_hot_ water, increasing the temperature at each attempt, when they
will find that it is possible, with the aid of the lycopodium, to lift
an article out of a kettle of all but boiling water. The sensation of
heat is not destroyed, but it causes no injury to the tissues—in other
words, no scald.
HANGING WITHOUT A CORD.
Soak a thread in strong salt and water; dry thoroughly, and repeat this
two or three times. This must be done privately beforehand. When you
bring forward the thread thus prepared, the spectators have no reason
to suppose that it is other than the ordinary article.
Use this thread to suspend a ring, choosing as light a one as possible.
Set fire to the thread, which will burn from end to end, but the
spectators will be surprised to see that the ring does not fall, being
supported by the ash resulting from the combustion. In reality, the
fibrous particles of the thread have been destroyed, but there remains
a tiny filament of salt, strong enough, if there is no draught in the
room, to support the weight of the ring.
This experiment may be varied in this manner:
Attach four pieces of thread to the four corners of a little piece
of muslin, so as to form a miniature hammock. Soak the whole in salt
water; then dry it, and repeat the operation three or four times.
When the threads and the muslin are thoroughly saturated with salt
and perfectly dry, place a blown egg in the little hammock, suspended
as shown in the figure. Set fire to the hammock, which will burn
freely enough, as also the fine threads, but if the experiment has
been properly carried out, the egg will remain suspended, to the
astonishment of all who behold it.
THE MAGIC SCORPION.
Place on the surface of the water in a glass or basin a number of small
pieces of camphor of various sizes, together representing the form of
some animal, say a scorpion. After a little while the scorpion will
begin to stir in the water; you will see him move his claws, as though
trying to swim, and curl his tail convulsively, as if in pain.
This amusing experiment is easy to perform, and costs practically
nothing, for camphor is to be found in every household; but in spite
of its simplicity we may deduce from it, as you will see, several
interesting observations.
1. Our scorpion floats on the water, but lies almost entirely below the
surface. This proves to us that the specific gravity of camphor is
nearly, but not quite, equal to that of water.
2. The animal does not dissolve. Camphor is therefore insoluble in
water.
3. The different fragments of which our scorpion consists do not
separate, but remain one against the other as we originally placed
them. This is because they are held together by the force known as
cohesion.
4. Lastly, the eccentric movements we have mentioned depend on a
well-ascertained but mysterious property of camphor, viz., that when
placed on the surface of the water, it moves spontaneously. It is a
well-known fact that a morsel of camphor placed in a glass of water
will, after a few moments, begin to move either with a sidelong
or rotary movement; such movement being due, according to some
authorities, to the recoil produced by an escape of liberated gases;
according to others, to a mysterious force inherent in the surface of
liquids, and known as _superficial tension_.
AMUSING THE CHILDREN.
A clever way to amuse a party of children is to invite them to a peanut
party. Tiny cards of invitation are sent out, on each of which two half
peanut shells are fastened. A large quantity of the nuts are hidden
about the house, and when the young folks arrive they are told to hunt
them. They who find the most and least of them receive prizes.
Another is a soap bubble party. The invitations for this should have a
pen and ink sketch of a pipe and bubble. Provide plenty of clay pipes,
with the name of a guest written on each, and make the soapsuds with
the addition of glycerine to make the bubbles strong and tough. For
the prizes for the most successful bubble blower, a fancy pipe is
suitable. It can be made by gilding the handle and outside of the bowl
of a clay pipe and painting the inside of the bowl in water colors. A
bow of baby ribbon to match the paint improves it. For the booby prize
a little pipe can be made from a match and half an acorn shell.
A penny party furnishes amusement for an evening. With the invitations
is sent a request for each guest to bring a penny, not for an admission
fee, but for use. For each guest there are provided two cards and a
pencil; one card is blank; the other has a list of the things to be
found on a penny. The list is numbered, and each person is expected to
name as many as he can, prizes being awarded for the best and poorest
list. Find—1. Top of hill. 2. Place of worship. 3. An animal. 4. A
fruit. 5. A common fruit. 6. Links between absent friends. 7. Union of
youth and old age. 8. A vegetable. 9. Flowers. 10. What we fight for.
11. A metal. 12. A messenger. 13. A weapon of defence. 14. A weapon of
warfare. 15. A body of water. 16. A beverage. 17. What young ladies
want. 18. The most popular State. 19. What men work for. 20. Sign
of royalty. 21. A jolly dog. The answers are—1. Brow. 2. Temple. 3.
Hare (hair). 4. Date. 5. Apple. 6. Letters. 7. 1894 (the date of the
penny). 8. Ear. 9. Tulips (two lips). 10. Liberty. 11. Copper. 12. One
sent (cent). 13. Shield. 14. Arrow. 15. Sea (c). 16. Tea (t). 17. Beau
(bow). 18. United States (matrimony). 19. Money. 20. Crown. 21. A merry
cur (America). Usually a half hour is allowed for filling out the blank
cards, and after that some time for correcting the lists and awarding
prizes.
It is often hard to find games for evening amusements that will amuse
all. Some are so noisy that the sensitive cannot enjoy them, but the
following will instruct as well as amuse: One is to transpose the
misplaced letters of words, usually the name of a city. To prepare
for the game make a large quantity of small cards from pasteboards,
about an inch and a half square. Paste a large letter on each one, cut
from a newspaper or advertisement, having several for each letter of
the alphabet. Give to each the letters necessary to spell a word and
let him study it out. Thus the letters i l i s y a n t p can be made to
spell Ypsilanti, or s t o o n b Boston.
Another game which is quite entertaining is called a pronunciation
match. Any number can play. One is elected as leader. At first he will
call out a letter, as a, and each person must think quickly while he
counts five, and be ready to tell the name of a city in the State
agreed upon before the contest begins. For instance, the leader, while
he counts five, points to one of the company who must give the name of
a city beginning with the letter A, B or C, as the leader may announce.
When one answer has been given, he quickly counts again, and points to
another person until some one fails to respond, when he is declared
leader and also pays a forfeit. It is very amusing and teaches people
to think quickly and keep their wits about them.
GAMES OF ARITHMETIC.
HOW TO TELL ANY NUMBER THOUGHT OF.
Ask any person to think of a number, say a certain number of dollars;
tell him to borrow that sum of some one in the company, and add the
number borrowed to the amount thought of. It will here be proper to
name the person who lends him the money, and to beg the one who makes
the calculation to do it with great care, as he may readily fall into
an error, especially the first time. Then say to the person: “I do not
lend you, but give you $10; add them to the former sum.” Continue in
this manner: “Give the half to the poor, and retain in your memory the
other half.” Then add: “Return to the gentleman, or lady, what you
borrowed, and remember that the sum lent you was exactly equal to the
number thought of.” Ask the person if he knows exactly what remains; he
will answer “Yes.” You must then say: “And I know also the number that
remains; it is equal to what I am going to conceal in my hand.” Put
into one of your hands 5 pieces of money, and desire the person to tell
how many you have got. He will answer 5; upon which open your hand and
show him the 5 pieces. You may then say: “I well knew that your result
was 5; but if you had thought of a very large number, for example, two
or three millions, the result would have been much greater, but my
hand would not have held a number of pieces equal to the remainder.”
The person then supposing that the result of the calculation must be
different, according to the difference of the number thought of, will
imagine that it is necessary to know the last number in order to guess
the result; but this idea is false, for, in the case which we have here
supposed, whatever be the number thought of, the remainder must always
be 5. The reason of this is as follows: The sum, the half of which is
given to the poor, is nothing else than twice the number thought of,
plus 10; and when the poor have received their part, there remains only
the number thought of, plus 5; but the number thought of is cut off
when the sum borrowed is returned, and, consequently, there remain only
5. The result may be easily known, since it will be the half of the
number given in the third part of the operation; for example, whatever
be the number thought of, the remainder will be 36 or 25 according as
72 or 50 have been given. If this trick be performed several times
successively, the number given in the third part of the operation must
be always different; for if the result were several times the same,
the deception might be discovered. When the five first parts of the
calculation for obtaining a result are finished, it will be best not
to name it at first, but to continue the operation, to render it more
complex, by saying, for example: “Double the remainder, deduct two,
add three, take the fourth part,” etc.; and the different steps of the
calculation may be kept in mind, in order to know how much the first
result has been increased or diminished. This irregular process never
fails to confound those who attempt to follow it.
ANOTHER WAY.
Tell the person to take 1 from the number thought of, and then double
the remainder; desire him to take 1 from this double, and to add to it
the number thought of; in the last place, ask him the number arising
from this addition, and, if you add 3 to it, the third of the sum will
be the number thought of. The application of this rule is so easy that
it is needless to illustrate it by an example.
A THIRD WAY.
Ask the person to add 1 to the triple of the number thought of, and to
multiply the sum by three; then bid him add to this product the number
thought of, and the result will be a sum from which if 3 be subtracted,
the remainder will be ten times of the number required; and if the
cipher on the right be cut off from the remainder, the other figure
will indicate the number sought.
Example—Let the number thought of be 6, the triple of which is 18;
and if 1 be added, it makes 19; the triple of this last number is 57,
and if 6 be added it makes 63, from which if 3 be subtracted, the
remainder will be 60; now, if the cipher on the right be cut off, the
remaining figure, 6, will be the number required.
A FOURTH WAY.
Tell the person to multiply the number thought of by itself; then
desire him to add 1 to the number thought of, and to multiply it also
by itself; in the last place, ask him to tell the difference of these
two products, which will certainly be an odd number, and the least half
of it will be the number required.
Let the number thought of, for example, be 10; which, multiplied by
itself, gives 100; in the next place, 10 increased by 1 is 11, which,
multiplied by itself, makes 121; and the difference of these two
squares is 21, the least half of which, being 10, is the number thought
of.
This operation might be varied by desiring the person to multiply the
second number by itself, after it has been diminished by 1. In this
case, the number thought of will be equal to the greater half of the
difference of the two squares.
Thus, in the preceding example, the square of the number thought of
is 100, and that of the same number, less 1, is 81; the difference of
these is 19, the greater half of which, or 10, is the number thought of.
HOW TO TELL NUMBERS THOUGHT OF.
If one or more numbers thought of be greater than 9, we must
distinguish two cases; that in which the number of the numbers thought
of is odd, and that in which it is even. In the first case, ask the
sum of the first and second; of the second and third; the third and
fourth; and so on to the last; and then the sum of the first and the
last. Having written down all these sums in order, add together all
those, the places of which are odd, as the first, the third, the fifth,
etc.; make another sum of all those, the places of which are even, as
the second, the fourth, the sixth, etc.; subtract this sum from the
former, and the remainder will be the double of the first number. Let
us suppose, for example, that the five following numbers are thought
of, 3, 7, 13, 17, 20, which when added two and two as above, give 10,
20, 30, 37, 23: the sum of the first, third, and fifth is 63, and
that of the second and fourth is 57; if 57 be subtracted from 63, the
remainder, 6, will be the double of the first number, 3. Now, if 3 be
taken from 10, the first of the sums, the remainder, 7, will be the
second number; and by proceeding in this manner, we may find all the
rest.
In the second case, that is to say, if the number of the numbers
thought of be even, you must ask and write down, as above, the sum of
the first and the second; that of the second and third; and so on, as
before; but instead of the sum of the first and the last, you must
take that of the second and last; then add together those which stand
in the even places, and form them into a new sum apart; add also those
in the odd places, the first excepted, and subtract this sum from the
former, the remainder will be the double of the second number; and if
the second number, thus found, be subtracted from the sum of the first
and second, you will have the first number; if it be taken from that of
the second and third, it will give the third; and so of the rest. Let
the numbers thought of be, for example, 3, 7, 13, 17: the sums formed
as above are 10, 20, 30, 24; the sum of the second and fourth is 44,
from which if 30, the third, be subtracted, the remainder will be 14,
the double of 7, the second number. The first, therefore, is 3, third
13, and the fourth 17.
When each of the numbers thought of does not exceed 9, they may be
easily found in the following manner:
Having made the person add 1 to the double of the first number thought
of, desire him to multiply the whole by 5, and to add to the product
the second number. If there be a third, make him double this first sum,
and add 1 to it, after which, desire him to multiply the new sum by 5,
and to add to it the third number. If there be a fourth, proceed in the
same manner, desiring him to double the preceding sum; to add to it 1;
to multiply by 5; to add the fourth number; and so on.
Then, ask the number arising from the addition of the last number
thought of, and if there were two numbers, subtract 5 from it; if there
were three, 55; if there were four, 555; and so on; for the remainder
will be composed of figures, of which the first on the left will be the
first number thought of, the next the second, and so on.
Suppose the number thought of to be 3, 4, 6; by adding 1 to 6, the
double of the first, we shall have 7, which, being multiplied by 5,
will give 35; if 4, the second number thought of, be then added, we
shall have 39, which doubled, gives 78; and, if we add 1, and multiply
79, the sum, by 5, the result will be 395. In the last place, if we add
6, the number thought of, the sum will be 401; and if 55 be deducted
from it, we shall have, for remainder, 346, the figures of which, 3, 4,
6, indicate in order the three numbers thought of.
GOLD AND SILVER GAME.
One of the party having in one hand a piece of gold, and in the other
a piece of silver, you may tell in which hand he has the gold, and in
which the silver, by the following method: Some value, represented
by an even number, such as 8, must be assigned to the gold, and a
value represented by an odd number, such as 3, must be assigned to the
silver; after which, desire the person to multiply the number in the
right hand by any even number whatever, such as 2; and that in the left
by an odd number, as 3; then bid him add together the two products, and
if the whole sum be odd, the gold will be in the right hand, and the
silver in the left; if the sum be even, the contrary will be the case.
To conceal the trick better, it will be sufficient to ask whether the
sum of the two products can be halved without a remainder; for in that
case the total will be even, and in the contrary case odd.
It may be readily seen, that the pieces, instead of being in the two
hands of the same person, may be supposed to be in the hands of two
persons, one of whom has the even number, or piece of gold, and the
other the odd number, or piece of silver. The same operations may then
be performed in regard to these two persons, as are performed in regard
to the two hands of the same person, calling the one privately the
right and the other the left.
THE NUMBER BAG.
The plan is to let a person select several numbers out of a bag, and to
tell him the number which shall exactly divide the sum of those he has
chosen: Provide a small bag, divided into two parts, into one of which
put several tickets, numbered 6, 9, 15, 36, 63, 120, 213, 309, etc.;
and in the other part put as many other tickets, marked No. 3 only.
Draw a handful of tickets from the first part, and, after showing them
to the company, put them into the bag again, and, having opened it a
second time, desire any one to take out as many tickets as he thinks
proper; when he has done that, you open privately the other part of
the bag, and tell him to take out of it one ticket only. You may safely
pronounce that the ticket shall contain the number by which the amount
of the other numbers is divisible; for, as each of these numbers can
be multiplied by 3, their sum total must, evidently, be divisible by
that number. An ingenious mind may easily diversify this exercise, by
marking the tickets in one part of the bag, with any numbers that are
divisible by 9 only, the properties of both 9 and 3 being the same; and
it should never be exhibited to the same company twice without being
varied.
THE MYSTICAL NUMBER NINE.
The discovery of remarkable properties of the number 9 was accidentally
made, more than forty years since, though, we believe, it is not
generally known:
The component figures of the product made by the multiplication of
every digit into the number 9, when added together, make NINE.
The order of these component figures is reversed, after the said number
has been multiplied by 5.
The component figures of the amount of the multipliers (_viz._ 45),
when added together, make NINE.
The amount of the several products, or multiples of 9 (_viz._ 405),
when divided by 9, gives, for a quotient, 45; that is, 4+5=NINE.
The amount of the first product (_viz._ 9), when added to the other
product, whose respective component figures make 9, is 81; which is the
square of NINE.
The said number 81, when added to the above-mentioned amount of the
several products, or multiples of 9 (_viz._ 405) makes 486; which, if
divided by 9, gives, for a quotient, 54: that is, 5+4=NINE.
It is also observable, that the number of changes that may be rung on
nine bells, is 362,880; which figures, added together, make 27; that
is, 2+7=NINE.
And the quotient of 362,880, divided by 9, will be, 40,320; that is
4+0+3+2+0=NINE.
To add a figure to any given number, which shall render it divisible by
Nine: Add the figures together in your mind, which compose the number
named; and the figure which must be added to the sum produced, in order
to render it divisible by 9, is the one required. Thus
Suppose the given number to be 7521:
Add those together, and 15 will be produced; now 15 requires 3 to
render it divisible by 9; and that number, 3, being added to 7521,
causes the same divisibility: 7521 plus 3 gives 7524, and, divided by
9, gives 836.
This exercise may be diversified by your specifying, before the sum is
named, the particular place where the figure shall be inserted, to make
the number divisible by 9; for it is exactly the same thing, whether
the figure be put at the head of the number, or between any two of its
digits.
THE MAGIC HUNDRED.
Two persons agree to take, alternately, numbers less than a given
number, for example, 11, and to add them together till one of them
has reached a certain sum, such as 100. By what means can one of them
infallibly attain to that number before the other? The whole secret
in this, consists in immediately making choice of the numbers, 1, 12,
23, 34, and so on, or of a series which continually increases by 11,
up to 100. Let us suppose, that the first person, who knows the game,
makes choice of 1; it is evident that his adversary, as he must count
less than 11, can, at most, reach 11, by adding 10 to it. The first
will then take 1, which will make 12; and whatever number the second
may add, the first will certainly win, provided he continually add the
number which forms the complement of that of his adversary, to 11; that
is to say, if the latter take 8, he must take 3; if 9, he must take
2; and so on. By following this method, he will infallibly attain to
89; and it will then be impossible for the second to prevent him from
getting first to 100; for whatever number the second takes, he can
attain only to 99; after which the first may say—“and 1 makes 100.” If
the second take 1 after 89, it would make 90, and his adversary would
finish by saying—“and 10 make 100.” Between two persons who are equally
acquainted with the game, he who begins must necessarily win.
TO GUESS THE MISSING FIGURE.
To tell the figure a person has struck out of the sum of two given
numbers:—Arbitrarily command those numbers only, that are divisible by
9; such, for instance, as 36, 63, 81, 117, 126, 162, 261, 360, 315,
and 432. Then let a person choose any two of these numbers; and, after
adding them together in his mind, strike out from the sum any one of
the figures he pleases. After he has so done, desire him to tell you
the sum of the remaining figures; and it follows, that the number which
you are obliged to add to this amount, in order to make it 9 or 18, is
the one he struck out. Thus:—Suppose he chooses the numbers 162 and
261, making altogether 423, and that he strike out the centre figure,
the two other figures will, added together, make 7, which, to make 9,
requires 2, the number struck out.
THE KING AND THE COUNSELOR.
A King being desirous to confer a liberal reward on one of his
courtiers, who had performed some very important service, desired him
to ask whatever he thought proper, assuring him it should be granted.
The courtier, who was well acquainted with the science of numbers, only
requested that the monarch would give him a quantity of wheat equal
to that which would arise from one grain doubled sixty-three times
successively. The value of the reward was immense; for it will be seen,
by calculation, that the sixty-fourth term of the double progression
divided by 1: 2: 4: 8: 16: 32: etc., is 9223372036854775808. But the
sum of all the terms of a double progression, beginning with 1, may
be obtained by doubling the last term, and subtracting from it 1. The
number of the grains of wheat, therefore, in the present case, will be
18446744073709551615. Now, if a pint contains 9216 grains of wheat,
a gallon will contain 73728; and, as eight gallons make one bushel,
if we divide the above result by eight times 73728, we shall have
31274997411295 for the number of the bushels of wheat equal to the
above number of grains: a quantity greater than what the whole earth
could produce in several years.
THE NAILS IN THE HORSE’S SHOE.
A man took a fancy to a horse, which a dealer wished to dispose of
at as high a price as he could; the latter, to induce the man to
become a purchaser, offered to let him have the horse for the value
of the twenty-fourth nail in his shoes, reckoning one farthing for
the first nail, two for the second, four for the third, and so on to
the twenty-fourth. The man, thinking he should have a good bargain,
accepted the offer; the price of the horse was, therefore, necessarily
great. By calculating as before, the twenty-fourth term of the
progression 1 : 2 : 4 : 8: etc., will be found to be 8388608, equal to
the number of farthings the purchaser gave for the horse; the price,
therefore amounted to £8738. 2s. 8d.
THE DINNER PARTY PUZZLE.