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Example I: Multiply

Double the order is Add Multiply by...

Add..

Number for left hand 2 Multiply by...... 45-95-45100-552-55101 570 Number of finger.. 5 575 Multiply by...... 10 5750 Number of joint .. 2 5752 Add. 35 Subtract 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 1 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 ir 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 364 tons, reckoning a ton 2,000 pounds, that being the weight of a ton of sea-water; if the cargo of this ship exceeds 36½ 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 or 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 inven tion; 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 tor 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 tself 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 & 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 per pendicular 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 5 N 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.