Ella. How beautifully this illustrates the law of compensation which is said to pervade all nature!*

14. John. Does it not appear, from the principles already illustrated, that the pressure of a column of water is proportionate to its height and base?

Mr. M. Yes; its vertical height. If we fill with water a small vertical tube, twenty-four feet in height, and having the horizontal area of its orifice equal to one square inch, it is very plain that the water will press upon the base or bottom with its own weight, which is a little more than ten pounds. But if the base be enlarged, so that the water shall then cover an area of ten square feet, what will the pressure be on the entire base?

15. George. I think I can tell, for the principle has already

been explained. We shall get the entire pressure by multiplying the entire area of the base that is, its whole number of square inches-by the pressure on one square inch.

John. I have made the calculation; and I find the pressure on the entire base would be fourteen thousand and four hundred pounds, or more than seven tons!

Ella. I see, by the diagram, Fig. 9, that all the water in the vessel need not weigh more than twelve Fig. 9. pounds; how then is it possible that it can press on the bottom of the vessel with a force of more than seven tons? 16. Mr. M. And yet, strange as it may appear, such is the fact; the pressure of the water in the vessel is the same in all directions, upward as well as downward; it is the same on every square inch; and if the vessel could not yield any without breaking, it would require a very strong material to

The hydraulic press, as used for practical purposes (as for pressing bales of cotton, etc.), is illustrated in the accompanying figure. It is connected with a forcing-pump, which raises the water from the reservoir H, and then forces it through the tube K into the large cylinder B. Here the water acts to M raise the large piston P. If the area of the base of the small piston is a square inch in diameter, and the area of the base of the large piston P is one thousand square inches, then a downward pressure of one pound on the one will exert an upward pressure of one thousand pounds on the other. But it must be recollected that the small piston must move downward through the space of a thousand inches, while the large piston rises only one inch. By means of this machine cotton is pressed into bales, ships are raised for repairs, chain-cables are tested, etc., etc..

withstand the pressure. But you can see that a very little yielding of the top or bottom of the vessel would lower the water in the tube so as greatly to relieve the pressure. Yet if the vessel should yield, by continuing to pour water into the tube, a very strong vessel might thus be broken.

17. George. I now recollect seeing statements of the bursting of hills, and even of mountains, by the force of the water which had accumulated within them. Was this on the principle of the hydrostatic pressure which we have been considering?

Mr. M. It was. In mountainous regions this principle is

Fig. 10.

sometimes exhibited on a grand scale, and whole villages have been buried by these hidden powers of nature. This diagram will illustrate the principle.

18. Ella. But the channel which leads to the basin of water in the mountain is not vertical. Does this make any difference? Mr. M. When this is the case, the pressure is estimated by the vertical distance from the level at the top to the basin. But I see our time is exhausted. In conclusion, however, I will state the rule (the principle of which you have already discovered) for the pressure of fluids. It is this:

Multiply the area of the base, in feet, by the perpendicular depth of the water, and this product by the weight of a cubic foot of water: or the numbers may be inches throughout.*

LESSON IV.-FLOATING BODIES-SPECIFIC GRAVITY.

1. "As Master Frank was so much interested in boats during his vacation," said Mr. Maynard, "I suppose he will feel a corresponding interest in the theory of their flotation." Frank. I hope I have not shown any want of interest in

The accompanying diagram well illustrates the principle of hydrostatic pressure. Here are five vessels, differing in shape, but equal in capacity. The pressure of the water upon the

Fig. 11, the pressure is as the height multiplied by bottom of each is found by multiply

the base.

ing the vertical height by the extent of surface of its base, thereby indicating different amounts of pressure. The weight of a cubic inch of water, of the common temperature of 62 degrees, is a portion of a pound expressed by the decimal 0.036065. The pressure of a column of water one foot high, having a square inch for its base, will be twelve times this, or, 0.4328 lb. The pressure, therefore, produced upon a square foot by a column one foot high, will be found by multiplying this last number by 144, and will be 62.3232 lbs.

previous lessons; but I confess that this is to me an entertaining subject.

2. Mr. M. Ever since Jason1 built the Argo, the theory of floating bodies has been a most entertaining and important study. The poet Horace said that mortal's heart was cased

"In oak or brass, with triple fold,
Who first to the wild ocean's rage
Launched the frail bark."

3. Ida. Frank must have been very brave to have dared the raging waves of the harbor in his "frail bark." I confess I never get into a small boat without fear, but I hope to learn something in this lesson that will give me more confidence when on the water.

4. Mr. M. Have you thought of the conditions under which a body will float or sink?

ier.

Frank. It will float if lighter than water, and sink if heav

Mr. M. That is very true; but it is necessary to understand that a floating body displaces a quantity of water equivalent in weight to the body itself, as may be proved by ex

A

periment. Let the vessel A be filled with water till it runs out of the spout; if you then place on the surface of the water a wooden ball, a quantity of water will flow out, which will weigh the same as the ball. If an iron ball had been used, the water Fig. 12, the principle of overflowing would have been equal in bulk

specific gravity.

B

to the ball.

5. John. Would not that be a convenient way to measure the solidity of an irregular body, as a fragment of stone? George. It would be an excellent way to detect a counterfeit gold coin.

Ella. I would like to find a method of detecting spurious gold money. Do explain it.

6. George. Counterfeit gold coins are either too large or too light. If too light, the common balance will show it; but if too large, the quantity of water displaced will be more than if genuine. This can be carefully measured in a small glass.

Mr. M. This brings us directly to the subject of specific gravity. Can either of you give a concise definition of specific gravity?

7. John. I have learned from the book on Natural Philosophy which I have been studying, that the specific gravity of

a body is its weight, compared with the weight of an equal bulk of pure water-water being taken as a standard.

Mr. M. Can you tell me, then, how the specific gravity of a solid heavier than water is ascertained?

8. George. Weigh it first in air, and then in water. Divide the weight in air by the loss in water, the quotient will be the specific gravity of the body. Thus, if a solid weigh twenty pounds in the air and eighteen pounds in water, its specific gravity is ten; that is, it is ten times heavier than water.

Ida. Is it of much use to find the specific gravity of bodies? 9. Mr. M. I will give you an example of its use, and let you judge for yourself of its importance. I have heard you express a doubt as to the value of the silver cup you obtained as a prize at the Union Seminary. As it becomes tarnished so easily, you fear it is not real silver. If it is alloyed, it will probably be lighter than standard silver, which has a specific gravity of 10.47; that is, silver is nearly ten and a half times heavier than water. Can either of you find the specific gravity of the cup which Ida has gone to bring for examination?

10. John. Now I have the cup I will carefully weigh it. It weighs five and ahalf ounces in the air. I will now suspend it by a thread in water, and find how much less it will weigh. It has lost ten and a half pennyweights. I find, by dividing the weight in air by the loss in Fig. 13, to find the specific water, that the specific gravity of the cup is 10.47, which shows it to be made of

B

gravity of a solid.

A

standard silver.

Ida. I am glad my suspicions were unfounded; and now I recollect they were first suggested by one of the disappointed competitors.

I

11. Mr. M. It is a pity we have no way to remove your new suspicions of the motive of your rival. have here a chain, bought for gold, which by chemical tests shows copper in its composition. It weighs two ounces, or forty pennyweights, in air, and thirtyseven pennyweights in water, from which I find the copper to be about three eighths of the whole weight. Fig. 14, the There is a very convenient instrument, called the hydrometer, for finding the specific gravity of liquids.

Hydrom

eter.

The hydrometer, figure 14, consists of a hollow ball, B, with a long, slender, graduated stem, A D; and the ball is so loaded by a weight, C, that the stem will stand upright in water. The lighter the fluid, the greater the depth to which the hydrometer will sink.

Who can give me an account of the manner in which the principle of specific gravity was first discovered?

12. Ida. I have purposely brought a book containing an account of the discovery, which, with your permission, I will read. The article is entitled

ARCHIMEDES AND THE CROWN.

"King Hiero of Syracuse, or his son Gelon, it seems, had given out a certain amount of gold to be made into a crown, and the workman to whom it had been intrusted had at last brought back a crown of corresponding weight. But a suspicion arose that it had been alloyed with silver, and Archimedes was applied to by the king either to disprove or to verify the allegation. The great problem, of course, was to ascertain the precise bulk of the crown in its existing form; for, gold being so much heavier than silver, it is obvious that if the weight had been in any degree made up by the substitution of silver, the bulk would be proportionately increased. Now it happened that Archimedes went to take a bath while this problem was exercising his mind, and, on approaching the bath-tub, he found it full to the very brim. It instantly occurred to him that a quantity of water of the same bulk with his own body must be displaced before his body could be immersed.

13. "Accordingly, he plunged in; and while the process of displacement was going on, and the water was running out, the idea suggested itself to him that, by putting a lump of gold of the exact weight of the crown into a vessel full of water, and then measuring the water which was displaced by it, and by afterward putting the crown itself into the same vessel after it had again been filled, and then measuring the water which this, too, should have displaced, the difference in their respective bulks, however minute, would be at once detected, and the fraud exposed. 'As soon as he had hit upon this method of detection,' we are told, he did not wait a moment, but jumped joyfully out of the bath, and, running toward his own house, called out with a loud voice that he had found what he had sought. For, as he ran, he called out in Greek, "Eureka, Eureka!" "I have found it, I have found it."'

14. "No wonder that this veteran geometer, rushing through the thronged and splendid streets of Syracuse, and making the welkin ring with his triumphant shouts-no wonder that he should have rendered the phrase, if not the guise, in which he announced his success, familiar to all the world, and that Eureka, Eureka,' should thus have become the proverbial ejaculation of successful invention and discovery in all ages and in all languages, from that day to this! The solution of this problem is supposed to have led the old philosopher not merely into this ecstatical exhibition of himself, but into that line of hydrostatical investigation and experiment which afterward secured him such lasting renown. And thus the accidents of a defective crown and an overflowing bath-tub gave occasion to some of the most remarkable demonstrations of ancient science."

15. "That account," said Mr. M.," which I perceive you have taken from a lecture of the Hon. Robert C. Winthrop on The scale should be so graduated that when the hydrometer is immersed in pure water at the standard temperature, it may sink to the point which is marked 1. Then, when the hydrometer is immersed in any other liquid, the figure on the scale to which it sinks will show the specific gravity of that liquid. When the quantity of liquid is too small to float the hydrometer, other methods are used.