Chapter XLVI: Appendix: To the Book of Curiosities; Containing Curious Experiments, and (1)

_AMUSING RECREATIONS_, WHICH MAY BE PERFORMED WITH EASE, AND AT A SMALL EXPENSE.

_A Person having an even Number of Counters in one Hand, and an odd Number in the other, to tell in which Hand each of them is._

Desire the person to multiply the number in his right hand by three, and the number in his left by two.

Bid him add the two products together, and tell you whether the sum be odd or even.

If it be even, the even number is in the right hand; but if it be odd, the even number is in the left hand.

EXAMPLE I.

No. in right hand. No. in left hand.
18 7
3 2
-- --
54 54 14
14
--
68 sum of the products.

EXAMPLE II.

No. in right hand. No. in left hand.
7 18
3 2
-- --
21 36 36
21
--
57 sum of the products.

_A Person having fixed on a Number in his Mind, to tell him what Number it is._

Bid him quadruple the number thought on, or multiply it by 4; and having done this, desire him to add 6, 8, 10, or any even number you please, to the product; then let him take the half of this sum, and tell you how much it is; from which, if you take away half the number you desired him at first to add to it, there will remain the double of the number thought on.

EXAMPLE.

Suppose the number thought on is 5
The quadruple of it is 20
8 added to the product is 28
And the half of this sum 14
4 taken from this leaves 10.--

Therefore 5 was the number thought on.

_Another Method of discovering a Number thought on._

After the person has fixed on a number, bid him double it, and add 4 to that sum; then let him multiply the whole by 5, and to that product add 12; desire him also to multiply this sum by 10, and after having deducted 302 from the product, to tell you the remainder, from which, if you cut off the last two figures, the number that remains will be the one thought on.

EXAMPLE.

Let the number thought on be 7
Then the double of this is 14
And 4 added to it makes 18
This multiplied by 5 is 90
And 12 added to it is 102
And this multiplied by 10 is 1020
From which deducting 302
There remains 718,--

which, by striking off the last two figures, gives 7,--the number thought on.

_To tell the Number a Person has fixed upon, without asking him any Questions._

The person having chosen any number in his mind, from 1 to 15, bid him add one to it, and triple the amount. Then,

If it be an even number, let him take the half of it, and triple that half; but if it be an odd number, he must add 1 to it, and then halve it, and triple that half.

In like manner let him take the half of this number, if it be even, or the half of the next greater, if it be odd; and triple that half.

Again, bid him take the half of this last number, if even, or of the next greater, if odd; and the half of that half in the same way; and by observing at what steps he is obliged to add 1 in the halving, the following table will shew the number thought on:

1--0--0 -- 4-- 8
2--0--0 --13-- 5
3--0--0 -- 3--11
1--2--0 -- 2--10
1--3--0 -- 8-- 0
1--2--3 -- 6--14
2--3--0 -- 1-- 9
0--0--0 --15-- 7

Thus, if he be obliged to add 1 only at the first step, or halving, either 4 or 8 was the number thought on; if there were a necessity to add 1 both at the first and second steps, either 2 or 10 was the number thought on, &c.

And which of the two numbers is the true one may always be known from the last step of the operation; for if 1 must be added before the last half can be taken, the number is in the second column, or otherwise in the first, as will appear from the following examples:

Suppose the number chosen to be 9
To which, if we add 1
The sum is 10
Then the triple of that number is 30
1. The half of which is 15
The triple of 15 is 45
2. And the half of that is 23
The triple of 23 is 69
3. The half of that is 35
And the half of that is 18

From which it appears, that it was necessary to add 1 both at the second and third steps, or halvings; and therefore, by the table, the number thought on is either 1 or 9. And as the last number was obliged to be augmented by 1 before the half could be taken, it follows also, by the above rule, that the number must be in the second column; and consequently it is 9.

Again, suppose the number thought on to be 6
To which, if we add 1
The sum is 7
Then the triple of that number is 21
1. The half of which is 11
The triple of 11 is 33
2. And the half of that is 17
The triple of 17 is 51
3. The half of that is 26
And the half of that half is 13

From which it appears, that it was necessary to add 1 at all the steps, or halvings, 1, 2, 3, therefore, by the table, the number thought on is either 6 or 14.

And as the last number required no augmentation before its half could be taken, it follows also, by the above rule, that the number must be in the first column; and consequently it is 6.

_A curious Recreation, usually called--The Blind Abbess and her Nuns._

A blind abbess visiting her nuns, who were twenty-four in number, and equally distributed in eight cells, built at the four corners of a square, and in the middle of each side, finds an equal number in every row, containing three cells. At a second visit, she finds the same number of persons in each row as before, though the company was increased by the accession of four men. And coming a third time, she still finds the same number of persons in each row, though the four men were then gone, and had each of them carried away a nun.

_Fig. 1._
+-----+
|3 3 3|
|3 3|
|3 3 3|
+-----+

_Fig. 2._
+-----+
|2 5 2|
|5 5|
|2 5 2|
+-----+

_Fig. 3._
+-----+
|4 1 4|
|1 1|
|4 1 4|
+-----+

Let the nuns be first placed as in fig. 1, three in each cell; then when the four men have got into the cells, there must be a man placed in each corner, and two nuns removed thence to each of the middle cells, as in fig. 2, in which case there will evidently be still nine in each row; and when the four men are gone, with the four nuns with them, each corner cell must contain four nuns, and every other cell one, as in fig. 3; it being evident, that in this case also, there will still be nine in a row, as before.

_Any Number being named, to add a Figure to it, which shall make it divisible by 9._

Add the figures together in your mind which compose the number named; and the figure which must be added to this sum, in order to make it divisible by 9, is the one required.

Suppose, for example, the number named was 8654; you find that the sum of its figures is 23; and that 4 being added to this sum will make it 27; which is a number exactly divisible by 9.

You therefore desire the person who named the number 8654, to add 4 to it; and the result, which is 8658, will be divisible by 9, as was required.

This recreation 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 end of the number, or between any two of its digits.

_A Person having made choice of several Numbers, to tell him what Number will exactly divide the Sum of those which 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, or any others you please, that are divisible by 3, and in the other part put as many different tickets marked with the number 3 only.

Draw a handful of tickets from the first part, and, after shewing 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 this, open privately the other part of the bag, and tell him to take out of it one ticket only.

You may then pronounce, that this ticket shall contain the number by which the amount of the other numbers is divisible; for, as each of these numbers is some multiple of 3, their sum must evidently be divisible by that number.

This recreation may also be diversified, by marking the tickets in one part of the bag with any numbers which are divisible by 9, and those in the other part of the bag with the number 9 only; the properties of both 9 and 3 being the same; or if the numbers in one part of the bag be divisible by 9, the other part of the bag may contain tickets marked both with 9 and 3, as every number divisible by 9 is also divisible by 3.

_To find the Difference between any two Numbers, the greater of which is unknown._

Take as many 9's as there are figures in the less number, and subtract the one from the other.

Let another person add that difference to the larger number; and then, if he take away the first figure of the amount, and add it to the remaining figures, the sum will be the difference of the two numbers, as was required.

Suppose, for example, that Matthew, who is 22 years of age, tells Henry, who is older, that he can discover the difference of their ages.

He privately deducts 22, his own age, from 99, and the difference, which is 77, he tells Henry to add to his age, and to take away the first figure from the amount.

Then if this figure, so taken away, be added to the remaining ones, the sum will be the difference of their ages; as, for instance:

The difference between Matthew's age and 99, is 77
To which Henry adding his age 35
----
The sum will be 112
And 1, taken from 112, gives 12
Which being increased by 1
--
Gives the difference of the two ages 13
And, this added to Matthew's age 22
--
Gives the age of Henry, which is 35

_A Person striking a Figure out of the Sum of two given Numbers, to tell him what that Figure was._

Such numbers must be offered as are divisible by 9; such, for instance, as 36, 63, 81, 117, 126, 162, 207, 216, 252, 261, 306, 315, 360, and 432.

Then let a person choose any two of these numbers, and after adding them together in his mind, strike out any one of the figures he pleases, from the sum.

After he has done this, desire him to tell you the sum of the remaining figures; and that number which you are obliged to add to this amount, in order to make it 9, or 18, is the one he struck out.

For example, suppose he chose the numbers 126 and 252, the sum of which is 378.

Then, if he strike out 7 from this amount, the remaining figures, 3 and 8, will make 11; to which 7 must be added to make 18.

If he strike out the 3, the sum of the remaining figures, 7 and 8, will be 15; to which 3 must be added, to make 18; and so in like manner, for the 8.

_By knowing the last Figure of the Product of two Numbers, to tell the other Figures._

If the number 73 be multiplied by each of the numbers in the following arithmetical progression, 3, 6, 9, 12, 15, 18, 21. 24, 27, the products will terminate with the nine digits, in this order, 9, 8, 7, 6, 5, 4, 3, 2, 1; the numbers themselves being as follows, 219, 438, 657, 876, 1095, 1314, 1533, 1752, and 1971.

Let therefore a little bag be provided, consisting of two partitions, into one of which put several tickets, marked with the number 73; and into the other part, as many tickets numbered 3, 6, 9, 12, 15, 18, 21, 24, and 27.

Then open that part of the bag which contains the number 73, and desire a person to take out one ticket only; after which, dexterously change the opening, and desire another person to take a ticket from the other part.

Let them now multiply their two numbers together, and tell you the last figure of the product, and you will readily determine, from the foregoing series, what the remaining figures must be.

Suppose, for example, the numbers taken out of the bag were 73, and 12; then, as the product of these two numbers, which is 876, has 6 for its last figure, you will readily know that it is the fourth in the series, and that the remaining figures are 87.

_A curious Recreation with a Hundred Numbers, usually called the Magical Century._

If the number 11 be multiplied by any one of the nine digits, the two figures of the product will always be alike, as appears from the following example:--

11 11 11 11 11 11 11 11 11
1 2 3 4 5 6 7 8 9
-- -- -- -- -- -- -- -- --
11 22 33 44 55 66 77 88 99

Now, if another person and yourself have fifty counters apiece, and agree never to stake more than ten at a time, you may tell him, that if he will permit you to stake first, you will always undertake to make the even century before him.

In order to this you must first stake one, and remembering the order of the above series, constantly add to what he stakes as many as will make one more than the numbers 11, 22, 33, &c. of which it is composed, till you come to 89; after which, the other party cannot possibly make the even century himself, or prevent you from making it.

If the person who is your opponent have no knowledge of numbers, you may stake any other number first, under 10, provided you afterwards take care to secure one of the last terms, 56, 67, 78, &c.: or you may even let him stake first, provided you take care afterwards to secure one of these numbers.

This recreation may be performed with other numbers; but, in order to succeed, you must divide the number to be attained, by a number which is an unit greater than what you can stake each time; and the remainder will then be the number you first stake. Suppose, for example, the number to be attained is 52, and that you are never to add more than six; then dividing 52 by 7, the remainder, which is 3, will be the number you must stake first; and whatever the other stakes, you must add as much to it as will make it equal to 7, the number by which you divided; and so on.

_A Person in Company having privately put a Ring on one of his fingers, to Name the Person, the Hand, the Finger, and even the Joint on which it is placed._

Desire a third person to double the number of the order in which the wearer of the ring stands, and add 5 to that number, then multiply that sum by 5, and to the product add 10. Let him then add 1 to the last number, if the ring be on the right hand, and 2 if on the left, and multiply the whole by 10: to this product he must add the number of the finger, beginning with the thumb, and multiply the whole again by 10. Desire him then to add the number of the joint; and lastly, to increase the whole by 35.

This being done, he is to declare the amount of the whole, from which you are to subtract 3535; and the remainder will consist of four figures, the first of which will give the place in which the person stands, the second the hand, 1 denoting the right, and 2 the left hand, the third number the finger, and the fourth the joint.

EXAMPLE.

Suppose the person stands the second in order, and has put the ring on the second joint of the little finger of the left hand:

Double the order is 4
Add 5
--
9
Multiply by 5
--
45
Add 10
--
55
Number for left hand 2
--
57
Multiply by 10
----
570
Number of finger 5
----
575
Multiply by 10
----
5750
Number of joint 2
----
5752
Add 35
----
5787
Subtract 3535
----
2252

Hence it will appear that the first 2 denotes the second person in order, the second 2 the left hand, 5 the little finger, and 2 the second joint.

_To make a Deaf Man hear the Sound of a Musical Instrument._

It must be a stringed instrument, with a neck of some length, as a lute, a guitar, or the like; and before you begin to play, you must by signs direct the deaf man to take hold with his teeth of the end of the neck of the instrument; for then, if one strikes the strings with the bow one after another, the sound will enter the deaf man's mouth, and be conveyed to the organ of hearing through a hole in the palate, and thus the deaf man will hear with a great deal of pleasure the sound of the instrument, as has been several times experienced; nay, those who are not deaf may make the experiment upon themselves, by stopping their ears so as not to hear the instrument, and then holding the end of the instrument in their teeth, while another touches the strings.

_When two Vessels or Chests are like one another, and of equal Weight, being filled with different Metals, to distinguish the one from the other._

This is easily resolved, if we consider that two pieces of different metals, of equal weight in air, do not weigh equally in water, because that of the greatest specific gravity takes up a lesser space in water; it being a certain truth, that any metal weighs less in water than in air, by reason of the water, the room of which it fills; for example, if the water weighs a pound, the metal will weigh in that water a pound less than in the air: this gravitation diminishes more or less, according as the specific gravity of the metal is greater than that of the water.

We will suppose, then, two chests perfectly like one another, of equal weight in the air, one of which is full of gold, and the other of silver; we weigh them in water, and that which then weighs down the other must needs be the gold chest, the specific gravity of gold being greater than that of silver, which makes the gold lose less of its gravitation in water than silver. We know by experience, that gold loses in water about an eighteenth part only, whereas silver loses near a tenth part; so that if each of the two chests weighs in the air, for example, 180 pounds, the chest that is full of gold will lose in the water ten pounds of its weight; and the chest that is full of silver will lose eighteen: that is, the chest full of gold will weigh 170 pounds, and that of silver only 162.

Or, if you will, considering that gold is of a greater specific gravity than silver, the chest full of gold, though similar and of equal weight with the other, must needs contain a less bulk, and consequently it contains the gold.

_To find the Burden of a Ship at Sea, or in a River._

It is a certain truth, that a ship will carry a weight equal to that of a quantity of water of the same bulk with itself; subtracting from it the weight of the iron about the ship, for the wood is of much the same weight with water; and so, if it were not for the iron, a ship might sail full of water.

The consequence of this is, that, however a ship be loaded, it will not totally sink, as long as the weight of its cargo is less than that of an equal bulk of water: now, to know this bulk or extent, you must measure the capacity or solidity of the ship, which we here suppose to be 1000 cubical feet, and multiply that by 73 pounds, the weight of a cubical foot of sea-water; then you have in the product 73,000 pounds for the weight of a bulk of water equal to that of the ship; so that in this example, we may call the burden of the ship 73,000 pounds, or 36-1/2 tons, reckoning a ton 2,000 pounds, that being the weight of a ton of sea-water; if the cargo of this ship exceeds 36-1/2 tons, she will sink; and if her loading is just 73,000 pounds, she will swim very deep in the water upon the very point of sinking; so that she cannot sail safe and easy, unless her loading be considerably short of 73,000 pounds weight; if the loading come near to 73,000 pounds, as being, for example, just 36 tons, she will swim at sea, but will sink when she comes into the mouth of a fresh water river; for this water being lighter than sea-water will be surmounted by the weight of the vessel, especially if that weight is greater than the weight of an equal bulk of the same water.

_To Measure the Depth of the Sea._

Tie a great weight to a very long cord, or rope, and let it fall into the sea till you find it can descend no further, which will happen when the weight touches the bottom of the sea: if the quantity or bulk of water, the room of which is taken up by the weight, and the rope, weighs less than the weight and rope themselves; for if they weigh more, the weight would cease to descend, though it did not touch the bottom of the sea.

Thus one may be deceived in measuring the length of a rope let down into the water, in order to determine the depth of the sea; and therefore, to prevent mistakes, you had best tie to the end of the same rope another weight heavier than the former, and if this weight does not sink the rope deeper than the other did, you may rest assured that the length of the rope is the true depth of the sea; if it does sink the rope deeper, you must tie a third weight, yet heavier, and so on, till you find two weights of unequal gravitation, that run just the same length of the rope, upon which you may conclude, that the length of the wet rope is certainly the same with the depth of the sea.

_Method of Melting Steel, and causing it to Liquefy._

Heat a piece of steel in the fire, almost to a state of fusion, then holding it with a pair of pincers or tongs, take in the other hand a stick of brimstone, and touch the piece of steel with it: immediately after the contact, you will see the steel melt and drop like a liquid.

_How to dispose two little Figures, so that one shall light a Candle, and the other put it out._

Take two little figures of wood or clay, or any other materials you please, only taking care that there is a little hole at the mouth of each: put in the mouth of one a few grains of bruised gunpowder, and a little bit of phosphorus in the mouth of the other, taking care that these preparations are made beforehand.

Then take a lighted wax candle, and present it to the mouth of the figure with the gunpowder, which, taking fire, will put the candle out; then present your candle, having the snuff still hot, to the other figure; it will immediately light again by means of the phosphorus.

You may propose the same effects to be produced by two figures drawn on a wall with a pencil or coal, by applying with a little starch, or water, a few grains of bruised gunpowder to the mouth of one, and a bit of phosphorus to the mouth of the other.

_The Camera Obscura, or Dark Chamber._

We shall here give a short description of this optical invention; for though it is very common, it is also very pleasing: but every one knows not how to construct it.

Make a circular hole in the shutter of a window, from whence there is a prospect of the fields, or any other object not too near: and in this hole place a convex glass, either double or single, whose focus is at the distance of five or six feet: the distance should not be less than three feet; if it be, the images will be too small, and there will not be sufficient room for the spectators to stand conveniently; on the other hand, the focus should never be more than fifteen or twenty feet, for then the images would be obscure, and the colouring faint; the best distance is from six to twelve feet:--take care that no light enters the room but by this glass: at a distance from it, equal to that of its focus, place a pasteboard, covered with the whitest paper; this paper should have a black border, to prevent any of the side rays from disturbing the picture; let it be two feet and a half long, and eighteen or twenty inches high; bend the length of it inwards to the form of part of a circle, whose diameter is equal to double the focal distance of the glass: then fix it on a frame of the same figure, and put it on a moveable foot, that it may be easily fixed at that exact distance from the glass where the objects paint themselves to the greatest perfection: when it is thus placed, all the objects that are in the front of the window will be painted on the paper in an inverted position; this inverted position of the images may be deemed an imperfection, but it is easily remedied; for if you stand above the board on which they are received, and look down on it, they will appear in their natural position; or if you stand before it, and, placing a common mirror against your breast in an oblique direction, look down in it, you will there see the images erect, and they will receive an additional lustre from the reflection of the glass: or place two lenses in a tube that draws out: or, lastly, if you place a large concave mirror at a proper distance before the picture, it will appear before the mirror in the air, and in an erect position, with the greatest regularity, and in the most natural colours.

If you place a moveable mirror without the window, by turning it more or less, you will have on the paper all the objects that are on each side of the window.

There is another method of making the dark chamber, which is by a scioptric ball, that is, a ball of wood, through which a hole is made, in which hole a lens is fixed; this ball is placed in a wooden frame, in which it turns freely round: the frame is fixed to the hole in the shutter, and the ball by turning about answers, in great part, the use of the mirror on the outside of the window: if the hole in the window be no bigger than a pea, the objects will be represented without any lens.

If instead of placing the mirror without the window, you place it in the room, and above the hole, (which must then be made near the top of the shutter,) you may receive the representation on a paper placed horizontally on a table; and draw at your leisure all the objects that are there painted.

Nothing can be more pleasing than this recreation, especially when the objects are strongly enlightened by the sun; and not only land prospects, but a sea-port, when the water is somewhat agitated, or at the setting of the sun, presents a very delightful appearance.

This representation affords the most perfect model for painters, as well for the tone of colours, as that gradation of shades occasioned by the interposition of the air, which has been so justly expressed by some modern painters.

It is necessary that the paper have a circular form, for otherwise, when the centre of it was in the focus of the glass, the two sides would be beyond it, and consequently the images would be confused: if the frame were contrived of a spherical figure, and the glass were in its centre, the representation would be still more accurate. If the object without be at the distance of twice the focal length of the glass, the image in the room will be of the same magnitude with the object.

The lights, shades, and colours in the camera obscura, appear not only just, but, by the images being reduced to a smaller compass, much stronger than in nature; add to this, that these pictures exceed all others, by representing the motion of the several objects: thus we see the animals walk, run, or fly, the clouds float in the air, the leaves quiver, the waves roll, &c. and all in strict conformity to the laws of nature. The best situation for a dark chamber is directly north, and the best time of the day is noon.

_To shew the Spots in the Sun's Disk, by its image in the Camera Obscura._

Put the object-glass of a ten or twelve feet telescope into the scioptric ball, and turn it about till it be directly opposite the sun: when the sun is directly opposite the hole, the lens will itself be sufficient; or by means of the mirror on the outside of the window, as in the last recreation, in the focus of the lens, and you will see a clear bright image of the sun, of about an inch diameter, in which the spots on the sun's surface will be exactly described.

As this image is too bright to be seen with pleasure by the naked eye, you may view it through a lens, whose focus is six or eight inches diameter, which, at the same time that it prevents the light from being offensive, will, by magnifying both the image and the spots, make them appear to greater advantage.

_To magnify small Objects by means of the Sun's Rays let into a dark Chamber._

Let the rays of light that pass through the lens in the shutter be thrown on a large concave mirror, properly fixed in a frame; then take a slip, or thin plate of glass, and sticking any small object on it, hold it in the incident rays, at a little more than the focal distance from the mirror, and you will see, on the opposite wall, amidst the reflected rays, the image of that object, very large, and extremely clear and bright. This experiment never fails to give the spectator the highest satisfaction.

_To cut a Looking-glass, or piece of Crystal, let it be ever so thick, without the help of a Diamond, in the same shape as the Mark of the Drawing made on it with Ink._

This remarkable operation unites utility with amusement; for being in the country, or in a place where there is no glazier to be had, the following means will answer the purpose without their help.

Take a bit of walnut-tree, about the thickness of a candle, and cut one of its ends to a point; put that end in the fire, and let it burn till it is quite red: while the stick is burning, draw on the glass or crystal, with ink, the design or outline of the form in which you mean to cut it out: then take a file, or bit of glass, and scratch a little the place where you mean to begin your section; then take the wood red-hot from the fire, and lay the point of it about the twentieth part of an inch, or thickness of a guinea, from the marked place, taking care to blow always on that point, in order to keep it red; following the drawing traced on the glass, leaving, as before, about the twentieth part of an inch interval every time that you present your piece of wood, which you must take care to blow often.

After having followed exactly the outlines of your drawing, to separate the two pieces thus cut, you need only pull them up and down, and they will divide.

_By the means of two plain Looking-glasses, to make a Face appear under different forms._

Having placed one of the two glasses horizontally, raise the other to about right angles over the first; and while the two glasses continue in this posture, if you come up to the perpendicular glass, you will set your face quite deformed and imperfect; for it will appear without forehead, eyes, nose, or ears, and nothing will be seen but a mouth and a chin boldly raised: do but incline the glass ever so little from the perpendicular, and your face will appear with all its parts, excepting the eyes and the forehead; stoop a little more, and you will see two noses and four eyes; and then a little further, and you will see three noses and six eyes;--continue to incline it still a little more, and you will see nothing but two noses, two mouths, and two chins; and then a little further again, and you will see one nose and one mouth; at last incline a little further, that is, till the angle of inclination comes to be 44 degrees, and your face will quite disappear.

If you incline the two glasses, the one towards the other, you will see your face perfect and entire; and by the different inclinations, you will see the representation of your face, upright and inverted, alternately.

_To know which of two different Waters is the lightest, without any Scales._

Take a solid body, the specific gravity of which is less than that of water, deal, or fir-wood, for instance, and put it into each of the two waters, and rest assured that it will sink deeper in the lighter than in the heavier water; and so, by observing the difference of the sinking, you will know which is the lightest water, and consequently the wholesomest for drinking.

_To know if a suspicious Piece of Money is good or bad._

If it be a piece of silver that is not very thick, as a crown, or half a crown, the goodness of which you want to try; take another piece of good silver, of equal balance with it, and tie both pieces with thread or horse hair to the scales of an exact balance, (to avoid the wetting of the scales themselves,) and dip the two pieces thus tied, in water; for then, if they are of equal goodness, that is, of equal purity, they will hang in equilibrio in the water as well as in the air: but if the piece in question is lighter in the water than the other, it is certainly false, that is, there is some other metal mixed with it, that has less specific gravity than silver, such as copper; if it is heavier than the other, it is likewise bad, as being mixed with a metal of greater specific gravity than silver, such as lead.

If the piece proposed is very thick, such as that crown of gold which Hiero, king of Syracuse, sent to Archimedes, to know if the goldsmith had put into it all the eighteen pounds of gold that he had given him for that end; take a piece of pure gold of equal weight with the crown proposed, viz. eighteen pounds; and without taking the trouble of weighing them in water, put them into a vessel full of water, one after another, and that which drives out most water, must necessarily be mixed with another metal of less specific gravity than gold, as taking up more space, though of equal weight.

_To hold a Glass full of Water with the Mouth downwards, so that the Water shall not run out._

Take a glass full of water, cover it with a cup that is a little hollow, inverting the cup upon the glass; hold the cup firm in this position with one hand, and the glass with the other; then with a jerk turn the glass and the cup upside down, and so the cup will stand upright, and the glass will be inverted, resting its mouth upon the interior bottom of the cup: this done, you will find that part of the water contained in the glass will run out by the void space between the bottom of the cup, and the brim of the glass; and when that space is filled, so that the water in it reaches the brim of the glass, all passage being then denied to the air, so that it cannot enter the glass, nor succeed in the room of the water, the water remaining in the glass will not fall lower, but continue suspended in the glass.

If you would have a little more water descend into the cup, you must, with a pipe or otherwise, draw the water out of the cup, to give passage to the air in the glass; upon which, part of the water will fall into the glass till it has stopped up the passage of the air afresh, in which case no more will come down; or, without sucking out the water in the cup, you may incline the cup and glass so that the water in the cup shall quit one side of the brim of the glass, and so give passage to the air, which will then suffer the water in the glass to descend till the passage is stopped again.

This may likewise be resolved by covering the brim of the glass that is full of water, with a leaf of strong paper, and then turn the glass as above; and without holding your hand any longer upon the paper, you will find it as it were glued for some time to the brim of the glass, and during that time the water will be kept in the glass.

_The Mysterious Watch._

Desire any person to lend you his watch, and ask if he thinks it will or will not go when it is laid on the table: if he says it will, place it over the end of a magnet, and it will presently stop; then mark with chalk, or a pencil, the precise point where you placed the watch, and, moving the position of the magnet, give the watch to another person, and desire him to make the experiment; in which he not succeeding, give it to a third person, at the same time replacing the magnet, and he will immediately perform the experiment.

_To make a Glass of Water appear to boil and sparkle._

Take a glass nearly full of water, or other liquor, and setting one hand upon the foot of it to hold it fast, turn slightly one of the fingers of your other hand upon the brim or edge of the glass, (having before privately wet your finger,) and so passing softly on, with your finger pressing a little, then the glass will begin to make a noise, the parts of the glass will sensibly appear to tremble with notable rarefaction and condensation, the water will shake, seem to boil, cast itself out of the glass, and leap out by small drops, to the great astonishment of the observers, if they are ignorant of the cause, which is only the rarefaction of the parts of the glass, occasioned by the motion and pressure of the finger.

_How to make a Cork fly out of a Bottle._

Put a little chalk or pounded marble into a phial, and pour on some water, with about a third part of sulphuric acid, and put in a cork: in a few seconds, the cork will be sent off with great violence.

_To produce Gas Light, on a small Scale._

Take an ordinary tobacco pipe, and nearly fill the bowl with small coals, and stop the mouth of the bowl with any suitable luting, as pipe-clay, or the mixture of sand and common clay, or, as clay is apt to shrink, of sand and beer, and place the bowl in a fire between the bars of a grate, so that the pipe may stand nearly perpendicular. In a few minutes, if the luting be good, the gas will begin to escape from the stem of the pipe, when, if a piece of lighted paper or candle be applied, it will take fire and burn for several minutes with an intense light. When the light goes out, a residuum of useful products will be found in the bowl.

_Thunder Powder._

Take separately, three parts of good dry saltpetre, two parts of dry salt of tartar, and pound them well together in a mortar; then add thereto one part, or rather more, of flour of brimstone, and take care to pound and mix the whole perfectly together: put this composition into a bottle with a glass stopper, for use.

Put about two drams of this mixture in an iron spoon, over a moderate fire, but not in the flame; in a short time it will melt, and go off with an explosion like thunder or a loaded cannon.

_To tell, by the Dial of a Watch, at what hour any Person intends to rise._

Let the person set the hand of the dial to any hour he pleases, and tell you what hour that is, and to the number of that hour you add, in your mind, 12. After this, tell him to call the hour the index stands at that which he has fixed upon; and by reckoning backwards from this number to the former, it will bring him to the hour required.

EXAMPLE.

Suppose the hour at which he intends to rise be 8, and that he has placed the hand at 5.

Then, adding 12 to 5, you bid him call the hour at which the index stands, the number on which he thought; and by reckoning back from this number to 17, it will bring him to 8, the hour required.

_The following Experiment shews the Power of Attraction._

If we take two pieces of lead, as two musket or pistol balls, and with a knife smooth two plane surfaces, and press them together, they will firmly adhere.

Two plates of metal made very smooth, when rubbed with oil and put together, will so firmly adhere, that it will require a great force to separate them.

If two pieces of wood, or of glass, be wetted with water, and placed together, the one may be lifted up by means of the other. Boys often have a piece of leather on the end of a string, which they wet and put on a stone, and thereby lift it up.

If we take a small tube of glass with a narrow bore, and put it in water, the fluid will rise higher within the tube than in the vessel. The narrower the tube is, the higher the water rises. This is called Capillary Attraction. If we put two pieces of glass together, and place the lower edge in water, it will rise between them, as it does in the capillary tubes. This experiment may be made more pleasing, by putting a shilling or a piece of paper between the two pieces of glass at one end. The water will then rise in a curve line, called an hyperbola, higher and higher as it recedes from the shilling or piece of paper, and the pieces of glass get nearer to each other.

Place a balance equally poised, so that one scale may be made to touch water in a vessel; considerable weight must be put in the other scale, to make it rise up. Put three or four bits of cork to float in a basin of water; they will gradually draw nearer to each other, and the more rapidly as the distance diminishes.

_Experiments to shew the Power of Repulsion._

Dip a ball in oil and put it in water; a ditch will be formed all round it. Pour water on oiled paper, and it will run off.

Sprinkle water on a dusty floor, it rolls over it in globules. Sprinkle it upon a floor that has been swept, and this will not be the case, as it then comes in contact with the wood, and is diffused over it.

We may observe that rain water stands in globules on the leaves of cabbages. If we blow up soap-bubbles, and let them fall on the carpet, they will not for some time burst. Let them fall on the table, or any smooth surface, and they will burst instantly.

If we pour as much water into a cup as it will possibly hold, we shall see the water above the level of the sides, if the edge be dry, but otherwise we shall not.

Lay a very fine needle, or a piece of tinfoil, on the surface of water, and it will float, until it become wet, when it sinks.

Lay a piece of gold on mercury, and it will float on the surface; but if depressed below the surface, it will sink to the bottom, like the needle on water.

_Experiments respecting the Centre of Gravity._

The centre of gravity is that part of a body, round which all its parts are so equally balanced, that, if it be supported, the whole body will be so too.

Take a book, and find, by trial, under what part the finger must be placed to keep the book from falling; that point is the centre of gravity.

Take a rod, or stick, and find that place about the middle of it, under which the finger being placed, it will be balanced; that is the centre of gravity. The moment the centre of gravity ceases to be supported, the whole body falls.

Move a piece of board to the edge of a table, and gradually farther and farther off it; the instant the centre of gravity gets beyond the edge of the table, the board falls.

Run the point of a knife much slanting into the same board, it may then be brought much farther over the edge of the table than it could before, as the knife, leaning the way of the table, brings the centre of gravity that way.

Take a bottle, with a cork in it; stick in the middle of the cork a needle, with the point, upwards; then take another cork, and with a knife make a slit in one of its ends, in which place a shilling so far as to make it fast; then take two forks, or penknives, and stick one on each side the cork, slanting a little downwards; then place the edge of the shilling on the point of the needle, and it will rest secure. It may be made to revolve, with great rapidity, on the point of the needle, without falling off.

_The following Experiment shews the Power of Steam._

Put a little water in a bottle, and cork it securely, covering it with sealing wax; then put the bottle into a kettle of water, and let it boil a short time, and the steam will force out the cork.

_Diminution of Heat by Evaporation._

Pour water on a piece of writing-paper, and hold it over a candle; it will boil without burning the paper.

Water may be boiled in an egg-shell on the fire.

_Experiment to ascertain the Strength of Spirits of Wine._

It is a common practice for apothecaries, in order to ascertain if spirit of wine be sufficiently strong, to pour some into a cup upon some gunpowder, and then to set fire to it. If the spirit be sufficiently strong, after burning down to the gunpowder, it will make it go off; but if too much water has been poured in, that will not take place, as, after the spirit is consumed, there will still be water enough to keep the powder wet.

_To ascertain the Strength of Brine._

To ascertain the strength of brine for salting meat, it is usual to put an egg in the boiling water, and gradually put in salt until the egg be made to swim.

_The following Experiments shew the Pressure and Elasticity of Air._

Put an empty bottle with a cork in it near the fire; the cork will be driven out.

Get a vessel of hot water, and put a phial into it, with the mouth downwards; the expanded air will bubble out. Let the water cool, or pour cold water on the phial, of which the mouth has not been drawn above the surface of the water, and as the air is now cooled, and occupies less space, a considerable part of the bottle will be filled with water.

Boil a little water in a glass phial over a candle for a few minutes; then invert the mouth of the phial in water, and, as it cools, the air will contract, and water will be forced up the bottle, by the external air, to occupy the vacant space.

Lay a weighty book on a bladder, and blow into it with a pipe, and the book will be raised. Increase the weight on the bladder very much indeed, and you may still raise it as before.

A bladder filled with air may be compressed, and the moment the force is removed, it will recover its size. If thrown on the ground it will rise like a ball.

Take a cup, and burn a few pieces of paper in it, the heat will expand the air in it. Invert the cup now in a saucer of water, and, as the enclosed air cools, it will return to its former density, and leave a vacuum, and the pressure of the external air will force a great deal of water up into the cup. If this experiment be performed with a large drinking-glass, the water may be seen to rise in the glass.

The pressure of the air may be very sensibly felt, by putting the hole of a common bellows over the knee, and then attempting to raise the upper part of it.

Boil water in a glass phial over a candle for a few minutes, then suddenly removing it, tie a piece of wetted bladder over the mouth, making it fast with a string; the pressure of the air will stretch the bladder, if it do not burst it.

Get a glass vessel, as a common tumbler, if no better be at hand, and put a piece of wetted bladder over the mouth, pressing it down in the middle, and then tie it firm with a string; then lay hold of the bladder in the middle, and try to pull it straight, or level with the rest, and the pressure of the external air will not permit it.

Do exactly the same as before, except that the vessel must be nearly full of water. Turn the vessel upside-down, and the bladder will still continue as it was placed, the pressure of the air overcoming the weight of the water.

Though air be capable of compression, it makes a resistance, and that very considerable. The ball of an air-gun has been burst asunder by overcharging it. If bottles are filled too much, they may be burst in attempting to cork them, from the air between the cork and the liquor being too much condensed.