The Pile of Draughtsmen.
“Matter is inert.” That is what you read in every treatise on
physics--what does it mean? Here is a very simple experiment that will
prove this truth to anyone.
Pile up ten draughtsmen, as shown in Fig. 1. Before this pile place
another piece on edge, and pressing its circumference with the
forefinger, let it glide from underneath so that it strikes the pile
with considerable force. The piece so thrown must, you will think,
upset the whole pile of draughts; but no: the piece thus sharply sent
forward will strike only one piece of the pile, and this alone will be
dislodged without putting the others out of their equilibrium, and the
whole column above will settle down together on the bottom piece.
[Illustration: Fig. 1.]
In effect, the force of the impulse, making itself felt on the piece
that is touched, the latter leaves the pile without transmitting its
movement to the other pieces, which, following another physical law,
that of gravity, descend vertically to fill the place left vacant.
The experiment may be varied by using a knife and striking with it a
sharp horizontal blow on one of the pieces. The piece struck will fall
out of the pile without disturbing the symmetry of the others.
The Decanter, Card, and Coin.
This law of “Inertia” will provide us with a few more experiments as
curious as they are conclusive.
Place a playing or an ordinary visiting card on a decanter; upon the
card and just in the center, over the aperture of the decanter, put a
small coin (a dime). Now, if with a sharp fillip, given horizontally
on the edge of the card, you succeed in whisking it off (which is
very easy), the coin will fall to the bottom of the decanter. The
following phenomenon has taken place: the movement was too rapid to be
transmitted to the coin, and the card alone was whisked off.
[Illustration]
The coin being no longer sustained by the card falls, of course,
vertically, without having in the least come out of position.
A sharp horizontal knock given with a penholder or small stick on the
edge of the card, will produce the same result, but the fillip is more
effective.
A Clever Blow.
Take a thin stick about a yard long, and thrust a pin firmly in each of
its extremities. This done, place the stick on the bowls of two pipes,
which a couple of persons hold by the stems, in such a manner that the
pins only rest on the pipes. A third person then strikes the stick
sharply in the middle, and it will break without injuring the pipes.
Ordinary clay pipes will do very well, as the more brittle the pipes
are, the more striking is the experiment. How is this explained?
[Illustration]
The mechanical effect of the shock has not time to reach the bowls of
the pipes (inertia), and is only manifested at the very point on which
the blow falls, hence the stick unable to resist the force of the blow
at the one point breaks in two pieces.
The Obedient Coin.
Take an ordinary wooden matchbox, and remove the drawer holding the
matches. In the center place a small coin, a cent will be the best for
the experiment, the object of which is to make the coin fall into the
interior without touching it. Tap lightly on that side of the box to
which you desire the coin to come, until it rests upon the edge.
[Illustration]
Then slightly raise the end of the box whereon the coin rests, and
lightly tap with the finger once more. At once the coin will fall into
the box. The secret of the experiment is this: the taps on the box only
move the box, while the coin retains its position by reason of its own
inertia, until the edge of the box reaches it. The last tap knocks
away the support, and the coin, obedient to the law of gravity, falls
vertically into the interior of the box. This little experiment is
easily performed, and extremely interesting when done neatly.
To Cut a String With Your Hands.
With a little practice, and some briskness of movement, you may be able
to break a string of considerable thickness by proceeding as follows:
Wind the string round your left hand, so as to make a loop, as shown in
the figure. Pass it three or four times round the fingers to insure the
solidity of the loop. Seize firmly the other end of the string with
your right hand, around which you wind it three or four times, then
give a brisk pull. The string will be clean cut at the junction of the
loop in the left hand.
[Illustration]
When the knack is well acquired, one may break the string on two
fingers only, by following always the same theory as above.
The Rebound.
On the neck of a bottle place a cork in an upright position. The cork
must be large enough to rest on the neck without falling in.
Now give a sharp fillip on the neck of the bottle, and you will see the
cork fall, not on the other side of the bottle as most people expect,
but forward in the direction of the hand giving the blow. This, again,
is an illustration of the principle of inertia. A rapid blow tends to
push the bottle from the cork before the movement is transmitted to the
latter.
Few people will execute this experiment properly the first time,
for the instinctive fear to break the bottle and cut their fingers,
will prevent them giving a blow sharp enough to make this experiment
successfully at the first attempt; but with a little perseverance, the
necessary degree of force will be gauged to a nicety.
[Illustration]
A Fiery Catapult.
Take a match-box and place it upright edge-wise and place two matches
in each side between the inner and outer box, heads up. They must be
inserted deeply enough to stick firmly.
Place a third match cross-wise between them and it will stay there by
the pressure the latter exercises on them.
Now light the middle of the horizontal match and wait. What do you
think will happen? Ask the bystanders which will first catch fire?
The natural conclusion they will draw will be the following.
From the middle the frame will spread of course to the two extremities
and light the other two matches, probably this side first where the two
phosphorous heads meet.
[Illustration]
Well, nothing of the sort happens. When the volume of the burning match
has diminished, and consequently its rigidity also, the force of its
resistance grows weaker as the combustion proceeds.
A moment comes when the two vertical matches, trying to assume again
their original position, throw off, with a sway, the burning horizontal
match.
The burning match was rendered flexible in the middle, and is not at
all burned at the ends, and the two matches remain standing as before.
To Make an Exact Balance.
To construct by yourselves, with the help of simple materials a balance
of great precision may seem impossible. Nevertheless it can be done.
A ruler, a tin box, (in which blacking was contained, for example)
three blocks of wood, two pins, thread, four nails, a small piece of
glass, and cardboard are all the necessary materials, and now to work.
At a short distance from the center of the ruler, and on a cross line
with one another, stick two pins so that they come out a little on the
other side. At one end of the ruler, in C, nail a small piece of your
box.
[Illustration]
At the spot, where the hook to which the scale is suspended, is to
hang, make an indentation with the point of a nail, so that the hook
does not shift at the other extremity, in A, fasten a flat piece of
tin, which will form one of the scales of your balance.
At the end of this pan solder a pin point downwards. Your second scale,
B, destined to contain the object or substances to be weighed, will be
formed by the lid of the blacking-tin.
On its rim at nearly equal distances pierce four holes, on which the
suspension-strings will be tied, the latter at their upper end being
united together in one string, which is tied to a hook (a bent pin or
fishing hook will do.)
Now the point of support remains to be constructed. On a wooden square,
rather thick, E, fix another block, G, on which gum a piece of glass.
In the largest block knock four nails to prevent the shaft of the
balance swerving from right to left.
The small truncated pyramid, D, which you perceive on the left of the
design, and which is graduated, serves as bench-mark.
In order to weigh you use the method due to Borda, called the method of
double weights.
Place in the scale A a weight which you think is slightly over the
one of the substance or object to be weighed. Then the scale B being
occupied, get equilibrium by shifting more or less towards the ruler,
the weight on the scale A.
Then note the division indicated by the pin point, and take from scale
B the article placed there, and put therein weights until the point
of scale A tells you that the equilibrium is the same as when the
substance was in the scale.
It is not necessary that this balance be exact, provided it answers the
very small differences in the pans.
The one we have indicated will weigh down to a fifty-thousandth part of
a pound.
The Recomposition of Light.
It is a great pity that exquisitely beautiful facts and mysteries are
wrapped up in the crack-jaw terms of foreign languages, and so made to
appear ugly.
There is no branch of knowledge more fascinating than light. To follow
up its study is like walking along a shady lane, where at certain
distances apart the wayfarer lights upon jewels of great brilliance.
It has been said above that white light is formed by the union or
combination of seven colors. When a ray of light passes through a prism
it is split up into the parts of which it is composed, and seven colors
as in the rainbow appear.
These colors shade off into one another with every variety of tint,
like a band of rainbow-colored ribbon. This band is called a spectrum.
Now, where science classes are held there may be seen a complicated
instrument, which is used to show how the seven colors unite to form
white light. It is a disc on which the colors of the spectrum are
painted, and it is made to spin round with great rapidity.
The impression received by the eye, when looking at the revolving disc
is total abstinence of color. In other words it is white light.
Fortunately, you can satisfy yourselves on this point without any other
materials than a cardboard disc and a piece of string. On this disc
paint in small sections the colors of the spectrum, repeating them
four or five times in the following order: red, orange, yellow, green,
blue, indigo, violet.
[Illustration]
That the experiment may be entirely successful, the sections must be
marked off according to the following scale of width of section. Let
orange, next to the circumference represent 2: then
Red will be represented by 5
Orange “ “ “ 2
Yellow “ “ “ 5
Green “ “ “ 4
Blue “ “ “ 5
Indigo “ “ “ 3
Violet “ “ “ 5
Now, in any diameter of the disc bore two holes not too near the edge.
Through them pass a piece of string, and knot the two ends together.
Take hold of the string with both hands, and make the disc spin round.
Then extend and approach the hands alternately to give a very rapid
movement to the disc. When revolving rapidly enough you will not be
able to distinguish the separate colors. They all become blended into
white light.
The Mysterious Apple.
Pierce an apple in such a manner as to obtain two holes tending toward
the middle, and forming a pretty large angle as shown in the figure.
Two quills or tin tubes should be inserted to make the inside passages
smooth. Pass a string through the hole and your apple is prepared for a
little trick, which, you may be sure will astonish all persons before
whom you practice it, and who of course are not yet initiated.
You fasten one extremity of the string to your foot, and take the
other in your hand so as to produce at will the rigidity of the string.
You can then command the apple to go down, or to stop, and it will obey
your order immediately. Indeed, when you straighten the string, the
part which enters the apple pushes against the angle formed by the two
passages, and by the pressure, holds the apple. When on the contrary
you let go a little, you take away the rigidity and the apple glides
down.
[Illustration]
You can therefore alternately let the apple go down or stop its course,
and we repeat it, persons not in the secret cannot imagine by what
means you get this curious result.
If, instead of an apple one takes a wooden ball, the experiment will be
more interesting and the article will last longer.
Economical Letter-Scales.
Take a watch or small clock spring, and fix it by the center on a
stick. At the other end attach a small brass hook to hold letters,
etc., as shown in the figure.
At the top of the hook fix horizontally a small band, running over a
strip of cardboard, likewise hanging on the stick.
Now graduate the cardboard strip with real weights, or their exact
equivalents, and after this any small articles may be weighed with
sufficient accuracy. The spring, being of steel, always turns to its
original position when the scale is empty.
[Illustration]
Tracing a Spiral.
In geometry the process for tracing a spiral by the help of compasses
is pretty long and tedious. The following method will enable you to do
it far more quickly and as accurately.
[Illustration]
Take a wooden or cardboard cylinder, with a diameter equal to a fourth
part of the distance you require between the spires (or trelices) to be
traced. On this cylinder fasten one end of a string, B, and wind it up,
and attach to the other end a pencil, C, or a point, according to what
you want to do.
Now you have only to turn to right or left according to the direction
in which the string was wound up, by holding the pencil down and
keeping the string tight, and a spiral of perfect regularity will be
traced.
The above figure clearly shows the process. The cylinder A has a
diameter equal to the distance R S divided by 4.
The Inclined Plane.
Take a piece of paper, roll it up into a tube large enough to hold a
marble, and gum it lengthwise. Then introduce a marble and close the
extremities with a strip of paper as shown below.
[Illustration]
When you think that it is well dried you place it upright on the upper
end of an inclined board, or flat ruler, leaning on a pile of books for
example. You will then see the paper cylinder lie down, get up and so
on till it reaches the bottom of its course.
The effect is very curious and will be more so if you are somewhat of
an artist, and able to draw or paint a figure on the cylinder.
To Cut a Bottle With a String.
Gum first two circular pads of paper on each side of the spot where you
intend to cut your bottle. These pads are obtained by gumming several
strips of paper one over the other, so as to leave between them a
groove on which you wind the string round once.
Catch hold of the extremities of the string, and draw it to and fro,
see-saw fashion, by which friction the part of the glass operated on
will be heated.
[Illustration]
As soon as you think that the glass is hot enough, plunge the bottle in
cold water, which you will have placed handy before, and at the spot
where the friction was exercised the glass will be clean cut. According
to the thickness of the glass, more or less heat must be produced.
This process is infallible.
The same result can also be produced in another way. It is, when once
the heat is sufficient to let glide a few drops of water along the
string. The string must be well wetted. The cut will be as clean as by
the other process.
Equilibrium of a Knife in Mid-Air.
Be reassured dear readers, we are not going to ask you to make a
balance in mid air, that would be too much for our weak capabilities.
The question is simply to swing a knife horizontally in the space which
surrounds us. The experiment is curious and easily executed.
[Illustration]
Take the cork of a champagne bottle. Pierce it lengthwise with a sharp
knife, and let the knife stick out a third of its length from the thin
end of the cork. Then insert into each side of the cork the prongs of
two forks, so that they are perpendicular with the blade of the knife
as shown in figure.
This operation accomplished, you have only to suspend the point of the
blade on the loop of a string, and the knife will hang horizontally.
You may then swing it if you choose, and the movement will not destroy
the equilibrium.
A Trick With Four Matches.
Speaking of matches, there is yet one more trick to be played with four
of them.
At the non-phosphoric ends of two matches cut a small notch so that
they fit into each other. Stretch the matches apart so as to form an
angle, and place them vertically upon the table. Then lean a third
match against them so as to form a tripod, standing by itself.
The question now is to take up this trivet with a fourth match and
carry it to another place without disturbing the harmony of the little
construction.
[Illustration]
At first sight this seems impossible; it is, however, easily done. You
have only to slide the fourth match between the two stuck together, and
the one serving as support.
By lightly pressing against the two first ones the third one will
slide, and its upper extremity will come between the angle formed
by the two others. By taking it up briskly, this extremity will be
maintained, and you are then enabled to carry the little tripod to
another place.
The Distance of an Inaccessible Point.
Everyone knows what an angle is, and you say at once it is the
inclination of two lines that meet each other. These lines by their
branching off form an opening more or less wide. This opening is
measured by the aid of an instrument called a _protractor_ made
of brass or horn, which finds its place in nearly every box of
mathematical instruments.
It represents a semi-circumference, divided into 180 equal parts,
called degrees, written thus: 180°. Each degree is divided into 60
minutes, expressed thus: 60 min.; and finally the minutes are divided
again in 60 parts, called seconds, indicated thus: 60 sec. There are
therefore in a whole circumference, 360 deg., 2,160 min., and 12,960
sec.
One degree, therefore, is the 360th part of a circumference, and thus
we have a measure independent of all dimensions. For example, on a
round table of 36 yards in circumference, one degree will be marked
by one tenth of a yard; on a pond of 360 yards in circumference, one
degree will be equal to one yard.
The degree, therefore, may be more or less, but it is always the 360th
part of the circumference of a circle. Let it be quite understood that,
whether an angle is to be on a sheet of paper, or in the skies, the
divisions do not change.
[Illustration]
This must be well grasped, it is of the utmost importance for the
explanations which follow. It is therefore settled: the measure of the
angles has nothing to do whatever with a measure of length.
We have shown how to measure an angle. Let us examine now what is a
triangle, without pondering too much over this geometrical figure,
which every one knows. The essential property of this three-cornered
figure is that the sum of its three angles is always equal to 180
degrees.
In other words, the protractor placed successively at each angle will
give three numbers, which, added, make up 180 degrees. Keep this
property well in mind, as it will serve us hereafter.
Now, to what distance does a degree correspond? For example, take a
yardstick, and with the _graphometer_ (an instrument by which angles
are measured), in readiness, carry it from the latter instrument to a
certain distance, till the two extremities of the yardstick measure one
degree; this yard is then said to subtend an angle of one degree.
Now, measure the distance which divides the yardstick from the
instrument, and you will find it to be 57 yards. Therefore, one degree
corresponds to an object being at a distance of 57 times its height. A
man two yards high at a distance of 57 times his height, or 114 yards
will measure one degree.
One minute will be represented by a piece of cardboard of a hundreth
part of a yard long seen from a distance of 34 yards; and finally, a
second will be given by a card a hundreth part of a yard seen from a
distance of 2062 yards.
A hair seen at 20 yards about represents a second. This perhaps, you
think to be too small to be seen by the naked eye.
Suppose that you to measure the distance of a church situated on a
height, and from which you are separated by a river (see fig.) Choose
on the river’s bank two spots from which the steeple C can be seen, say
A and B. At B plant a surveying-staff, and with the graphometer, go to
A and find the angle formed by B A C.
Suppose for example, it reads 84 degrees. Repeating the operation at
B for the measure of the angle C B A, suppose it to be 95 degrees.
Measure the distance from A to B and let it be 80 yards.
Now here is the statement of our problem:
How to resolve a triangle of which the base is known to be 10 yards,
and two of its angles. Well, we have said above that the sum of the
three angles is always the same, equal to 180 degrees, having on one
side 84, and on the other 95, that makes together 84 by 95, equal to
179 degrees. The difference between this number and 180 is 1 degree,
therefore the angle ABC measures one degree.
We know that an angle of one degree corresponds to a distance of 57
yards. Multiply the base of our triangle by 57 yards and you obtain a
distance of the church from the points A and B, 10 by 57, equal to 570
yards. Nothing is more simple than this.
[Illustration]
The smaller the measured angle the further off the object will be. As
seen in our figure, the upright lines, _m o_, _m’ o’_, _m, o,_, do not
vary, but according to their distances from point C, they form various
angles, _ac_, _a’c’_, _a,c,_, becoming smaller and smaller.
A graphometer is not always to be had. When approximate distances
only are required, the following contrivance may be used. Trace on a
cardboard of large size a semi-circumference which one divides first
into 180 equal parts, then each of these is divided again in 2, 3, 4
divisions, etc., according to the size given to the circumference,
which constitutes a large protractor.
To measure an angle place the cardboard upright in an horizontal
position, supporting it by the center of the semi-circumference by
means of a screw fixed on a stick. Then proceed as stated above.
From a pin stuck in the center mark the spot where the visual ray
passes, go to A and to B, and you get approximately the desired result.
Practical Tracing of a Meridian Line.
The meridian line of a place is an imaginary line passing through this
place and the center of the sun, when the latter is at the highest
point of the arc of the circle, which it daily describes. At that very
moment it is noonday exactly at the place in question.
As the position of the earth changes from day to day, the sun does not
every day touch the meridian line at noon; sometimes it is in advance,
sometimes behind.
Various instruments have been invented to indicate in a practical
manner the meridian of a place. We owe the following construction to
Mr. E. Brunner of the longitudinal office.
[Illustration]
On a window-sill in a southerly position, fix in a solid, permanent
manner, a small cupful of quicksilver; cover it with a lid made of
varnished metal, and pierced in its center by a small round hole about
a quarter of an inch in diameter. This lid must fit well, but not too
tightly, so as to permit its being lowered in close proximity to the
surface of the quicksilver.
When the window is open the solitary ray reflected on the mercury will
be projected on the ceiling of the room. At the exact noonday the
center of the mirror and the center of the reflected image are in the
meridian plane. It remains only to be traced.
At the moment of its passage one marks in B, for example, a spot
corresponding to the center of the reflected image; one knocks a
small nail there, and with a string connect this point with another
outside the window, so that the string passes through the center of the
diaphragm, M. The line, B M, is the meridian plane. From A, suspend a
lead-line which meets the string, B M.
All you have to do now is to join on the ceiling the points, A B, and
continue them to D. A black thread may be stretched to serve as the
line, and this is the meridian required.
To get the mean time one has only to note the exact passage, and deduct
the corrections given in various astronomical papers.
To Measure the Height of a Mountain.
One can, without instruments, take the height of a building or a
mountain, provided you are able to measure their base. A yardstick and
two ordinary sticks are enough. Suppose the height of the tower, E F,
is to be taken.
[Illustration]
Some distance off plant a stick, a yard high, A B; one yard from this
we plant another and longer one, C D. Measure exactly the distance,
B F, and applying the eye at A, we aim at the summit of the tower, E;
mark on the stick, C D, the point where the visual ray meets the stick,
_i.e._, point G.
Then, by measuring the distance, D G, and subtracting one yard you get
G I, and may be expressed in the following statement: