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.
[Illustration: 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?
CONVERSATION III.
ON THE LAWS OF MOTION.
OF MOTION. OF THE INERTIA OF BODIES. OF FORCE TO PRODUCE MOTION.
DIRECTION OF MOTION. VELOCITY, ABSOLUTE AND RELATIVE. UNIFORM MOTION.
RETARDED MOTION. ACCELERATED MOTION. VELOCITY OF FALLING BODIES.
MOMENTUM. ACTION AND REACTION EQUAL. ELASTICITY OF BODIES. POROSITY OF
BODIES. REFLECTED MOTION. ANGLES OF INCIDENCE AND REFLECTION.
MRS. B.
The science of mechanics is founded on the laws of motion; it will
therefore be necessary to make you acquainted with these laws before we
examine the mechanical powers. Tell me, Caroline, what do you understand
by the word motion?
_Caroline._ I think I understand it perfectly, though I am at a loss to
describe it. Motion is the act of moving about, of going from one place
to another, it is the contrary of remaining at rest.
_Mrs. B._ Very well. Motion then consists in a change of place; a body
is in motion whenever it is changing its situation with regard to a
fixed point.
Now since we have observed that one of the general properties of bodies
is inertia, that is, an entire passiveness, either with regard to
motion or rest, it follows that a body cannot move without being put
into motion; the power which puts a body into motion is called _force_;
thus the stroke of the hammer is the force which drives the nail; the
pulling of the horse that which draws the carriage, &c. Force then is
the cause which produces motion.