J. A. COOLIDGE

We saw in our last chapter that every solid sub-stance, when floating or immersed in a liquid, lost part or all of its weight, and that in bodies capable of floating, the shapes could be made such that additional weights could be carried. In this paper it is our purpose to study the buoyant effect of liquids on bodies that will cink, and to see whether this knowledge will

Fig. 26

Fig. 2 7

be of any practical value. In beginning we wi6h to find the exact relation between the buoyancy of the liquid and the substance immersed in it. Experiment XXIII. A cylindrical piece of curtain pole, 4 in. long and 2 in. in diameter, with a hole \ in. diameter bored in the centre of one end to within 1/4 inch of the other, will serve our purpose. Put enough lead shot or scraps of lead in this hole to make the cylinder sink in water, fit a wooden plug in the open end and soak the whole cylinder in melted paraffine so that it shall not absorb water. Weigh it carefully, and with a pair of calipers get its diameter as accurately as possible. The volume of the cylinder, radius x radius x 3 1-7 x length we must next find. It should be needless to say that the radius is one-half of the diameter and that the volume is equal to the base, radius x radius x 3 1-7, multiplied by the length. Next hang the cylinder by a thread and weigh it immersed in a jar of water. See Fig. 27. The buoyancy of the water is found by subtracting the weight in water from the weight in air. The weight of an equal volume of water is found by multiplying the volume expressed in cubic inches by .58. This will give the number of ounces of water displaced by the cylinder. When we compare this with the loss of weight just found we see that they are the same, and if the experiment should be performed with some other liquid than water, the same principle will be found true; that is, that the amount of loss of a body in any liquid is equal to the weight of the displaced liquid. The discovery of this made Archimedes famous in history and the word, eureka, well known to all. The story of King Hiero and the crown that he feared was not true gold, and how Archimedes proved that the king had been deceived, is a tale of interest to old and young. '

Experiment XXIV. Having studied this principle we are now prepared to examine a number of different substances and to compare them. Get a piece of coal, of glass, marble, lead, iron, zinc and, if possible, aluminum; weigh these in air and then in water, hanging them by a thread, as you did the cylinder in Fig. 27. The loss of each in water is equal to the weight of the displaced water. Is it not a simple matter to compare each with the weight of the same volume of water and then with another substance? For instance, our marble weighs 8.1 ounces in air and 5.1 ounces in water. The loss is 3 ounces, therefore three ounces is the weight of a body of water equal in volume to the marble. 'The ratio of the marble, 8.1, to the water, 3, gives us 2.7. We know that marble is 2.7 times as heavy as water. This ratio of a substance to the equal volume of water is called the specific gravity of that substance. Let us find the specific gravity of coal, glass, lead, iron, zinc, aluminum and others, and arrange as in the table below:

 Substance Wt. in air. Wt. in water. Loss. Sp. Gr. Marble 8.1 5.1 3 2.7 Coal Lead

Of all the substances we have seen, gold is the heaviest, having a specific gravity of over 19. Lead is heavier than iron, and aluminum is the lightest of all the metals. Many metals are seldom used in a pure state but are mixed with some other metal (or alloy) to make them harder, stronger, more brittle or more elastic. Gold coins are not of pure gold but are mixed with copper to make them harder. The statement that gold is 18 k, means that 18 parts are gold and 6 parts copper. It can be seen that one might tell the purity of a metal if one knew its specific gravity.

Fig. 28

Fig. 29

The finding of the specific gravity of woods and other bodies that float gives a little more trouble, as the shapes are often irregular, and as the body floats we must adopt some other means of finding the weight of the displaced liquid.

Experiment XXV.

Given an irregular piece of wood; find the specific gravity. Weigh it first and call its weight W. Take a piece of stone and weigh that in air, calling the result S, and in water, calling the result S'. Find the loss of the sinker. S - S'. Tie the stone to the piece of wood and weigh both in water, as seen in Fig. 28. From the sum of their weights in air take the weight of both tied together in water, and we have the loss of both. From this subtract the loss of the sinker, S-S', and we have the loss of the wood. The weight of the wood divided by this loss will be the specific gravity of wood. This varies much for different woods, being as low as .11 for porous cork, up to .8 and .9 for heavy oak woods and others.

We must now find the specific gravity of liquids. Of the tests made for milk, vinegar, etc., the specific gravity forms a part. There are several ways of finding thi6, but we shall speak of two only. A small bottle with a tightly fitting glass stopple with the exact amount of water it contains marked upon it, and with a brass weight that just balances the empty bottle can be bought. This is filled with a liquid and the weight of the liquid alone obtained at once. This weight divided by the figure on the bottle will give the specific gravity of the liquid.

Experiment XXVI.

Take a small bottle with a tightly fitting glass stopple and find its weight, B. Fill with water and weigh again, calling this T. T - B gives the weight of the water. Fill the bottle with auother liquid and call this L. L - B is the weight of the liquid in the bottle. Divide L by T - B and the quotient will be the specific gravity of that liquid.

Experiment XXVII.

Take a cylindrical wooden rod 1/2 in. in diameter, flatten a lead bullet, or make a thick washer of lead and fasten to one end so that when placed in water it will float erect, as in Fig. 29. A very small elastic band, or thread, around it may be made to serve as a marker. It should be covered with wax to prevent soaking in water. Place it in water, mark the depth it sinks, and call this Dw. Do the same in some other liquid, such as vinegar, oil, or a solution of blue vitriol. Call this depth Dl. As a floating body displaces its own weight, the depths Dw and Dl give amounts of water and the liquid that have the same weight. Suppose those figures were 7.2 in. in water, and 5.4 in. in the liquid; then 5.4 in. of this liquid equals7.2 in. in water, and this liquid is as many times as heavy as water as 5.4 is contained in 7.2, or 1.33. We see that this liquid is 1.33 times as heavy as water. This wooden cylinder might be called a hydrometer, but those in actual use are made of a glass tube with a bulb at the bottom and a scale on the tube. The distance it sinks in water is usually marked 100 on the scale and this is divided by the distance it sinks in other liquids. Many hydrometers are made to suit the needs of special operators and their U6es are very simple.