Читать книгу Conversations on Natural Philosophy, in which the Elements of that Science are Familiarly Explained - Thomas P. Jones - Страница 6

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ATTRACTION OF GRAVITATION, CONTINUED. OF WEIGHT. OF THE FALL OF BODIES. OF THE RESISTANCE OF THE AIR. OF THE ASCENT OF LIGHT BODIES.

EMILY.

I have related to my sister Caroline all that you have taught me of natural philosophy, and she has been so much delighted by it, that she hopes you will have the goodness to admit her to your lessons.

Mrs. B. Very willingly; but I did not think you had any taste for studies of this nature, Caroline.

Caroline. I confess, Mrs. B., that hitherto I had formed no very agreeable idea either of philosophy, or philosophers; but what Emily has told me has excited my curiosity so much, that I shall be highly pleased if you will allow me to become one of your pupils.

Mrs. B. I fear that I shall not find you so tractable a scholar as Emily; I know that you are much biased in favour of your own opinions.

Caroline. Then you will have the greater merit in reforming them, Mrs. B.; and after all the wonders that Emily has related to me, I think I stand but little chance against you and your attractions.

Mrs. B. You will, I doubt not, advance a number of objections; but these I shall willingly admit, as they will afford an opportunity of elucidating the subject. Emily, do you recollect the names of the general properties of bodies?

Emily. Impenetrability, extension, figure, divisibility, inertia and attraction.

Mrs. B. Very well. You must remember that these are properties common to all bodies, and of which they cannot be deprived; all other properties of bodies are called accidental, because they depend on the relation or connexion of one body to another.

Caroline. Yet surely, Mrs. B., there are other properties which are essential to bodies, besides those you have enumerated. Colour and weight, for instance, are common to all bodies, and do not arise from their connexion with each other, but exist in the bodies themselves; these, therefore, cannot be accidental qualities?

Mrs. B. I beg your pardon; these properties do not exist in bodies independently of their connexion with other bodies.

Caroline. What! have bodies no weight? Does not this table weigh heavier than this book; and, if one thing weighs heavier than another, must there not be such a thing as weight?

Mrs. B. No doubt: but this property does not appear to be essential to bodies; it depends upon their connexion with each other. Weight is an effect of the power of attraction, without which the table and the book would have no weight whatever.

Emily. I think I understand you; it is the attraction of gravity which makes bodies heavy.

Mrs. B. You are right. I told you that the attraction of gravity was proportioned to the quantity of matter which bodies contain: now the earth consisting of a much greater quantity of matter than any body upon its surface, the force of its attraction must necessarily be greatest, and must draw every thing so situated towards it; in consequence of which, bodies that are unsupported fall to the ground, whilst those that are supported, press upon the object which prevents their fall, with a weight equal to the force with which they gravitate towards the earth.

Caroline. The same cause then which occasions the fall of bodies, produces their weight also. It was very dull in me not to understand this before, as it is the natural and necessary consequence of attraction; but the idea that bodies were not really heavy of themselves, appeared to me quite incomprehensible. But, Mrs. B., if attraction is a property essential to matter, weight must be so likewise; for how can one exist without the other?

Mrs. B. Suppose there were but one body existing in universal space, what would its weight be?

Caroline. That would depend upon its size; or more accurately speaking, upon the quantity of matter it contained.

Emily. No, no; the body would have no weight, whatever were its size; because nothing would attract it. Am I not right, Mrs. B.?

Mrs. B. You are: you must allow, therefore, that it would be possible for attraction to exist without weight; for each of the particles of which the body was composed, would possess the power of attraction; but they could exert it only amongst themselves; the whole mass having nothing to attract, or to be attracted by, would have no weight.

Caroline. I am now well satisfied that weight is not essential to the existence of bodies; but what have you to object to colours, Mrs. B.; you will not, I think, deny that they really exist in the bodies themselves.

Mrs. B. When we come to treat of the subject of colours, I trust that I shall be able to convince you, that colours are likewise accidental qualities, quite distinct from the bodies to which they appear to belong.

Caroline. Oh do pray explain it to us now, I am so very curious to know how that is possible.

Mrs. B. Unless we proceed with some degree of order and method, you will in the end find yourself but little the wiser for all you learn. Let us therefore go on regularly, and make ourselves well acquainted with the general properties of bodies before we proceed further.

Emily. To return, then, to attraction, (which appears to me by far the most interesting of them, since it belongs equally to all kinds of matter,) it must be mutual between two bodies; and if so, when a stone falls to the earth, the earth should rise part of the way to meet the stone?

Mrs. B. Certainly; but you must recollect that the force of attraction is proportioned to the quantity of matter which bodies contain, and if you consider the difference there is in that respect, between a stone and the earth, you will not be surprised that you do not perceive the earth rise to meet the stone; for though it is true that a mutual attraction takes place between the earth and the stone, that of the latter is so very small in comparison to that of the former, as to render its effect insensible.

Emily. But since attraction is proportioned to the quantity of matter which bodies contain, why do not the hills attract the houses and churches towards them?

Caroline. What an idea, Emily! How can the houses and churches be moved, when they are so firmly fixed in the ground!

Mrs. B. Emily's question is not absurd, and your answer, Caroline, is perfectly just; but can you tell us why the houses and churches are so firmly fixed in the ground?

Caroline. I am afraid I have answered right by mere chance; for I begin to suspect that bricklayers and carpenters could give but little stability to their buildings, without the aid of attraction.

Mrs. B. It is certainly the cohesive attraction between the bricks and the mortar, which enables them to build walls, and these are so strongly attracted by the earth, as to resist every other impulse; otherwise they would necessarily move towards the hills and the mountains; but the lesser force must yield to the greater. There are, however, some circumstances in which the attraction of a large body has sensibly counteracted that of the earth. If whilst standing on the declivity of a mountain, you hold a plumb-line in your hand, the weight will not fall perpendicular to the earth, but incline a little towards the mountain; and this is owing to the lateral, or sideways attraction of the mountain, interfering with the perpendicular attraction of the earth.

Emily. But the size of a mountain is very trifling, compared to the whole earth.

Mrs. B. Attraction, you must recollect, is in proportion to the quantity of matter, and although that of the mountain, is much less than that of the earth, it may yet be sufficient to act sensibly upon the plumb-line which is so near to it.

Caroline. Pray, Mrs. B., do the two scales of a balance hang parallel to each other?

Mrs. B. You mean, I suppose, in other words to inquire whether two lines which are perpendicular to the earth, are parallel to each other? I believe I guess the reason of your question; but I wish you would endeavour to answer it without my assistance.

Caroline. I was thinking that such lines must both tend by gravity to the same point, the centre of the earth; now lines tending to the same point cannot be parallel, as parallel lines are always at an equal distance from each other, and would never meet.

Mrs. B. Very well explained; you see now the use of your knowledge of parallel lines: had you been ignorant of their properties, you could not have drawn such a conclusion. This may enable you to form an idea of the great advantage to be derived even from a slight knowledge of geometry, in the study of natural philosophy; and if after I have made you acquainted with the first elements, you should be tempted to pursue the study, I would advise you to prepare yourselves by acquiring some knowledge of geometry. This science would teach you that lines which fall perpendicular to the surface of a sphere cannot be parallel, because they would all meet, if prolonged to the centre of the sphere; while lines that fall perpendicular to a plane or flat surface, are always parallel, because if prolonged, they would never meet.

Emily. And yet a pair of scales, hanging perpendicular to the earth, appear parallel?

Mrs. B. Because the sphere is so large, and the scales consequently converge so little, that their inclination is not perceptible to our senses; if we could construct a pair of scales whose beam would extend several degrees, their convergence would be very obvious; but as this cannot be accomplished, let us draw a small figure of the earth, and then we may make a pair of scales of the proportion we please. (fig. 1. pl. I.)

Caroline. This figure renders it very clear: then two bodies cannot fall to the earth in parallel lines?

Mrs. B. Never.

Caroline. The reason that a heavy body falls quicker than a light one, is, I suppose, because the earth attracts it more strongly.

Mrs. B. The earth, it is true, attracts a heavy body more than a light one; but that would not make the one fall quicker than the other.

Caroline. Yet, since it is attraction that occasions the fall of bodies, surely the more a body is attracted, the more rapidly it will fall. Besides, experience proves it to be so. Do we not every day see heavy bodies fall quickly, and light bodies slowly?

Emily. It strikes me, as it does Caroline, that as attraction is proportioned to the quantity of matter, the earth must necessarily attract a body which contains a great quantity more strongly, and therefore bring it to the ground sooner than one consisting of a smaller quantity.

Mrs. B. You must consider, that if heavy bodies are attracted more strongly than light ones, they require more attraction to make them fall. Remember that bodies have no natural tendency to fall, any more than to rise, or to move laterally, and that they will not fall unless impelled by some force; now this force must be proportioned to the quantity of matter it has to move: a body consisting of 1000 particles of matter, for instance, requires ten times as much attraction to bring it to the ground in the same space of time as a body consisting of only 100 particles.

Plate i.

Caroline. I do not understand that; for it seems to me, that the heavier a body is, the move easily and readily it falls.

Emily. I think I now comprehend it; let me try if I can explain it to Caroline. Suppose that I draw towards me two weighty bodies, the one of 100 lbs. the other of 1000 lbs. must I not exert ten times as much strength to draw the larger one to me, in the same space of time, as is required for the smaller one? And if the earth draws a body of 1000 lbs. weight to it in the same space of time that it draws a body of 100 lbs. does it not follow that it attracts the body of 1000 lbs. weight with ten times the force that it does that of 100 lbs.?

Caroline. I comprehend your reasoning perfectly; but if it were so, the body of 1000 lbs. weight, and that of 100 lbs. would fall with the same rapidity; and the consequence would be, that all bodies, whether light or heavy, being at an equal distance from the ground, would fall to it in the same space of time: now it is very evident that this conclusion is absurd; experience every instant contradicts it; observe how much sooner this book reaches the floor than this sheet of paper, when I let them drop together.

Emily. That is an objection I cannot answer. I must refer it to you, Mrs. B.

Mrs. B. I trust that we shall not find it insurmountable. It is true that, according to the laws of attraction, all bodies at an equal distance from the earth, should fall to it in the same space of time; and this would actually take place if no obstacle intervened to impede their fall. But bodies fall through the air, and it is the resistance of the air which makes bodies of different density fall with different degrees of velocity. They must all force their way through the air, but dense heavy bodies overcome this obstacle more easily than rarer or lighter ones; because in the same space they contain more gravitating particles.

The resistance which the air opposes to the fall of bodies is proportioned to their surface, not to their weight; the air being inert, cannot exert a greater force to support the weight of a cannon ball, than it does to support the weight of a ball (of the same size) made of leather; but the cannon ball will overcome this resistance more easily, and fall to the ground, consequently, quicker than the leather ball.

Caroline. This is very clear and solves the difficulty perfectly. The air offers the same resistance to a bit of lead and a bit of feather of the same size; yet the one seems to meet with no obstruction in its fall, whilst the other is evidently resisted and supported for some time by the air.

Emily. The larger the surface of a body, then, the more air it covers, and the greater is the resistance it meets with from it.

Mrs. B. Certainly: observe the manner in which this sheet of paper falls; it floats awhile in the air, and then gently descends to the ground. I will roll the same piece of paper up into a ball: it offers now but a small surface to the air, and encounters therefore but little resistance: see how much more rapidly it falls.

The heaviest bodies may be made to float awhile in the air, by making the extent of their surface counterbalance their weight. Here is some gold, which is one of the most dense bodies we are acquainted with; but it has been beaten into a very thin leaf, and offers so great an extent of surface in proportion to its weight, that its fall, you see, is still more retarded by the resistance of the air, than that of the sheet of paper.

Caroline. That is very curious: and it is, I suppose, upon the same principle that a thin slate sinks in water more slowly than a round stone.

But, Mrs. B., if the air is a real body, is it not also subjected to the laws of gravity?

Mrs. B. Undoubtedly.

Caroline. Then why does it not, like all other bodies, fall to the ground?

Mrs. B. On account of its spring or elasticity. The air is an elastic fluid; and the peculiar property of elastic bodies is to resume, after compression, their original dimensions; and you must consider the air of which the atmosphere is composed as existing in a state of compression, for its particles being drawn towards the earth by gravity, are brought closer together than they would otherwise be, but the spring or elasticity of the air by which it endeavours to resist compression, gives it a constant tendency to expand itself, so as to resume the dimensions it would naturally have, if not under the influence of gravity. The air may therefore be said constantly to struggle with the power of gravity without being able to overcome it. Gravity thus confines the air to the regions of our globe, whilst its elasticity prevents it from falling, like other bodies, to the ground.

Emily. The air then is, I suppose, thicker, or I should rather say more dense, near the surface of the earth, than in the higher regions of the atmosphere; for that part of the air which is nearer the surface of the earth must be most strongly attracted.

Mrs. B. The diminution of the force of gravity, at so small a distance as that to which the atmosphere extends (compared with the size of the earth) is so inconsiderable as to be scarcely sensible; but the pressure of the upper parts of the atmosphere on those beneath, renders the air near the surface of the earth much more dense than in the upper regions. The pressure of the atmosphere has been compared to that of a pile of fleeces of wool, in which the lower fleeces are pressed together by the weight of those above; these lie light and loose, in proportion as they approach the uppermost fleece, which receives no external pressure, and is confined merely by the force of its own gravity.

Emily. I do not understand how it is that the air can be springy or elastic, as the particles of which it is composed must, according to the general law, attract each other; yet their elasticity, must arise from a tendency to recede from each other.

Mrs. B. Have you forgotten what I told you respecting the effects of heat, a fluid so subtile that it readily pervades all substances, and even in solid bodies, counteracts the attraction of cohesion? In air the quantity of heat interposed is so great, as to cause its particles actually to repel each other, and it is to this that we must ascribe its elasticity; this, however, does not prevent the earth from exerting its attraction upon the individual particles of which it consists.

Caroline. It has just occurred to me that there are some bodies which do not gravitate towards the earth. Smoke and steam, for instance, rise instead of falling.

Mrs. B. It is still gravity which produces their ascent; at least, were that power destroyed, these bodies would not rise.

Caroline. I shall be out of conceit with gravity, if it is so inconsistent in its operations.

Mrs. B. There is no difficulty in reconciling this apparent inconsistency of effect. The air near the earth is heavier than smoke, steam, or other vapours; it consequently not only supports these light bodies, but forces them to rise, till they reach a part of the atmosphere, the weight of which is not greater than their own, and then they remain stationary. Look at this bason of water; why does the piece of paper which I throw into it float on the surface?

Emily. Because, being lighter than the water, it is supported by it.

Mrs. B. And now that I pour more water into the bason, why does the paper rise?

Emily. The water being heavier than the paper, gets beneath it, and obliges it to rise.

Mrs. B. In a similar manner are smoke and vapour forced upwards by the air; but these bodies do not, like the paper, ascend to the surface of the fluid, because, as we observed before, the air being less dense, and consequently lighter as it is more distant from the earth, vapours rise only till they attain a region of air of their own density. Smoke, indeed ascends but a very little way; it consists of minute particles of fuel, carried up by a current of heated air, from the fire below: heat, you recollect, expands all bodies; it consequently rarefies air, and renders it lighter than the colder air of the atmosphere; the heated air from the fire carries up with it vapour and small particles of the combustible materials which are burning in the fire. When this current of hot air is cooled by mixing with the atmosphere, the minute particles of coal, or other combustible, fall; it is this which produces the small black flakes which render the air, and every thing in contact with it, in London, so dirty.

Caroline. You must, however, allow me to make one more objection to the universal gravity of bodies; which is the ascent of air balloons, the materials of which are undoubtedly heavier than air: how, therefore, can they be supported by it?

Mrs. B. I admit that the materials of which balloons are made are heavier than the air; but the air with which they are filled is an elastic fluid, of a different nature from atmospheric air, and considerably lighter; so that on the whole the balloon is lighter than the air which it displaces, and consequently will rise, on the same principle as smoke and vapour. Now, Emily, let me hear if you can explain how the gravity of bodies is modified by the effect of the air?

Emily. The air forces bodies which are lighter than itself to ascend; those that are of an equal weight will remain stationary in it; and those that are heavier will descend through it: but the air will have some effect on these last; for if they are not much heavier, they will with difficulty overcome the resistance they meet with in passing through it, they will be borne up by it, and their fall will be more or less retarded.

Mrs. B. Very well. Observe how slowly this light feather falls to the ground, while a heavier body, like this marble, overcomes the resistance which the air makes to its descent much more easily, and its fall is proportionally more rapid. I now throw a pebble into this tub of water; it does not reach the bottom near so soon as if there were no water in the tub, because it meets with resistance from the water. Suppose that we could empty the tub, not only of water, but of air also, the pebble would then fall quicker still, as it would in that case meet with no resistance at all to counteract its gravity.

Thus you see that it is not the different degrees of gravity, but the resistance of the air, which prevents bodies of different weight from falling with equal velocities; if the air did not bear up the feather, it would reach the ground as soon as the marble.

Caroline. I make no doubt that it is so; and yet I do not feel quite satisfied. I wish there was any place void of air, in which the experiment could be made.

Mrs. B. If that proof will satisfy your doubts, I can give it you. Here is a machine called an air pump, (fig. 2. pl. 1.) by means of which the air may be expelled from any close vessel which is placed over this opening, through which the air is pumped out. Glasses of various shapes, usually called receivers, are employed for this purpose. We shall now exhaust the air from this tall receiver which is placed over the opening, and we shall find that bodies within it, whatever their weight or size, will fall from the top to the bottom in the same space of time.

Caroline. Oh, I shall be delighted with this experiment; what a curious machine! how can you put the two bodies of different weight within the glass, without admitting the air?

Mrs. B. A guinea and a feather are already placed there for the purpose of the experiment: here is, you see, a contrivance to fasten them in the upper part of the glass; as soon as the air is pumped out, I shall turn this little screw, by which means the brass plates which support them will be removed, and the two bodies will fall.—Now I believe I have pretty well exhausted the air.

Caroline. Pray let me turn the screw.—I declare, they both reached the bottom at the same instant! Did you see, Emily, the feather appeared as heavy as the guinea?

Emily. Exactly; and fell just as quickly. How wonderful this is! what a number of entertaining experiments might be made with this machine!

Mrs. B. No doubt there are a great many; but we shall reserve them to elucidate the subjects to which they relate: if I had not explained to you why the guinea, and the feather fell with equal velocity, you would not have been so well pleased with the experiment.

Emily. I should have been as much surprised, but not so much interested; besides, experiments help to imprint on the memory the facts they are intended to illustrate; it will be better therefore for us to restrain our curiosity, and wait for other experiments in their proper places.

Caroline. Pray by what means is this receiver exhausted of its air?

Mrs. B. You must learn something of mechanics in order to understand the construction of a pump. At our next meeting, therefore, I shall endeavour to make you acquainted with the laws of motion, as an introduction to that subject.

Questions

1.(Pg. 22) What are those properties of bodies called, which are not common to all?

2.(Pg. 23) Why are they so called?

3.(Pg. 23) What is the cause of weight in bodies?

4.(Pg. 23) What is the reason that all bodies near to the surface of the earth, are drawn towards it?

5.(Pg. 24) If attraction is the cause of weight, could you suppose it possible for a body to possess the former and not the latter property?

6.(Pg. 24) When a stone falls to the ground, in which of the two bodies does the power of attraction exist?

7.(Pg. 24) If the attraction be mutual, why does not the earth approach the stone, as much as the stone approaches the earth?

8.(Pg. 24) If attraction be in proportion to the mass, why does not a hill, draw towards itself, a house placed near it?

9.(Pg. 25) How can the attraction of a mountain be rendered sensible?

10.(Pg. 25) Why cannot two lines which are perpendicular to the surface of the earth be parallel to each other?

11.(Pg. 26) Draw a small figure of the earth to exemplify this, as in fig. 1. plate 1.

12.(Pg. 27) If bodies were not resisted by the air, those which are light, would fall as quickly as those which are heavy, how can you account for this?

13.(Pg. 27) What then is the reason that a book, and a sheet of paper, let fall from the same height, will not reach the ground in the same time?

14.(Pg. 28) What then will be the effect of increasing the surface of a body?

15.(Pg. 28) What could you do to a sheet of paper, to make it fall quickly, and why?

16.(Pg. 28) Inform me how a very dense body may be made to float in the air?

17.(Pg. 28) The air is a real body, why does it not fall to the ground?

18.(Pg. 29) The air is more dense near the surface of the earth, and decreases in density as you ascend, how is this accounted for, and to what is it compared?

19.(Pg. 29) What is it which causes the particles of air to recede from each other, and seems to destroy their mutual attraction?

20.(Pg. 29) Smoke and vapour ascend in the atmosphere, how can you reconcile this with gravitation?

21.(Pg. 30) How would you illustrate this by the floating of a piece of paper on water?

22.(Pg. 30) Does smoke rise to a great height in the air, and if not, what prevents its so doing?

23.(Pg. 30) What limits the height to which vapours rise?

24.(Pg. 30) Of what does smoke consist?

25.(Pg. 30) Air balloons are formed of heavy materials, how will you account for their rising in the air?

26.(Pg. 30) What influence does the air exert, on bodies less dense than itself, on those of equal, and on those of greater density?

27.(Pg. 31) If the air could be entirely removed, what influence would this have upon the falling of heavy and light bodies?

28.(Pg. 31) How could this be exemplified by means of the air pump?