thousand times eight inches, or about half a mile; when it is plain that the variation must be as much as the earth's radius, or four thousand miles instead of half a mile! a wonderful difference.

Mr. M. I think Frank must see that he is mistaken.

9. Frank. I am very sure it was so stated in the Philosophy I studied, but I see it can not be right.

Mr. M. The distance the straight line varies from the curve may be found, for short distances, by multiplying the square of the distance in miles by eight inches. Now can Frank tell the deviation for two miles?

10. Frank. The square of two is four; and four, multiplied by eight, gives thirty-two inches, which must be the deviation for two miles.

Mr. M. You have now given a correct reply. If John's eye had been six feet above the surface of the ice of the lake, he could have seen just three miles, as you will find by reversing the process I gave you. Will John show how to do it?

11. John. Six feet are seventy-two inches, which, divided by eight, gives nine for a quotient, and the square root of nine is three, which is miles.

Mr. M. As you may have occasion to put such calculations into practice, I would request you to notice that the difference between the true and apparent level varies as the square of the distance for any distance that can occur in leveling.

12. Ida. I think the engineers of the Erie Canal must have had occasion to put that rule into practice when they gave the levels to the workmen who constructed it.

Mr. M. I am glad so important a matter can be so interesting to you. Are you aware that water will rise to the same level when in different vessels which have a communicating pipe between them?

John. I have often seen such a result. Is not that the principle on which water is distributed in cities?

13. Mr. M. In most of our large cities, water is conveyed into the upper stories of houses by this very principle. Water will rise to the level of its source, whether the pipes are of cast iron or porous strata of the earth. In this way water is obtained in many places by boring wells two thousand feet or more in depth. The water which fell as rain on some distant mountain, and which was slowly making its subterranean way hundreds of feet below the surface, rises where an opening is made to supply the necessities of man on the otherwise arid plain.

14. George. Are not these called Artesian wells? I have read of several recently bored in the Sahara Desert.

Mr. M. The inhabitants of the oases where these wells have been bored were wild with delight and wonder as they saw the water rush forth from the dry sands; and they have given them such names as "the well of bliss," "the well of gratitude," etc.

15. John. I do not wonder the wandering tribes of the B desert believed that the French, who bored the wells, had wrought a miracle. To them it was a miracle; but to us, only water rising to its level, as we see every day in a tea-kettle.

Fig. 2.

16. Ida. I have just read a verse from Eliza Cook's poems which I will repeat:

"Traverse the desert, and then ye can tell
What treasures exist in the cold deep well;
Sink in despair on the red parched earth,

And then ye may reckon what water is worth."

17. Mr. M. It is thought that these wells will work a great social revolution in those regions. The various tribes, instead of wandering, like their ancestors, from one place to another, will settle around these fertilizing springs, and begin to cultivate the earth even in those sandy deserts. Artesian wells have been bored in Charleston, S. C., St. Louis, Mo., Columbus, O., La Fayette, Ind., Louisville, Ky., and many other places in this country. In Alabama they are of incalculable value, and are very numerous on plantations and in villages. 18. The annexed cut of a vertical section of the earth's crust shows the principle of the Artesian well.

The stratum A, and the one below it, are impervious to water, but between them is a fissure or seam along which the water penetrates from the lake on the hills. Wells are bored

in the valley through which the water rises with great force as soon as the boring enters the fissure between the strata. The water may be carried up in pipes to the very level of the lake.

Mr. M. In our next lesson I hope to finish what we shall have to say on Hydrostatics.

1 STAT'-ICS, from the Greek statike (OTаTIKN), 2 HY-DRO-STAT'-ICS, from the Greek hudor "rest," or "stand still :" the science which treats of the forces which keep bodies at rest, or in equilibrium.

(Yowp), "water," and statike: the science which treats of the properties and pressure of fluids at rest.

LESSON III.-HYDROSTATICS- Continued.

1. "I WILL introduce the subject for this lesson," said Mr. M., "by showing you one of the ways in which an ignorant contriver tried to obtain a constant flow of water-a kind of perpetual B motion-by means of a vessel like this.

"He reasoned thus: A pound of water in A must more than balance an ounce in B, and must therefore be constantly pushing the ounce forward into A again, thus causing a constant flow of water in continuous current. Fig. 5, an ounce of wa- What think you of his success?" ter balances a pound. 2. Ella. I think he found the water to rise no higher in B than in A.

Mr. M. You think correctly. You must see that as the downward pressure in B is equal to that in A, the pressure of water is by no means as the mass, but as the vertical height of the fluid.

George. I have been reading about this hydrostatic paradox-how any quantity of water, however small, may balance any quantity, however great. I think I see how it is, as the tube may be very small, and the vessel with which it Fig. 6, the water in communicates very large, and the water will

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!