take a silver coin (I have always used an old one), and after polishing the surface as much as possible, make the parts of it which are raised rough by the action of an acid, the parts not raised, or those which are to be rendered darkest, retaining their polish. If the coin thus prepared is placed upon a mass of red-hot iron, and removed into a dark room, the inscription upon it will become less luminous than the rest, so that it may be distinctly read by the spectator. The mass of red-hot iron should be concealed from the observer's eye, both for the purpose of rendering the eye fitter for observing the effect, and of removing all doubt that the inscription is really read in the dark, that is, without receiving any light, direct or reflected, from any other body. If, in place of polishing the depressed parts, and roughening its raised parts, we make the raised parts polished, and roughen the depressed parts, the inscription will now be less luminous than the depressed parts.

FOOTNOTES:

[Footnote 6: The eye is to be applied to the little circular hole seen on the upper surface.]

[Footnote 7: The thinnest substance ever observed is the aqueous film of the soap-bubble previous to bursting; yet it is capable of reflecting the faint image of a candle, or the sun. Hence its thickness must correspond with what Sir Isaac Newton calls the beginning of black, which appears in water at the thickness of the seven hundred and fifty thousandth part of an inch.]

TRICKS IN MECHANICS.

There is no subject of such importance as Mechanics, as its principles are founded upon the properties of matter and the laws of motion; and in knowing something of these, the tyro will lay the foundation of all substantial knowledge.

The properties of matter are the following: Solidity (or Impenetrability), Divisibility, Mobility, Elasticity, Brittleness, Malleability, Ductility, and Tenacity.

The laws of motion are as follow:

1. Every body continues in a state of rest or of uniform rectilineal motion, unless affected by some extraneous force.

2. The change of motion is always proportionate to the impelling force.

3. Action and reaction are always equal and contrary.

EXPERIMENT OF THE LAW OF MOTION.

In shooting at "taw," if the marble be struck "plump," as it is called, it moves forward exactly in the same line of direction; but if struck sideways, it will move in an oblique direction, and its course will be in a line situated between the direction of its former motion and that of the force impressed. This is called the resolution of forces.

BALANCING.

The center of gravity in a body is that part about which all the other parts equally balance each other. In balancing a stick upon the finger, or upon the chin, it is necessary only to keep the chin or finger exactly under the point which is called the center of gravity.

THE PRANCING HORSE.

Cut out the figure of a horse, and having fixed a curved iron wire to the under part of its body, place a small ball of lead upon it. Place the hind legs of the horse on the table, and it will rock to and fro. If the ball be removed, the horse would immediately tumble, because unsupported, the center of gravity being in the front of the prop; but upon the ball being replaced, the center of gravity immediately changes its position, and is brought under the prop, and the horse is again in equilibrio.

TO CONSTRUCT A FIGURE, WHICH, BEING PLACED UPON A CURVED SURFACE,
AND INCLINED IN ANY POSITION, SHALL, WHEN LEFT TO ITSELF, RETURN TO
ITS FORMER POSITION.

The feet of the figure rest on a curved pivot, which is sustained by two loaded balls below; for the weight of these balls being much greater than that of the figure, their effect is to bring the center of gravity of the whole beneath the point on which it rests; consequently the equilibrium will resist any slight force to disturb it.

TO MAKE A CARRIAGE RUN IN AN INVERTED POSITION WITHOUT FALLING.

It is pretty well known to most boys, that if a tumbler of water be placed within a broad wooden hoop, the whole may be whirled round without falling, owing to the centrifugal force. On the same principle, if a small carriage be placed on an iron band or rail, it will ascend the curve, become inverted, and descend again, without falling.

TO CAUSE A CYLINDER TO ROLL BY ITS OWN WEIGHT UP HILL.

Procure a coffee canister, and loading it at F with a piece of lead, which may be fixed in with solder, the position of the center of gravity is thus altered. If a cylinder so constructed be placed on an inclined plane, and the loaded part above, it will roll up hill without assistance.

THE BALANCED STICK.

Procure a piece of wood, about nine inches in length and about half an inch in thickness, and thrust into its upper end the blades of two penknives, on either side one. Place the other end upon the tip of the fore-finger, and it will keep its place without falling.

THE CHINESE MANDARIN.

Construct out of the pith of elder a little mandarin; then provide a base for it to sit in, like a kettle-drum. Into this put some heavy substance, such as half a leaden bullet; fasten the figure to this, and in whatever position it may be placed, it will, when left to itself, immediately return to its upright position.

TO MAKE A QUARTER DOLLAR TURN ON ITS EDGE ON THE POINT OF A NEEDLE.

Take a bottle, with a cork in its neck, and in it, in a perpendicular position, a middle-sized needle. Fix a quarter dollar into another cork, by cutting a nick in it; and stick into the same cork two small table-forks, opposite each other, with the handles inclining downwards. If the rim of the quarter dollar be now poised on the point of the needle, it may easily be made to spin round without falling, as the center of gravity is below the the center of suspension.

THE SELF-BALANCED PAIL.

You lay a stick across the table, letting one third of it project over the edge; and you undertake to hang a pail of water on it, without either fastening the stick on the table, or letting the pail rest on any support; and this feat the laws of gravitation will enable you literally to accomplish.

You take the pail of water, and hang it by the handle upon the projecting end of the stick, in such a manner that the handle may rest on it in an inclined position, with the middle of the pail within the edge of the table. That it may be fixed in this situation, place another stick with one of its ends resting against the side at the bottom of the pail, and its other end against the first stick, where there should be a notch to retain it. By these means, the pail will remain fixed in that situation, without being able to incline to either side; nor can the stick slide along the table, or move along its edge, without raising the center of gravity of the pail, and the water it contains.

TO LIFT A BOTTLE WITH A STRAW.

Take a straw, and having bent the thicker end of it in a sharp angle, as in figure subjoined, put this hooked end into the bottle, so that the bent part may rest against its side; you may then take the other end, and lift up the bottle by it, without breaking the straw, and this will be the more readily accomplished as the angular part of the straw approaches nearer to that which comes out of the bottle. It is necessary, in order to succeed in this feat, to be particularly careful in choosing a stout straw, which is neither broken nor bruised; if it have been previously bent or damaged, it is unfit for the purpose of performing this trick, as it will be too weak in the part so bent, or damaged, to support the bottle.

THE DANCING PEA.

If you stick through a pea, or small ball of pith, two pins[8] at right angles, and defend the points with pieces of sealing wax, it may be kept in equilibrio at a short distance from the end of a straight tube by means of a current of breath from the mouth, which imparts a rotary motion to the pea.

THE TOPER'S TRIPOD.

Place three tobacco pipes in the position shown in the engraving, the mouth of the bowls downwards, and the lower end of the stems upon the stem just by the bowls. This tripod, if carefully put together, will support considerably more than a pot of ale.

OBLIQUITY OF MOTION.

Cut a piece of pasteboard into the following shape, and describe on it a spiral line; cut this out with a penknife, and then suspend it on a large skewer or pin, as seen in the engraving. If the whole be now placed on a warm stove, or over the flame of a candle or lamp, it will revolve with considerable velocity. The card, after being cut into the spiral, may be made to represent a snake or dragon, and when in motion will produce a very pleasing effect.

THE BRIDGE OF KNIVES.

Place three glasses, A A A, in the form of a triangle, and arrange three knives upon them, as shown in the figure, the blade of No. 1 over that of No. 2, and that over No. 3, which rests on No. 1. The bridge so made will be self-supported.

SAND IN THE HOUR-GLASS.

It is a remarkable fact, that the flow of sand in the hour-glass is perfectly equable, whatever may be the quantity in the glass; that is, the sand runs no faster when the upper half of the glass is quite full than when it is nearly empty. It would, however, be natural enough to conclude that, when full of sand, it would be more swiftly urged through the aperture, than when the glass was only a quarter full, and near the close of the hour.

The fact of the even flow of sand may be proved by a very simple experiment. Provide some silver sand, dry it over or before the fire, and pass it through a tolerably fine sieve. Then take a tube, of any length or diameter, closed at one end, in which make a small hole, say the eighth of an inch; stop this with a peg, and fill up the tube with the sifted sand. Hold the tube steadily, or fix it to a wall, or frame, at any height from a table; remove the peg, and permit the sand to flow in any measure for any given time, and note the quantity. Then, let the tube be emptied, and only half or a quarter filled with the sand; measure again, for a like time, and the same quantity of sand will flow: even if you press the sand in the tube with a ruler or stick, the flow of the sand through the hole will not be increased.

The above is explained by the fact, that when the sand is poured into the tube, it fills it with a succession of conical heaps, and that all the weight which the bottom of the tube sustains is only that of the heap which _first_ falls upon it; as the succeeding heaps do not press downwards, but only against the sides or walls of the tube.

RESISTANCE OF SAND.

From the above experiment it may be concluded, that it is extremely difficult to thrust sand out of a tube by means of a fitting plug or piston; and this, upon trial, is found to be the case. Fit a piston to a tube (exactly like a boy's pop-gun,) pour some sand in, and try with the utmost strength of the arm to push out the sand. It will be found impossible to do this: rather than the sand should be shot out, the tube will burst at the sides.

FOOTNOTES:

[Footnote 8: The pins are only used to hold the pea steady before it is blown from the pipe, as the pea alone will dance quite as well.]

TRICKS IN HYDRAULICS.

The science of Hydraulics comprehends the laws which regulate non-elastic fluids in motion, and especially water, &c.

Water can only be set in motion by two causes--the pressure of the atmosphere, or its own gravity. The principal law concerning fluids is, that they always preserve their own level. Hence water can be distributed over a town from any reservoir that is higher than the houses to be supplied; and the same principle will enable us to form fountains in a garden, or other place. Should any of our young friends wish to form a fountain, or jet-d'-eau, they may, by bringing a pipe from T, a water-tank, which should be at the upper part of the house, convey the water down to the garden. Then by leading it through the earth, underneath the path or grass plot, and turning it to a perpendicular position, the water will spring out, and rise nearly as high as the level of that in the tank. The part of the pipe at B should have a turnkey, so that the water may be let on or shut off at pleasure.

THE PUMP.

The action of the common pump is as follows: When the handle A is raised, the piston-rod B descends, and brings the piston-valve, called the sucker, or bucket, to another valve, C, which is fixed, and opens inwards towards the piston. When the handle is drawn down, the piston is raised, and, as it is air-tight, a vacuum is produced between the two valves; the air in the valve of the pump, betwixt the lower valve and the water, then forces open the lower valve, and rushes through to fill up this vacuum; and the air in the pump being less dense than the external atmosphere, the water is forced a short way up the barrel. When the piston again descends to the lower valve, the air between them is again forced out by forcing open the upper valve; and when the piston is raised, a vacuum is again produced, and the air below the lower valve rushes up, and the water in consequence is again raised a little further. This operation continues until the water rises above the lower valve; at every stroke afterwards, the water passes through the valve of the descending piston, and is raised by it, on its ascent, until it issues out of the spout.

THE HYDRAULIC DANCER.

Make a little figure of cork, in the shape of a dancing mountebank, sailor, &c. In this figure place a small hollow cone, made of thin leaf brass. When this figure is placed upon any jet-d'-eau, such as that of the fountain recommended to be constructed, it will be suspended on the top of the water, and perform a great variety of amusing motions. If a hollow ball of very thin copper, about an inch in diameter, be placed on a similar cone, it will remain suspended, turning round and spreading the water all about it.

THE SYPHON.

The syphon is a bent tube, having one leg shorter than the other. It acts by the pressure of the atmosphere being removed from the surface of a fluid, which makes it to rise above its common level at B. In order to make a syphon act, it is necessary first to fill both legs quite full of the fluid; and then the shorter leg must be placed in the vessel to be emptied. Immediately upon withdrawing the finger from the longer leg, the liquor will flow. Any young person may form a syphon by a small piece of leaden pipe, bent into the form above.

THE WATER SNAIL, OR ARCHIMEDIAN SCREW

may easily be constructed. Purchase a yard of small leaden pipe, and twist it round a pole, as in the following figure, A; place a handle at its upper end, B, and let its lower end rest in the water. Between the last turn of the pipe and the orifice place a paddle-wheel, C. Now, should the water be that of a running stream, the force of the stream will turn the pipe, and the water will rise in it till it empties itself into the trough at D. Should the water have no motion, the turning of the handle at B will elevate the water from the lower to the higher level.

THE BOTTLE EJECTMENT.

Fill a small white glass bottle, with a very narrow neck, full of wine; place it in a glass vase, which must previously have sufficient water in it to rise above the mouth of the bottle. Immediately you will perceive the wine rise, in the form of a little column, toward the surface of the water, and the water will, in the mean time, begin to take the place of the wine at the bottom of the bottle. The cause of this is, that the water is heavier than the wine, which it displaces, and forces it to rise toward the surface.

THE MAGIC OF HYDROSTATICS WITH THE ANCIENTS.

The principles of _Hydrostatics_ were available in the work of magical deception. The marvelous fountain which Pliny describes in the island of Andros as discharging wine for seven days, and water during the rest of the year,--the spring of oil which broke out in Rome to welcome the return of Augustus from the Sicilian war,--the three empty urns which filled themselves with wine at the annual feast of Bacchus in the city of Elis,--the glass tomb of Belus, which was full of oil, and which, when once emptied by Xerxes, could not again be filled,--the weeping statues, and the perpetual lamps of the ancients,--were all the obvious effect of the equilibrium and pressure of fluids.

TO EMPTY A GLASS UNDER WATER.

Fill a wine-glass with water, place over its mouth a card, so as to prevent the water from escaping, and put the glass, mouth downwards, into a basin of water. Next, remove the card, and raise the glass partly above the surface, but keep its mouth below the surface, so that the glass still remains completely filled with water. Then insert one end of a quill or reed in the water below the mouth of the glass, and blow gently at the other end, when air will ascend in bubbles to the highest part of the glass, and expel the water from it; and, if you continue to blow through the quill, all the water will be emptied from the glass, which will be filled with air.

TRICKS IN ACOUSTICS.

Acoustics is the science relating to sound and hearing. Sound is heard when any shock or impulse is given to the air, or to any other body which is in contact directly or indirectly with the ear.

DIFFERENCE BETWEEN SOUND AND NOISE.

Noises are made by the cracks of whips, the beating of hammers, the creak of a file or saw, or the hubbub of a multitude. But when a bell is struck, the bow of a violin drawn across the strings, or the wetted finger turned round a musical glass, we have what are properly called sounds.

SOUNDS, HOW PROPAGATED.

Sounds are propagated on all bodies much after the manner that waves are in water, with a velocity of 1,142 feet in a second. Sounds in liquids and in solids are more rapid than in air. Two stones rubbed together may be heard in water at half a mile; solid bodies convey sounds to great distances, and pipes may be made to convey the voice over every part of the house.

VISIBLE VIBRATION.

Provide a glass goblet about two thirds filled with colored water, draw a fiddle bow against its edge, and the surface of the water will exhibit a pleasing figure, composed of fans, four, six, or eight in number, dependent on the dimensions of the vessel, but chiefly on the pitch of the note produced.

Or, nearly fill a glass with water, draw the bow strongly against its edge, the water will be elevated and depressed; and when the vibration has ceased, and the surface of the water has become tranquil, these elevations will be exhibited in the form of a curved line, passing round the interior surface of the glass, and above the surface of the water. If the action of the bow be strong, the water will be sprinkled on the inside of the glass, above the liquid surface, and this sprinkling will show the curved line very perfectly, as in the engraving. The water should be carefully poured, so that the glass above the liquid be preserved dry; the portion of the glass between the edge and curved line will then be seen partially sprinkled; but, between the level of the water and the curved line, it will have become wholly wetted, thereby indicating the height to which the fluid has been thrown.

TRANSMITTED VIBRATION.

Provide a long, flat glass ruler or rod, as in the engraving, and cement it with mastic to the edge of a drinking glass, fixed into a wooden stand; support the other end of the rod very lightly on a piece of cork, and strew its upper surface with sand; set the glass in vibration by a bow, at a point opposite where the rod meets it, and the motions will be communicated to the rod without any change in their direction. If the apparatus be inverted, and sand be strewed on the under side of the rod, the figures will be seen to correspond with those produced on the upper surface.

DOUBLE VIBRATION.

Provide two disks of metal or glass, precisely of the same dimensions, and a glass or metal rod; cement the two disks at their centers to the ends of the rod, as in the engraving, and strew their upper surfaces with sand. Cause one of the disks, viz., the upper one, to vibrate by a bow, and its vibration will be exactly imitated by the lower disk, and the sand strewed over both will arrange itself in precisely the same forms on both disks.

CHAMPAGNE AND SOUND.

Pour sparkling champagne into a glass, until it is half full, when the glass will lose its power of ringing by a stroke upon its edge, and will emit only a disagreeable and puffy sound. Nor will a glass ring while the wine is brisk, and filled with air-bubbles; but as the effervescence subsides, the sound will become clearer and clearer, and when the air-bubbles have entirely disappeared, the glass will ring as usual. If a crumb of bread be thrown into the champagne, and effervescence be reproduced, the glass will again cease to ring. The same experiment will also succeed with soda water, ginger wine, or any other effervescing liquid.

MUSIC OF THE SNAIL.

Place a garden snail upon a pane of glass, and in drawing itself along, it will frequently produce sounds similar to those of musical glasses.

THE TUNING-FORK A FLUTE PLAYER.

Take a common tuning-fork, and on one of its branches fasten with sealing-wax a circular piece of card, of the size of a small wafer, or sufficient nearly to cover the aperture of a pipe, as the sliding of the upper end of a flute with the mouth stopped: it may be tuned in unison with the loaded tuning-fork (a C fork), by means of the moveable stopper or card, or the fork may be loaded till the unison is perfect. Then set the fork in vibration by a blow on the unloaded branch, and hold the card closely over the mouth of the pipe, as in the engraving, when a note of surprising clearness and strength will be heard. Indeed, a flute may be made to "speak" perfectly well, by holding close to the opening a vibrating tuning-fork, while the fingering proper to the note of the fork is at the same time performed.

MUSICAL BOTTLES.

Provide two glass bottles, and tune them by pouring water into them, so that each corresponds to the sound of a different tuning-fork. Then apply both tuning-forks to the mouth of each bottle alternately, when that sound only will be heard, in each case, which is reciprocated by the unisonant bottle; or, in other words, by that bottle which contains a column of air, susceptible of vibrating in unison with the fork.

THEORY OF WHISPERING.

Apartments of a circular or elliptical form are best calculated for the exhibition of this phenomenon. If a person stand near the wall, with his face turned to it, and whisper a few words, they may be more distinctly heard at nearly the opposite side of the apartment, than if the listener was situated near to the speaker.

THEORY OF THE VOICE.

Provide a species of whistle, common as a child's toy or a sportsman's call, in the form of a hollow cylinder, about three fourths of an inch in diameter, closed at both ends by flat circular plates, with holes in their centers. Hold this toy between the teeth and lips; blow through it, and you may produce sounds varying in pitch with the force with which you blow. If the air be cautiously graduated, all the sounds within the compass of a double octave may be produced from it; and, if great precaution be taken in the management of the wind, tones even yet graver may be brought out. This simple instrument, or toy, has indeed the greatest resemblance to the larynx, which is the organ of voice.

TO TUNE A GUITAR WITHOUT THE ASSISTANCE OF THE EAR.

Make one string to sound, and its vibrations will, with much force, be transferred to the next string: this transference may be seen, by placing a saddle of paper (like an inverted Λ) upon the string, at first in a state of rest. When this string _hears_ the other, the saddle will be shaken, or fall off; when both strings are in harmony, the paper will be very little, or not at all shaken.

PROGRESS OF SOUND.

When a bow is drawn across the strings of a violin, the impulses produced may be rendered evident by fixing a small steel bead upon the bow; when looked at by light, or in sunshine, the bead will seem to form a series of dots during the passage of the bow.

TO MAKE AN ÆOLIAN HARP.

This instrument consists of a long narrow box of very thin pine, about six inches deep, with a circle in the middle of the upper side, of an inch and half in diameter, in which are to be drilled small holes. On this side seven, ten, or more strings of very fine catgut are stretched over bridges at each end like the bridge of a fiddle, and screwed up or relaxed with screw pins. The strings must all be tuned to one and the same note,[9] and the instrument should be placed in a window partly open, in which the width is exactly equal to the length of the harp, with the sash just raised to give the air admission. When the air blows upon these strings with different degrees of force it will excite different tones of sound. Sometimes the blast brings out all the tones in full concert, and sometimes it sinks them to the softest murmurs.

A colossal imitation of the instrument just described was invented at Milan in 1786, by the Abbate Gattoni. He stretched seven strong iron wires, tuned to the notes of the gamut, from the top of a tower sixty feet high, to the house of a Signor Moscate, who was interested in the success of the experiment, and this apparatus, called the "giant's harp," in blowing weather yielded lengthened peals of harmonious music. In a storm this music was sometimes heard at the distance of several miles.

THE INVISIBLE GIRL.

The facility with which the voice circulates through tubes was known to the ancients, and no doubt has afforded the priests of all religions means of deception to the ignorant and credulous. But of late days the light of science dispels all such wicked deceptions. A very clever machine was produced at Paris several years ago, and afterwards exhibited in New York and other cities in the United States, under the name of the "Invisible Girl," since the apparatus was so constructed that the voice of a female at a distance was heard as if it originated from a hollow globe, not more than a foot in diameter. It consisted of a wooden frame something like a tent bedstead, formed by four pillars _a a a a_, connected by upper cross rails _b b_, and similar rails below, while it terminated above in four bent wires _c c_, proceeding at right angles of the frame, and meeting in a central point. The hollow copper ball _d_, with four trumpets, _t t_, crossing from it at right angles, hung in the center of the frame, being connected with the wires alone by four narrow ribbons _r r_. The questions were proposed close to the open mouth of one of these trumpets, and the reply was returned from the same orifice. The means used in the deception were as follows: a pipe or tube was attached to one of the hollow pillars, and carried into another apartment, in which a female was placed; and this tube having been carried up the leg or pillar of the instrument to the cross-rails, had apertures exactly opposite two of the trumpet mouths; so that what was spoken was immediately answered through a very simple mode of communication.

THE MAGIC OF ACOUSTICS.

The science of _Acoustics_ furnished the ancient sorcerers with some of their best deceptions. The imitation of thunder in their subterranean temples could not fail to indicate the presence of a supernatural agent. The golden virgins whose ravishing voices resounded through the temple of Delphos,--the stone from the river Pactolus, whose trumpet notes scared the robber from the treasure which it guarded,--the speaking head which uttered its oracular responses at Lesbos,--and the vocal statue of Memnon, which began at the break of day to accost the rising sun,--were all deceptions derived from science, and from a diligent observation of the phenomena of nature.

TO SHOW HOW SOUND TRAVELS THROUGH A SOLID.

Take a long piece of wood, such as the handle of a hair broom, and placing a watch at one end, apply your ear to the other, and the tickings will be distinctly heard.

TO SHOW THAT SOUND DEPENDS ON VIBRATION.

Touch a bell when it is sounding, and the noise ceases; the same may be done to a musical string with the same results. Hold a musical pitchfork to the lips, when it is made to sound, and a quivering motion will be felt from its vibrations. These experiments show that sound is produced by the quick motions and vibrations of different bodies.

FOOTNOTES:

[Footnote 9: D is a good note for it. The upper string may be tuned to the upper D, and the two lower to the lower D, and D D. The "harmonics," are the sounds produced.]

THE MAGIC OF NUMBERS

OR, CURIOUS PROBLEMS IN ARITHMETIC.

As the principal object of this volume is to enable the young reader to learn something in his sports, and to understand what he is doing, we shall, before proceeding to the curious tricks and feats connected with the science of numbers, present him with some arithmetical aphorisms, upon which most of the following examples are founded.

APHORISMS OF NUMBER.

1. If two even numbers be added together, or subtracted from each other, their sum or difference will be an even number.

2. If two uneven numbers be added or subtracted, their sum or difference will be an even number.

3. The sum or difference of an even and an uneven number added or subtracted, will be an uneven number.

4. The product of two even numbers will be an even number, and the product of two uneven numbers will be an uneven number.

5. The product of an even and uneven number will be an even number.

6. If two different numbers be divisible by any one number, their sum and their difference will also be divisible by that number.

7. If several different numbers, divided by 3, be added or multiplied together, their sum and their product will also be divisible by 3.

8. If two numbers, divisible by 9, be added together, the sum of the figures in the amount will be either 9, or a number divisible by 9.

9. If any number be multiplied by 9, or by any other number divisible by 9, the amount of the figures of the product will be either 9, or a number divisible by 9.

10. In every arithmetical progression, if the first and last term be each multiplied by the number of terms, and the sum of the two products be divided by 2, the quotient will be the sum of the series.

11. In every geometric progression, if any two terms be multiplied together, their product will be equal to that term, which answers to the sum of these two indices. Thus, in the series--

1 2 3 4 5
2 4 8 16 32

If the third and fourth terms 8 and 16 be multiplied together, the product 128 will be the seventh term of the series. In like manner, if the fifth term be multiplied into itself, the product will be the tenth term, and if that sum be multiplied into itself, the product will be the twentieth term. Therefore, to find the last, or any other term of a geometric series, it is not necessary to continue the series beyond a few of the first terms.

Previous to the numerical recreations, we shall here describe certain mechanical methods of performing arithmetical calculations, such as are not only in themselves entertaining, but will be found more or less useful to the young reader.

PALPABLE ARITHMETIC.

The blind mathematician, Dr. Saunderson, adopted a very ingenious device for performing arithmetical operations by the sense of touch.

Small cubes of wood were provided, and in one face of each, nine holes were pierced, thus:

1 2 3 o o o
4 5 6 o o o
7 8 9 o o o

These holes represented the nine digits, as in the figure, and to denote any figure, a small peg was inserted into the hole corresponding to it. If the number consisted of several figures, more cubes were used, one for each. A cipher was represented by a peg of different shape from that of the others, and inserted in the central hole.

To perform any arithmetical process, a square board was provided, divided by ridges into recesses of the same width as the cubes, and by this the cubes were retained in the required horizontal and perpendicular lines. Suppose it was necessary to add together the numbers 763, 124, 859, the cubes and pegs would be arranged thus:

o o o o o o o o ☻
o o o o o o o o o
o o o o o o o o o

☻ o o o ☻ o o o o
o o o o o o ☻ o o
o o o o o o o o o

o o o o o o o o o
o o o o ☻ o o o o
o ☻ o o o o o o ☻

☻ o o o o o o o o o o o
o o o o o o ☻ o o o o ☻
o o o o o o o o o o o o

THE ABACUS.

This instrument is used for teaching numeration, and the first principles of arithmetic.

Upon a frame are placed wires, parallel to one another, and at equal distances. Ten small balls are strung upon each wire, being placed as in the margin. The right wire denotes units, the next tens, and so on, the 7th wire being the place of millions. In using the abacus, all the balls are first ranged at one end, and a number of them are then moved to the other end of each wire, to correspond to the figures required. The example given in the margin is 15,781, the height of Mount Blanc.

NAPIER'S RODS.

The object of this contrivance is to render arithmetical multiplication more easy, and to secure its correctness; it was much used by astronomers before the invention of logarithms.

To appreciate the merits of this invention, we must consider the process of multiplication as usually performed. Suppose we had to multiply 8,679 by 8:

8,679
8
------
69,432

We first multiply 9 by 8 = 72, and putting down 2 as the first figure in the product, carry the 7 to add to the next product of 7 by 8 = 56; this gives us 63, the 3 being put down as the second figure; 6 is carried to add to the product of 6 by 8, and so on.

A blunder may be made in each part of this process; for 1st, we might reckon 8 times 9 as some other number than 72; 2d, after multiplying the 7 by the 8, we might add to the resulting 56 some other figure than the 7, which we carried; 3d, we may add 56 to 7 inaccurately, making some other sum of it than the right one, 63. Errors in a long multiplication problem are usually made in one of these three ways, and to prevent such errors, Lord Napier[10] introduced this useful contrivance. Thin strips of card, wood, or bone, 9 times as long as they are broad, are each divided into 9 equal squares, a figure is printed or written on the top square, and in each of the squares underneath is the product of multiplying that figure by 2, 3, 4, &c., up to 9.