stand at the same level in both. Fig. 6 therefore seems to illustrate the same principle as Fig. 5-the water in the pipe a balancing the whole mass in b.

3. Ida. I now understand what has always been a mystery to me: I mean the experiment with the hydrostatic bellows, where a boy can raise himself, as shown in the figure in this book, by standing on a bellows, and pouring water into the small tube which is connected with it.

Mr. M. What is the statement in the case there given?

4. Ida. It is stated that the water in the small pipe, or tube, having a vertical height of three feet, and a surface area of one inch, will balance a column in the bellows, with which it is connected, of the same height, and of any area, however great. In the case here represented, as the bellows has an area of two feet, the water in the small pipe, weighing a little more than a pound and a quarter, will support a column of water in the bellows of two square feet in area and three feet in height, or a weight of about three hundred and seventy-four pounds. 5. Mr. M. Very well. Now let me ask George a question. If a tightly-fitting piston should be inserted in the top of the small pipe, and a man weighing one hundred and fifty times as much as the water in the pipe should get on the top of the piston, what additional amount of upward pressure do you suppose he would thereby exert on the top board of the bellows?

Fig. 7, the Hydro

static Bellows.

6. George. Evidently, from the principle stated, he would exert an additional pressure of one hundred and fifty times three hundred and seventy-four pounds, which would be equal to fifty-six thousand and one hundred pounds, or a little more than twenty-eight tons! This certainly beats the power of the levers which I planned for pulling up stumps!

Ida. And it is stated that if the area of the bellows were ten times greater, or the force applied to the piston ten times greater, a weight ten times heavier would be raised on the bellows!

7. Frank. I do not see any limit to the power of a machine constructed on this principle; for if the area of the top of the bellows were one thousand feet instead of two feet, the power of this same machine, with the weight of the man on the piston, would be equal to a pressure of more than fourteen thousand tons!

8. George. Yes; and if the small tube were no bigger than a pipe-stem, the bellows would sustain just as great a weight. Mr. M. There is, indeed, no limit to the power of such a machine, except the strength of the material of which it is made.

John. Was the press used by Mr. Stephenson in raising the tubes of the Britannia Bridge, which weighed fifteen hundred tons each, constructed on this principle?

9. Mr. M. Yes. Mr. Stephenson had presses made which weighed forty tons each. The cast-iron of the cylinders was eleven inches thick; and it was estimated that if one of these presses were used as a forcing-pump, it would be capable of throwing water, in a vacuum, five and a half miles high.

10. Frank. Was it necessary to make the cylinders so thick?

Mr. M. Thick as they were, one of them suddenly burst, throwing off a piece of iron weighing a ton and a half.

Ida. I do not wonder this is reckoned one of the most powerful existing machines, and that when Mr. Brunel had to launch the Great Eastern, weighing twelve thousand tons, he resorted to the hydraulic press.

11. Mr. M. Mr. Brunel used a large number of these powerful presses; and so great was the pressure put upon them that the water was forced through the pores of the thick iron cylinders, and stood like dew on the outside.

George. And I recollect that some of the men standing near said those presses had to work so hard that it made them sweat.

12. John. As the power of this hydraulic press is so tremendous, why is it not used to propel machinery?

Mr. M. I think you yourself could answer that question if you would refer to the principle illustrated in the Lessons on Mechanical Powers in the Fourth Reader. You there learned that, in all machinery, "what is gained in power is lost in velocity." If a pressure of one pound exerted on a piston placed in the small tube, in Fig. 7, should press the piston down one foot, and exert a pressure of a thousand pounds on the top board of the bellows, how much would it raise the board?

13. John. I understand now the application of the principle; for it is very evident that a downward movement of the piston to the extent of one foot would result in an upward movement of the top board of the bellows of only the thousandth part of a foot!

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

compensa

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

Fig. 10.

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 Jason' 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?

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

a

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 experiment. 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 to the ball.

A

specific gravity.

B

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