that time, therefore, at full and at change, she is in the same
direction as the sun; both, then act in conjunction on the earth, and
produce very great tides, called spring tides, as represented in fig. 4,
at A and B; but when the moon is at the intermediate parts of her orbit,
that is in her quadratures, the sun, instead of affording assistance,
weakens her power, by acting in opposition to it; and smaller tides are
produced, called neap tides, as represented at M, in fig. 5.
_Emily._ I have often observed the difference of these tides, when I
have been at the sea side.
But since attraction is mutual between the moon and the earth, we must
produce tides in the moon; and these must be more considerable in
proportion as our planet is larger. And yet the moon does not appear of
an oval form.
_Mrs. B._ You must recollect, that in order to render the explanation of
the tides clearer, we suppose the whole surface of the earth to be
covered with the ocean; but that is not really the case, either with the
earth or the moon, and the land which intersects the water, destroys the
regularity of the effect. Thus, in flowing up rivers, in passing round
points of land, and into bays and inlets, the water is obstructed, and
high water must happen much later, than would otherwise be the case.
_Caroline._ True; we may, however, be certain that whenever it is high
water, the moon is immediately over our heads.
_Mrs. B._ Not so either; for as a similar effect is produced on that
part of the globe immediately beneath the moon, and on that part most
distant from it, it cannot be over the heads of the inhabitants of both
those situations, at the same time. Besides, as the orbit of the moon is
very nearly parallel to that of the earth, she is never vertical, but to
the inhabitants of the torrid zone.
_Caroline._ In the torrid zone, then, I hope you will grant that the
moon is immediately over, or opposite the spots where it is high water?
_Mrs. B._ I cannot even admit that; for the ocean naturally partaking of
the earth's motion, in its rotation from west to east, the moon, in
forming a tide, has to contend against the eastern motion of the waves.
All matter, you know, by its inertia, makes some resistance to a change
of state; the waters, therefore, do not readily yield to the attraction
of the moon, and the effect of her influence is not complete, till three
hours after she has passed the meridian, where it is full tide.
When a body is impelled by any force, its motion may continue, after the
impelling force ceases to act: this is the case with all projectiles. A
stone thrown from the hand, continues its motion for a length of time,
proportioned to the force given to it: there is a perfect analogy
between this effect, and the continued rise of the water, after the moon
has passed the meridian at any particular place.
_Emily._ Pray what is the reason that the tide is three-quarters of an
hour later every day?
_Mrs. B._ Because it is twenty-four hours and three-quarters before the
same meridian, on our globe, returns beneath the moon. The earth
revolves on its axis in about twenty-four hours; if the moon were
stationary, therefore, the same part of our globe would, every
twenty-four hours, return beneath the moon; but as during our daily
revolution, the moon advances in her orbit, the earth must make more
than a complete rotation, in order to bring the same meridian opposite
the moon: we are three-quarters of an hour in overtaking her. The tides,
therefore, are retarded, for the same reason that the moon rises later
by three-quarters of an hour, every day.
We have now, I think, concluded the observations I had to make to you on
the subject of astronomy; at our next interview, I shall attempt to
explain to you the elements of hydrostatics.
Questions
1. (Pg. 108) In what time does the moon revolve round the earth? what is
the inclination of her orbit? and how does she accompany the earth?
2. (Pg. 108) As the moon revolves round the earth, and also accompanies
it in its annual revolution, in what form would you draw the moon's
orbit?
3. (Pg. 109) What causes the moon always to present the same face to the
earth, and what must be the length of a day and night to its
inhabitants?
4. (Pg. 109) Can the earth be seen from every part of the moon, and will
it always exhibit the same appearance?
5. (Pg. 109) What are the changes of the moon called?
6. (Pg. 109) How are these changes explained by fig. 2. plate 11?
7. (Pg. 109) What is meant by her first quarter?
8. (Pg. 109) What by her being horned, and her being gibbous?
9. (Pg. 109) What by her being full?
10. (Pg. 109) What by her third quarter?
11. (Pg. 110) What is meant by her conjunction?--what by her being in
opposition?--what by her quadratures?
12. (Pg. 110) By what are eclipses of the sun caused?
13. (Pg. 110) What causes eclipses of the moon?
14. (Pg. 110) What is meant by the moon's nodes?
15. (Pg. 110) Why do not eclipses happen at every new and full moon?
16. (Pg. 110) What causes partial eclipses of the moon?
17. (Pg. 110) When the moon is exactly in one of her nodes, what length
of time will she be eclipsed?
18. (Pg. 110) Are total eclipses of the sun frequent, and when they
happen what is their extent?
19. (Pg. 111) What does this prove respecting the size of the moon?
20. (Pg. 111) What is shown in fig. 1, plate 12?
21. (Pg. 111) How are lunar eclipses visible, and what is proved by
their duration?
22. (Pg. 111) What is illustrated by fig. 2, plate 12?
23. (Pg. 111) What remark is made respecting those planets which have
several moons?
24. (Pg. 111) What use is made of the eclipses of the satellites of
Jupiter?
25. (Pg. 112) How is the latitude of a place usually found?
26. (Pg. 112) By what other means may latitude be found?
27. (Pg. 112) From what is longitude reckoned?
28. (Pg. 112) How does the rotation of the earth upon its axis, govern
the time at different places?
29. (Pg. 113) What two circumstances, if known, will enable you to find
your longitude from a given place?
30. (Pg. 113) By what means may a captain find the time at London, and
in the place where his ship may be?
31. (Pg. 113) How may the eclipses of Jupiter's satellites be used to
find the longitude?
32. (Pg. 113) Give an example.
33. (Pg. 114) How will you know whether the longitude is east or west?
34. (Pg. 114) What is meant by the transit of a planet?
35. (Pg. 114) Why can we see transits of Venus and Mercury only?
36. (Pg. 114) By what are tides caused?
37. (Pg. 114) Why is not a similar effect produced on the land?
38. (Pg. 115) In what two parts of the world is it high water at the
same time?
39. (Pg. 115) What circumstances respecting the decrease of attraction
are taken into account, in explaining the tides?
40. (Pg. 115) How are the high tides at A and D, and the low ones at B
and C, in fig. 3. pl. 12, accounted for?
41. (Pg. 116) Has the sun any influence on the tides, and why is it less
than that of the moon?
42. (Pg. 116) What is meant by spring tides, and how are they produced?
43. (Pg. 116) What by neap tides, and how are they caused?
44. (Pg. 116) What circumstances affect the time of the tide in rivers,
bays, &c.?
45. (Pg. 117) Why in the open ocean, is it high water, some hours after
the moon has passed the meridian?
46. (Pg. 117) Why are the tides three-quarters of an hour later every
day?
CONVERSATION X.
ON THE MECHANICAL PROPERTIES OF FLUIDS.
DEFINITION OF A FLUID. DISTINCTION BETWEEN FLUIDS AND LIQUIDS. OF
NON-ELASTIC FLUIDS. SCARCELY SUSCEPTIBLE OF COMPRESSION. OF THE COHESION
OF FLUIDS. OF THEIR GRAVITATION. OF THEIR EQUILIBRIUM. OF THEIR
PRESSURE. OF SPECIFIC GRAVITY. OF THE SPECIFIC GRAVITY OF BODIES HEAVIER
THAN WATER. OF THOSE OF THE SAME WEIGHT AS WATER. OF THOSE LIGHTER THAN
WATER. OF THE SPECIFIC GRAVITY OF FLUIDS.
MRS. B.
We have hitherto confined our attention to the mechanical properties of
solid bodies, which have been illustrated, and, I hope, thoroughly
impressed upon your memory, by the conversations we have subsequently
had, on astronomy. It will now be necessary for me to give you some
account of the mechanical properties of fluids--a science which, when
applied to liquids, is divided into two parts, hydrostatics and
hydraulics. Hydrostatics, treats of the weight and pressure of fluids;
and hydraulics, of the motion of fluids, and the effects produced by
this motion. A fluid is a substance which yields to the slightest
pressure. If you dip your hand into a basin of water, you are scarcely
sensible of meeting with any resistance.
_Emily._ The attraction of cohesion is then, I suppose, less powerful in
fluids, than in solids?
_Mrs. B._ Yes; fluids, generally speaking, are bodies of less density
than solids. From the slight cohesion, of the particles of fluids, and
the facility with which they slide over each other, it is inferred, that
they have but a slight attraction for each other, and that this
attraction is equal, in every position of their particles, and therefore
produces no resistance to a perfect freedom of motion among themselves.
_Caroline._ Pray what is the distinction between a fluid and a liquid?
_Mrs. B._ Liquids comprehend only one class of fluids. There is another
class, distinguished by the name of elastic fluids, or gases, which
comprehends the air of the atmosphere, and all the various kinds of air
with which you will become acquainted, when you study chemistry. Their
mechanical properties we shall examine hereafter, and confine our
attention this morning, to those of liquids, or non-elastic fluids.
Water, and liquids in general, are scarcely susceptible of being
compressed, or squeezed into a smaller space, than that which they
naturally occupy. Such, however, is the extreme minuteness of their
particles, that by strong compression, they sometimes force their way
through the pores of the substance which confines them. This was shown
by a celebrated experiment, made at Florence many years ago. A hollow
globe of gold was filled with water, and on its being submitted to great
pressure, the water was seen to exude through the pores of the gold,
which it covered with a fine dew. Many philosophers, however, think that
this experiment is too much relied upon, as it does not appear that it
has ever been repeated; it is possible, therefore, that there may have
been some source of error, which was not discovered by the
experimenters. Fluids, appear to gravitate more freely, than solid
bodies; for the strong cohesive attraction of the particles of the
latter, in some measure counteracts the effect of gravity. In this
table, for instance, the cohesion of the particles of wood, enables four
slender legs to support a considerable weight. Were the cohesion
destroyed, or, in other words, the wood converted into a fluid, no
support could be afforded by the legs, for the particles no longer
cohering together, each would press separately and independently, and
would be brought to a level with the surface of the earth.
_Emily._ This want of cohesion is then the reason why fluids can never
be formed into figures, or maintained in heaps; for though it is true
the wind raises water into waves, they are immediately afterwards
destroyed by gravity, and water always finds its level.
_Mrs. B._ Do you understand what is meant by the level, or equilibrium
of fluids?
_Emily._ I believe I do, though I feel rather at a loss to explain it.
Is not a fluid level when its surface is smooth and flat, as is the case
with all fluids, when in a state of rest?
_Mrs. B._ Smooth, if you please, but not flat; for the definition of the
equilibrium of a fluid is, that every part of the surface is equally
distant from the point to which they gravitate, that is to say, from the
centre of the earth; hence the surface of all fluids must be spherical,
not flat, since they will partake of the spherical form of the globe.
This is very evident in large bodies of water, such as the ocean, but
the sphericity of small bodies of water, is so trifling, that their
surfaces appear flat.
This level, or equilibrium of fluids, is the natural result of their
particles gravitating independently of each other; for when any particle
of a fluid, accidentally finds itself elevated above the rest, it is
attracted down to the level of the surface of the fluid, and the
readiness with which fluids yield to the slightest impression, will
enable the particle by its weight, to penetrate the surface of the
fluid, and mix with it.
_Caroline._ But I have seen a drop of oil, float on the surface of
water, without mixing with it.
_Mrs. B._ They do not mix, because their particles repel each other, and
the oil rises to the surface, because oil is a lighter liquid than
water. If you were to pour water over it, the oil would still rise,
being forced up by the superior gravity of the water. Here is an
instrument called a spirit-level, (fig. 1, plate 13.) which is
constructed upon the principle of the equilibrium of fluids. It consists
of a short tube A B, closed at both ends, and containing a little water,
or more commonly some spirits: it is so nearly filled, as to leave only
a small bubble of air; when the tube is perfectly horizontal, this
bubble will occupy the middle of it, but when not perfectly horizontal,
the water runs to the lower, and the bubble of air or spirit rises to
the upper end; by this instrument, the level of any situation, to which
we apply it, may be ascertained.
From the strong cohesion of their particles, you may therefore consider
solid bodies as gravitating in masses, while every particle of a fluid
may be considered as separate, and gravitating independently of each
other. Hence the resistance of a fluid, is considerably less, than that
of a solid body; for the resistance of the particles, acting separately,
is more easily overcome.
_Emily._ A body of water, in falling, does certainly less injury than a
solid body of the same weight.
_Mrs. B._ The particles of fluids, acting thus independently, press
against each other in every direction, not only downwards, but upwards,
and laterally or sideways; and in consequence of this equality of
pressure, every particle remains at rest, in the fluid. If you agitate
the fluid, you disturb this equality of pressure, and the fluid will
not rest, till its equilibrium is restored.
[Illustration: PLATE XIII.]
_Caroline._ The pressure downwards is very natural; it is the effect of
gravity; one particle, weighing upon another, presses on it; but the
pressure sideways, and particularly the pressure upwards, I cannot
understand.
_Mrs. B._ If there were no lateral pressure, water would not run out of
an opening on the side of a vessel. If you fill a vessel with sand, it
will not continue to run out of such an opening, because there is
scarcely any lateral pressure among its particles.
_Emily._ When water runs out of the side of a vessel, is it not owing to
the weight of the water, above the opening?
_Mrs. B._ If the particles of fluids were arranged in regular columns,
thus, (fig. 2.) there would be no lateral pressure, for when one
particle is perpendicularly above the other, it can only press
downwards; but as it must continually happen, that a particle presses
between two particles beneath, (fig. 3.) these last, must suffer a
lateral pressure.
_Emily._ The same as when a wedge is driven into a piece of wood, and
separates the parts, laterally.
_Mrs. B._ Yes. The lateral pressure proceeds, therefore, entirely from
the pressure downwards, or the weight of the liquid above; and
consequently, the lower the orifice is made in the vessel, the greater
will be the velocity of the water rushing out of it. Here is a vessel of
water (fig. 5.), with three stop cocks at different heights; we shall
open them, and you will see with what different degrees of velocity, the
water issues from them. Do you understand this, Caroline?
_Caroline._ Oh yes. The water from the upper spout, receiving but a
slight pressure, on account of its vicinity to the surface, flows but
gently; the second cock, having a greater weight above it, the water is
forced out with greater velocity, whilst the lowest cock, being near the
bottom of the vessel, receives the pressure of almost the whole body of
water, and rushes out with the greatest impetuosity.
_Mrs. B._ Very well; and you must observe, that as the lateral pressure,
is entirely owing to the pressure downwards, it is not affected by the
horizontal dimensions of the vessel, which contains the water, but
merely by its depth; for as every particle acts independently of the
rest, it is only the column of particles immediately above the orifice,
that can weigh upon, and press out the water.
_Emily._ The breadth and width of the vessel then, can be of no
consequence in this respect. The lateral pressure on one side, in a
cubical vessel, is, I suppose, not so great as the pressure downwards
upon the bottom.
_Mrs. B._ No; in a cubical vessel, the pressure downwards will be double
the lateral pressure on one side; for every particle at the bottom of
the vessel is pressed upon, by a column of the whole depth of the fluid,
whilst the lateral pressure diminishes from the bottom upwards to the
surface, where the particles have no pressure.
_Caroline._ And from whence proceeds the pressure of fluids upwards?
that seems to me the most unaccountable, as it is in direct opposition
to gravity.
_Mrs. B._ And yet it is in consequence of their pressure downwards.
When, for example, you pour water into a tea-pot, the water rises in the
spout, to a level with the water in the pot. The particles of water at
the bottom of the pot, are pressed upon by the particles above them; to
this pressure they will yield, if there is any mode of making way for
the superior particles, and as they cannot descend, they will change
their direction, and rise in the spout.
Suppose the tea-pot to be filled with columns of particles of water,
similar to that described in fig. 4., the particle 1, at the bottom,
will be pressed laterally by the particle 2, and by this pressure be
forced into the spout, where, meeting with the particle 3, it presses it
upwards, and this pressure will be continued from 3 to 4, from 4 to 5,
and so on, till the water in the spout, has risen to a level with that
in the pot.
_Emily._ If it were not for this pressure upwards, forcing the water to
rise in the spout, the equilibrium of the fluid would be destroyed.
_Caroline._ True; but then a tea-pot is wide and large, and the weight
of so great a body of water as the pot will contain, may easily force up
and support so small a quantity, as will fill the spout. But would the
same effect be produced, if the spout and the pot, were of equal
dimensions?
_Mrs. B._ Undoubtedly it would. You may even reverse the experiment, by
pouring water into the spout, and you will find that the water will rise
in the pot, to a level with that in the spout; for the pressure of the
small quantity of water in the spout, will force up and support, the
larger quantity in the pot. In the pressure upwards, as well as that
laterally, you see that the force of pressure, depends entirely on the
height, and is quite independent of the horizontal dimensions of the
fluid.
As a tea-pot is not transparent, let us try the experiment by filling
this large glass goblet, by means of this narrow tube, (fig. 6.)
_Caroline._ Look, Emily, as Mrs. B. fills it, how the water rises in the
goblet, to maintain an equilibrium with that in the tube.
Now, Mrs. B., will you let me fill the tube, by pouring water into the
goblet?
_Mrs. B._ That is impossible. However, you may try the experiment, and I
doubt not that you will be able to account for its failure.
_Caroline._ It is very singular, that if so small a column of water as
is contained in the tube, can force up and support the whole contents of
the goblet; that the weight of all the water in the goblet, should not
be able to force up the small quantity required to fill the tube:--oh, I
see now the reason, the water in the goblet, cannot force that in the
tube above its level, and as the end of the tube, is considerably higher
than the goblet, it can never be filled by pouring water into the
goblet.
_Mrs. B._ And if you continue to pour water into the goblet when it is
full, the water will run over, instead of rising above its level in the
tube.
I shall now explain to you the meaning of the _specific gravity_ of
bodies.
_Caroline._ What! is there another species of gravity, with which we are
not yet acquainted?
_Mrs. B._ No: the specific gravity of a body, means simply its weight,
compared with that of another body, of the same size. When we say, that
substances, such as lead, and stones, are heavy, and that others, such
as paper and feathers, are light, we speak comparatively; that is to
say, that the first are heavy, and the latter light, in comparison with
the generality of substances in nature. Would you call wood, and chalk,
light or heavy bodies?
_Caroline._ Some kinds of wood are heavy, certainly, as oak and
mahogany; others are light, as cedar and poplar.
_Emily._ I think I should call wood in general, a heavy body; for cedar
and poplar, are light, only in comparison to wood of a heavier
description. I am at a loss to determine whether chalk should be ranked
as a heavy, or a light body; I should be inclined to say the former, if
it was not that it is lighter than most other minerals. I perceive that
we have but vague notions of light and heavy. I wish there was some
standard of comparison, to which we could refer the weight of all other
bodies.
_Mrs. B._ The necessity of such a standard, has been so much felt, that
a body has been fixed upon for this purpose. What substance do you think
would be best calculated to answer this end?
_Caroline._ It must be one generally known, and easily obtained; lead or
iron, for instance.
_Mrs. B._ The metals, would not answer the purpose well, for several
reasons; they are not always equally compact, and they are rarely quite
pure; two pieces of iron, for instance, although of the same size, might
not, from the causes mentioned, weigh exactly alike.
_Caroline._ But, Mrs. B., if you compare the weight, of equal quantities
of different bodies, they will all be alike. You know the old saying,
that a pound of feathers, is as heavy as a pound of lead?
_Mrs. B._ When therefore we compare the weight of different kinds of
bodies, it would be absurd to take quantities of equal _weight_, we must
take quantities of equal _bulk_; pints or quarts, not ounces or pounds.
_Caroline._ Very true; I perplexed myself by thinking that quantity
referred to weight, rather than to measure. It is true, it would be as
absurd to compare bodies of the same size, in order to ascertain which
was largest, as to compare bodies of the same weight, in order to
discover which was heaviest.
_Mrs. B._ In estimating the specific gravity of bodies, therefore, we
must compare equal bulks, and we shall find that their specific gravity,
will be proportional to their weights. The body which has been adopted
as a standard of reference, is distilled, or rain water.
_Emily._ I am surprised that a fluid should have been chosen for this
purpose, as it must necessarily be contained in some vessel, and the
weight of the vessel, will require to be deducted.
_Mrs. B._ You will find that the comparison will be more easily made
with a fluid, than with a solid; and water you know can be every where
obtained. In order to learn the specific gravity of a solid body, it is
not necessary to put a certain measure of it in one scale, and an equal
measure of water into the other scale: but simply to weigh the body
under trial, first in air, and then in water. If you weigh a piece of
gold, in a glass of water, will not the gold displace just as much
water, as is equal to its own bulk?
_Caroline._ Certainly, where one body is, another cannot be at the same
time; so that a sufficient quantity of water must be removed, in order
to make way for the gold.
_Mrs. B._ Yes, a cubic inch of water, to make room for a cubic inch of
gold; remember that the bulk, alone, is to be considered; the weight,
has nothing to do with the quantity of water displaced, for an inch of
gold, does not occupy more space, and therefore will not displace more
water, than an inch of ivory, or any other substance, that will sink in
water.
Well, you will perhaps be surprised to hear that the gold will weigh
less in water, than it did out of it?
_Emily._ And for what reason?