LETTER XVIII.
ATMOSPHERIC PRESSURE.
When we have been laboring very hard, my dear child, and want to rest for a minute, we say, Let us take breath; because breathing is an action which takes place of itself, requiring neither effort nor attention on our part.
But, if it takes place of itself, it does not explain itself; consequently, when I say to you, Now, let us take breath, this is not a signal for my having a rest, for I have undertaken to explain Respiration to you.
If you were a German, I would remind you of what so often happens when you put a fork into a dish of sour-krout. You want to lay hold of a little bit merely, but the strips of cabbage-leaf are twisted one within the other, and hang together in spite of you, so that withoutintending it you get hold of a whole plateful at once.
Now this Respiration affair is something like the sour-krout story—begging your pardon for the comparison. I should have liked to give you only a small plateful—a child's plateful—of it; but I feel the explanations coming, hanging one upon the other; and, whether I will or no, I must treat you like a grown-up person, and we must give up for once the nice little doll's dinners with which we began.
In my opinion, you will lose nothing by the change if you will but pay attention; for about that soft little breath of yours, which is always coming and going over your pretty lips, there are many more things to be learnt than you have heard of yet. As I said just now, you will find you have got hold of a plateful all at once. A good appetite to you!
To prevent confusion we will divide the subject into two parts. I shall explain to you first, How we breathe?—a very curious question, as you will see. And afterwards we will examine, Why we breathe?—which is still more interesting.
First, I must tell you that air is heavy, and very heavy too; a thousand times more so than you may suppose. The air we breathe, through which we move backwards and forwards, that air is _some_thing, remember, although we do not see it; and when there is a wind, that is to say, when the air is in motion, like a stream of water running down a hill, we are forced to acknowledge its being something, for we see it throw down the largest trees and carry along the biggest ships. But without going so far out of the way for examples, try—you who run so well—to run for two minutes against a strong wind: and then you shall tell me whether the air is something or nothing. But if it be something it must have weight, for all substances have; paper as well as lead; with this sole difference, that the weight of lead is greater in proportion to its size than that of paper. Now a sheet of paper is very light, is it not? and you would be puzzled perhaps to say what it weighs. But many sheets of paper placed one upon the other, end by forming a thick book which has its undeniable weight; and if some one were to heap upon your head a pile of large books, like those you see on your papa's shelves, the end might be that you would be crushed to death.
In the same way, a small amount of air is by no means heavy; but you can conceive that a great quantity of it gathered together may end by weighing a great deal. Now get well into your head the fact, that we, here, on the surface of the earth, are at the bottom of an immense mass of air, extending to somewhere about forty or fifty miles above our heads. Let us say forty to make more sure, for learned men have not yet been able to calculate the precise height to a nicety; and for my own part, I think we have done wonders to get so near the mark even as this. But can you picture to yourself the distance which forty miles high really is? I will help you to form some idea.
One mile contains 5,280 feet, and your papa is six feet high. One mile high would therefore be 880 times as high as your papa, But this is a mere nothing—only one mile's height. In forty miles there would be no less than 211,200 feet; and setting papas aside, of whom it would take 35,200, one on the top of the other, to go so far into the sky, let us think of the height of the tallest buildings you know; church and cathedral towers for instance. Now the towers of many parish churches are 150 feet high; the towers of York Minister not 300. At that rate it would take 1,408 ordinary parish church-towers, or upwards of 704 York Minster towers, piled one above the other, to reach to the end of the forty miles of air above our heads. I leave you to judge what would be the weight of a mass of paper piled up as high as that. You may safely grant then, that this mass or pile, or if you like it better, this column of air (for that is the proper expression), must be of considerable weight; as is still further made certain by the fact of its having been weighed, so that I can even name the weight to you if you wish to hear it. Bear in mind too, that the weight of a column of air will be in proportion to its superficial extent—to its breadth and width, that is; for, as you may suppose, a column as large in extent as one of the towers of York Minster will weigh a good deal more than one the size of a single brick.
But wait; here is a book on the table which will serve me for a measure, and as you will probably find the same on your mamma's table, you can follow my measurement. It is a French Grammar. The back is seven inches long and four and a quarter wide. That is, there are four and a quarter rows, each seven inches long. In other words, the back contains nearly—and let us call it quite, for convenience' sake—thirty inches side by side. Thirty square inches as it is called. Measure your mamma's copy and you will see. Now, can you guess the weight of the column of air forty miles high which this volume supports? Upwards of four cwt.; 450 lbs., that is to say. If you want to be very exact, here is the rule. Air presses on all bodies at the rate of fifteen pounds to every square inch; so now you can make the calculation for yourself.
But I suspect you had no idea you were so strong; for I see you tossing up the book, heavily laden as it is, like a feather.
Comfort yourself. There is no magic in the matter. If a very strong man were to push you on one side, could you resist him? Certainly not. But if another man of equal strength were to push you at the same time on the other side, what would happen? Well, you would remain quietly in your place, without troubling yourself more about one than the other, the two forces mutually destroying each other. And this is the case here. While the air above your book is weighing down upon it with a force of 450 lbs., the air below it presses against it underneath with an equal weight, and this destroys the effect of the other. From 450 lbs. take 450 lbs., and nothing remains. Your grammar has nothing to carry after all, and you may toss it about as you please, without deserving much credit for the effort.
"What are you telling me?" you inquire. "If I put a stone on the top of my head, I can feel its weight easily enough; but if I put my hand on the top of the stone I no longer feel anything. How can the air below the stone press against it? And talking of columns—how pleasant it would be, for instance, if the people who go up the Monument were to have the weight of it on their heads when they get to the top!"
Well said, little one. And your objection reminds me of an argument which distracted my head as a lad, when I first heard the pressure of air explained by a good fellow who did not trouble himself to be quite as exact as you and I are in our discussions. I was told that the surface of the body, or the skin of a large man, measured sixteen feet square, which is equal to the surface of a table four feet long and four broad. Now, you know that in four feet there are forty-eight inches, and on the surface of the table are forty-eight rows, with forty-eight inches in each, or 2,304 square inches; so that a man's surface is 2,304 square inches, and the weight his body supports is 34,560 lbs., or upwards of fifteen tons—always at the rate of fifteen pounds to every square inch, you understand. Now, I was constantly asking myself how it happened that in entering a house one never seemed to get rid of this almost fabulous weight, since the roof of the house must naturally interpose itself between the air-column of forty miles high and the man who would then only have some few feet of air above his head. The roof would support the rest, that was clear. From whence, then, came the 34,560 lbs. which seemed to weigh as heavily as before; since, whether on the threshold of the door, while still under shelter of the roof, or two steps outside in the open air, under the tremendous column forty miles high, one never felt a bit lighter, not even to the extent of the weight of a single sheet of paper? This was a difficulty from which I could never extricate myself.
I found out the answer to the riddle afterwards, and a very simple one it is.
Air does not, in point of fact, weigh down like a solid fifty pounds' weight, which has no impulse but to descend, and has nothing to do with anything above it. It presses against rather, like a spring, which, having been compressed, tries to resume its natural position with a force equal to that which holds it back. Ask some one to show you the spring of a watch, and you will understand this better. Each atom of air is a spring of matchless elasticity, which nothing can break, which never wears out, which one can always compress, if one employs force sufficient, and which is always ready to expand indefinitely, in proportion as the compressing power is withdrawn.
Now, consider the column of air outside the door, where there is a pile of such springs forty miles high. The lower ones have to bear up all their comrades, which press upon them with their united weight, and these make desperate efforts to repulse the tremendous pressure, and to spread out in their turn. They endeavor to escape in every direction—to the right, to the left, above, below; but caught between the earth, which will not give way, and the compact mass of all the columns of air which surrounds the earth in every direction, and of which the lower part is equally compressed everywhere, they struggle unceasingly, but in vain; indefatigable, but powerless. You live in the midst of those little wrestlers, and naturally bear the punishment of the injury done to them. They press against you as against every thing else—before, behind, on all sides—with a force equal to thatwith which they are themselves compressed, or I would say, equal to the weight by which they are so horribly squeezed and contracted: so that, in fact, you bear this weight not only on your head and shoulders, as you might at first suppose, but also all along your body and limbs, under your arms, under your chin, in the hollow of your nostrils, everywhere.
Now we will suppose you to enter the house; and what do you find there? Outer air, which on its part has got in by the door, the window, and every little crevice in the wall. The column outside the roof no longer presses upon it, but what is the gain of that?
It was compressed when it got in, and the little springs will struggle as a matter of course, quite as much on this side of the door as on the other. The protecting roof has so little power that were it not itself protected by the air outside, the pressure of which keeps it in its place, the air within would shiver it into a thousand fragments in its efforts to get loose.
You laugh; but wait till I explain myself further. I will take the case of a miniature house to make the matter pleasanter to you; one fifteen feet long, fifteen feet wide, and with a flat roof, the most economical plan as regards space. Fifteen feet are five yards, and as the multiplication table tells us that five times five make twenty-five, our roof will in this case be twenty-five square yards (i. e. 225 square feet) in superficial extent, or area; it is not much, and you will find few as small.
Would you like to calculate the force with which the millions and thousand millions of little spring imps imprisoned under that poor unfortunate roof would press against it? We settled before that the quantity of them brought to bear upon a square inch had the power to push at the rate of fifteen pounds. Were they to push against a square yard (a surface 1296 times greater than the square inch) it would therefore be 19,440 lbs. This being so for one square yard, calculate for twenty-five square yards, and you will have the amount of pressure against our roof—viz. 486,000 lbs—merely that! And now tell me what cottage roof in the world was ever built so as to be able to stand against such a weight?
Perhaps though, you can scarcely appreciate the amount of heaviness, 486,000 lbs. Well, 486,000 lbs. is nearly 217 tons; and one of those railway trucks that you see laden with coals at the stations can carry, perhaps, from eight to ten tons, without breaking down. Say ten tons as an outside estimate, and then think of piling the contents of twenty-one such trucks on your roof, and yet you would still be short of the weight of air which is bearing down upon it. I need scarcely say now that were you to take away the air from within the roof, theair without would smash both it and the whole cottage flat, as a giant at a fair strikes an egg flat with one blow of his fist. To show you how in another way: take a moderate sized column or pillar, such as you see sometimes in a nobleman's grounds, of about the weight of the twenty-one tons, and set it up like a chimney on the roof of our cottage, then walk away to a little distance and watch what will happen!
There, little Miss Laugher! have you at last learned to value the weight of the air, or atmospheric pressure as it is more properly called; since it is the force with which the atmosphere presses against rather than weighs upon everything on the surface of the globe? It is no joke, as you perceive, and it affords plenty of subject forreflection. I have still to prove to you that I have not been making fun of you with my calculations, and that the weight of air upon a square inch is really what I have said—viz., fifteen pounds.
Now, there is a very simple way by which we might get to know your strength, and tell its amount in figures, if one chose; namely, by putting a weight on your arms—a heap of books, if you please—and keep adding and adding to it, until those poor little arms were unable to bear any more. Then weighing what they had borne, whether we should find it to be ten or thirty pounds—I cannot guess how much it might be at this distance—one might safely say, without fear of mistake, "The strength of this young lady is equal to ten, twenty, or thirty pounds"—in other words, "she represents a weight of ten, twenty, or thirty pounds" and by a similar plan people have ascertained the strength of the air—that is, the weight which it represents. They have weighed what it is capable of carrying.
I told you lately that the whole surface of the earth was covered by an immense army of little imps—otherwise called little air-springs, which, compressed by the giant mass of their comrades above, all of whom they have to carry on their backs, are always trying to protect themselves, by pushing back everything which comes across them. Imagine the bottom of a well. Our imps are permanently installed there as a matter of course, and face to face with the water they push against it, each one doing his best, on all points at once. As the pressure is equal everywhere therefore, and always the same, there are no signs of it to be seen.
Now insert in the water the end of a tube closed below by a cork which exactly fits the interior, but which can be moved up and down in the tube by means of a bar of iron or wood which runs through it. This is called a piston, I may as well tell you as we go on.
When the piston rises in the tube, it drives before it, as it goes, the air which was already there; and which cannot slip away down the sides because the piston fits so closely to them all the way along. The result of this is, that just underneath the piston there is a place in the water to which the air cannot reach, and at that place the water has no pressure upon it at all.
Now see what happens. Pressed upon heavily by the air in every other part and place, like a mouse hunted by a cat, who finds at last a hole through which to escape, the poor water darts at this and ascends the tube close after the piston.
So far so good; but if the tube is very long, and the piston rises rather high;—at thirty-three or thirty-four feet above the level of the water it has to continue its ascent alone. The water parts company, stopping quietly behind, half-way up the tube.
"What is the meaning of this?" you will ask.
It means that the force which presses on the well-water all round the tube, and thus drives it up, has done all it can, and that our little air-imps refuse to supply any more. The water which rises in the tube has a weight of its own of course, and with this weight it presses, as it is fair it should, on the water below. In proportion as the piston rises, the column of water which follows it gets bigger and bigger, and naturally its weight increases at the same time. At last there comes a moment when this weight becomes such that its pressure on the water below is equal to that with which the air-imps are pressing on the water in the well. Thenceforth they may push as they please; no more water will go up. They are in the same position now that they were before, when their comrades (afterwards driven out by the piston) were pressing upon the same point, which had only a moment's freedom; and this water column of thirty-three or thirty-four feet holds them in check, to exactly the same extent as the gay fellows whose place it has taken.
Nothing is easier now than to calculate, even to a few grains almost, the force of the pressure of air. One can get at the weight of water, thank goodness! and it has been ascertained that our water-column will weigh fifteen pounds if the tube is a square inch in size. You will comprehend after this that it might be any size you may please to imagine, without there being the slightest alteration in the height of the column. The larger it is, the heavier will be the column of water on the one hand; but on the other, the greater will be the number of air-imps turned out; so it comes to the same thing in the end.
If you should feel any doubt about the correctness of this reasoning, you have only to try the experiment over again, in a well, filled with mercury for instance. Ask to be shown some pure mercury, which is also called Quicksilver, because one wants to express melted silver, apt to be constantly on the move; it is often to be met with in houses. Mercury weighs thirteen and a half times more than water: according to our calculations, therefore, it would take thirteen and a half times less of it than of water to bring our little air-imps to reason. And this is just what you will find happens; you will see the column of mercury stop short exactly at the moment when it has attained the orthodox weight of fifteen pounds; that is to say, at a height of twenty-eight inches.
On the other hand, take some ether. You know that delicate spirit, which smells so strong, which makes your hand feel cold if it is put upon it, and which we give to sick people to inhale. Ether weighs one-quarter less than water. In a well of ether you would therefore see something quite different, and your column would rise without being asked, to something like forty-three feet, exactly up to the point of weighing—like the others—fifteen pounds to every square inch. Air will not be replaced with less.
That, then, is the measure of its strength, or our scales are deceitful.