by which a butcher weighs a ham in a spring-balance. When he picks the
ham up, he feels a pull of the ham towards the earth. When he hangs it
on the hook, this pull is transferred from his hand to the spring of
the balance. The stronger the pull, the farther the spring is pulled
down. What he reads on the scale is the strength of the pull. You know
that this pull is simply the attraction of the earth on the ham. But,
by a universal law of force, the ham attracts the earth exactly as much
as the earth does the ham. So what the butcher really does is to find
how much or how strongly the ham attracts the earth, and he calls that
pull the weight of the ham. On the same principle, the astronomer finds
the weight of a body by finding how strong is its attractive pull on
some other body. If the butcher, with his spring-balance and a ham,
could fly to all the planets, one after the other, weigh the ham on
each, and come back to report the results to an astronomer, the latter
could immediately compute the weight of each planet of known diameter,
as compared with that of the earth. In applying this principle to the
heavenly bodies, we at once meet a difficulty that looks
insurmountable. You cannot get up to the heavenly bodies to do your
weighing; how then will you measure their pull? I must begin the answer
to this question by explaining a nice point in exact science.
Astronomers distinguish between the weight of a body and its mass. The
weight of objects is not the same all over the world; a thing which
weighs thirty pounds in New York would weigh an ounce more than thirty
pounds in a spring-balance in Greenland, and nearly an ounce less at
the equator. This is because the earth is not a perfect sphere, but a
little flattened. Thus weight varies with the place. If a ham weighing
thirty pounds were taken up to the moon and weighed there, the pull
would only be five pounds, because the moon is so much smaller and
lighter than the earth. There would be another weight of the ham for
the planet Mars, and yet another on the sun, where it would weigh some
eight hundred pounds. Hence the astronomer does not speak of the weight
of a planet, because that would depend on the place where it was
weighed; but he speaks of the mass of the planet, which means how much
planet there is, no matter where you might weigh it.
At the same time, we might, without any inexactness, agree that the
mass of a heavenly body should be fixed by the weight it would have in
New York. As we could not even imagine a planet at New York, because it
may be larger than the earth itself, what we are to imagine is this:
Suppose the planet could be divided into a million million million
equal parts, and one of these parts brought to New York and weighed. We
could easily find its weight in pounds or tons. Then multiply this
weight by a million million million, and we shall have a weight of the
planet. This would be what the astronomers might take as the mass of
the planet.
With these explanations, let us see how the weight of the earth is
found. The principle we apply is that round bodies of the same specific
gravity attract small objects on their surface with a force
proportional to the diameter of the attracting body. For example, a
body two feet in diameter attracts twice as strongly as one of a foot,
one of three feet three times as strongly, and so on. Now, our earth is
about 40,000,000 feet in diameter; that is 10,000,000 times four feet.
It follows that if we made a little model of the earth four feet in
diameter, having the average specific gravity of the earth, it would
attract a particle with one ten-millionth part of the attraction of the
earth. The attraction of such a model has actually been measured. Since
we do not know the average specific gravity of the earth--that being in
fact what we want to find out--we take a globe of lead, four feet in
diameter, let us suppose. By means of a balance of the most exquisite
construction it is found that such a globe does exert a minute
attraction on small bodies around it, and that this attraction is a
little more than the ten-millionth part of that of the earth. This
shows that the specific gravity of the lead is a little greater than
that of the average of the whole earth. All the minute calculations
made, it is found that the earth, in order to attract with the force it
does, must be about five and one-half times as heavy as its bulk of
water, or perhaps a little more. Different experimenters find different
results; the best between 5.5 and 5.6, so that 5.5 is, perhaps, as near
the number as we can now get. This is much more than the average
specific gravity of the materials which compose that part of the earth
which we can reach by digging mines. The difference arises from the
fact that, at the depth of many miles, the matter composing the earth
is compressed into a smaller space by the enormous weight of the
portions lying above it. Thus, at the depth of 1000 miles, the pressure
on every cubic inch is more than 2000 tons, a weight which would
greatly condense the hardest metal.
We come now to the planets. I have said that the mass or weight of a
heavenly body is determined by its attraction on some other body. There
are two ways in which the attraction of a planet may be measured. One
is by its attraction on the planets next to it. If these bodies did not
attract one another at all, but only moved under the influence of the
sun, they would move in orbits having the form of ellipses. They are
found to move very nearly in such orbits, only the actual path deviates
from an ellipse, now in one direction and then in another, and it
slowly changes its position from year to year. These deviations are due
to the pull of the other planets, and by measuring the deviations we
can determine the amount of the pull, and hence the mass of the planet.
The reader will readily understand that the mathematical processes
necessary to get a result in this way must be very delicate and
complicated. A much simpler method can be used in the case of those
planets which have satellites revolving round them, because the
attraction of the planet can be determined by the motions of the
satellite. The first law of motion teaches us that a body in motion, if
acted on by no force, will move in a straight line. Hence, if we see a
body moving in a curve, we know that it is acted on by a force in the
direction towards which the motion curves. A familiar example is that
of a stone thrown from the hand. If the stone were not attracted by the
earth, it would go on forever in the line of throw, and leave the earth
entirely. But under the attraction of the earth, it is drawn down and
down, as it travels onward, until finally it reaches the ground. The
faster the stone is thrown, of course, the farther it will go, and the
greater will be the sweep of the curve of its path. If it were a
cannon-ball, the first part of the curve would be nearly a right line.
If we could fire a cannon-ball horizontally from the top of a high
mountain with a velocity of five miles a second, and if it were not
resisted by the air, the curvature of the path would be equal to that
of the surface of our earth, and so the ball would never reach the
earth, but would revolve round it like a little satellite in an orbit
of its own. Could this be done, the astronomer would be able, knowing
the velocity of the ball, to calculate the attraction of the earth as
well as we determine it by actually observing the motion of falling
bodies around us.
Thus it is that when a planet, like Mars or Jupiter, has satellites
revolving round it, astronomers on the earth can observe the attraction
of the planet on its satellites and thus determine its mass. The rule
for doing this is very simple. The cube of the distance between the
planet and satellite is divided by the square of the time of revolution
of the satellite. The quotient is a number which is proportional to the
mass of the planet. The rule applies to the motion of the moon round
the earth and of the planets round the sun. If we divide the cube of
the earth's distance from the sun, say 93,000,000 miles, by the square
of 365 1/4, the days in a year, we shall get a certain quotient. Let us
call this number the sun-quotient. Then, if we divide the cube of the
moon's distance from the earth by the square of its time of revolution,
we shall get another quotient, which we may call the earth-quotient.
The sun-quotient will come out about 330,000 times as large as the
earth-quotient. Hence it is concluded that the mass of the sun is
330,000 times that of the earth; that it would take this number of
earths to make a body as heavy as the sun.
I give this calculation to illustrate the principle; it must not be
supposed that the astronomer proceeds exactly in this way and has only
this simple calculation to make. In the case of the moon and earth, the
motion and distance of the former vary in consequence of the attraction
of the sun, so that their actual distance apart is a changing quantity.
So what the astronomer actually does is to find the attraction of the
earth by observing the length of a pendulum which beats seconds in
various latitudes. Then, by very delicate mathematical processes, he
can find with great exactness what would be the time of revolution of a
small satellite at any given distance from the earth, and thus can get
the earth-quotient.
But, as I have already pointed out, we must, in the case of the
planets, find the quotient in question by means of the satellites; and
it happens, fortunately, that the motions of these bodies are much less
changed by the attraction of the sun than is the motion of the moon.
Thus, when we make the computation for the outer satellite of Mars, we
find the quotient to be 1/3093500 that of the sun-quotient. Hence we
conclude that the mass of Mars is 1/3093500 that of the sun. By the
corresponding quotient, the mass of Jupiter is found to be about 1/1047
that of the sun, Saturn 1/3500, Uranus 1/22700, Neptune 1/19500.
We have set forth only the great principle on which the astronomer has
proceeded for the purpose in question. The law of gravitation is at the
bottom of all his work. The effects of this law require mathematical
processes which it has taken two hundred years to bring to their
present state, and which are still far from perfect. The measurement of
the distance of a satellite is not a job to be done in an evening; it
requires patient labor extending through months and years, and then is
not as exact as the astronomer would wish. He does the best he can, and
must be satisfied with that.
IX
THE MARINER'S COMPASS
Among those provisions of Nature which seem to us as especially
designed for the use of man, none is more striking than the seeming
magnetism of the earth. What would our civilization have been if the
mariner's compass had never been known? That Columbus could never have
crossed the Atlantic is certain; in what generation since his time our
continent would have been discovered is doubtful. Did the reader ever
reflect what a problem the captain of the finest ocean liner of our day
would face if he had to cross the ocean without this little instrument?
With the aid of a pilot he gets his ship outside of Sandy Hook without
much difficulty. Even later, so long as the sun is visible and the air
is clear, he will have some apparatus for sailing by the direction of
the sun. But after a few hours clouds cover the sky. From that moment
he has not the slightest idea of east, west, north, or south, except so
far as he may infer it from the direction in which he notices the wind
to blow. For a few hours he may be guided by the wind, provided he is
sure he is not going ashore on Long Island. Thus, in time, he feels his
way out into the open sea. By day he has some idea of direction with
the aid of the sun; by night, when the sky is clear he can steer by the
Great Bear, or "Cynosure," the compass of his ancient predecessors on
the Mediterranean. But when it is cloudy, if he persists in steaming
ahead, he may be running towards the Azores or towards Greenland, or he
may be making his way back to New York without knowing it. So, keeping
up steam only when sun or star is visible, he at length finds that he
is approaching the coast of Ireland. Then he has to grope along much
like a blind man with his staff, feeling his way along the edge of a
precipice. He can determine the latitude at noon if the sky is clear,
and his longitude in the morning or evening in the same conditions. In
this way he will get a general idea of his whereabouts. But if he
ventures to make headway in a fog, he may find himself on the rocks at
any moment. He reaches his haven only after many spells of patient
waiting for favoring skies.
The fact that the earth acts like a magnet, that the needle points to
the north, has been generally known to navigators for nearly a thousand
years, and is said to have been known to the Chinese at a yet earlier
period. And yet, to-day, if any professor of physical science is asked
to explain the magnetic property of the earth, he will acknowledge his
inability to do so to his own satisfaction. Happily this does not
hinder us from finding out by what law these forces act, and how they
enable us to navigate the ocean. I therefore hope the reader will be
interested in a short exposition of the very curious and interesting
laws on which the science of magnetism is based, and which are applied
in the use of the compass.
The force known as magnetic, on which the compass depends, is different
from all other natural forces with which we are familiar. It is very
remarkable that iron is the only substance which can become magnetic in
any considerable degree. Nickel and one or two other metals have the
same property, but in a very slight degree. It is also remarkable that,
however powerfully a bar of steel may be magnetized, not the slightest
effect of the magnetism can be seen by its action on other than
magnetic substances. It is no heavier than before. Its magnetism does
not produce the slightest influence upon the human body. No one would
know that it was magnetic until something containing iron was brought
into its immediate neighborhood; then the attraction is set up. The
most important principle of magnetic science is that there are two
opposite kinds of magnetism, which are, in a certain sense, contrary in
their manifestations. The difference is seen in the behavior of the
magnet itself. One particular end points north, and the other end
south. What is it that distinguishes these two ends? The answer is that
one end has what we call north magnetism, while the other has south
magnetism. Every magnetic bar has two poles, one near one end, one near
the other. The north pole is drawn towards the north pole of the earth,
the south pole towards the south pole, and thus it is that the
direction of the magnet is determined. Now, when we bring two magnets
near each other we find another curious phenomenon. If the two like
poles are brought together, they do not attract but repel each other.
But the two opposite poles attract each other. The attraction and
repulsion are exactly equal under the same conditions. There is no more
attraction than repulsion. If we seal one magnet up in a paper or a
box, and then suspend another over the box, the north pole of the one
outside will tend to the south pole of the one in the box, and vice
versa.
Our next discovery is, that whenever a magnet attracts a piece of iron
it makes that iron into a magnet, at least for the time being. In the
case of ordinary soft or untempered iron the magnetism disappears
instantly when the magnet is removed. But if the magnet be made to
attract a piece of hardened steel, the latter will retain the magnetism
produced in it and become itself a permanent magnet.
This fact must have been known from the time that the compass came into
use. To make this instrument it was necessary to magnetize a small bar
or needle by passing a natural magnet over it.
In our times the magnetization is effected by an electric current. The
latter has curious magnetic properties; a magnetic needle brought
alongside of it will be found placing itself at right angles to the
wire bearing the current. On this principle is made the galvanometer
for measuring the intensity of a current. Moreover, if a piece of wire
is coiled round a bar of steel, and a powerful electric current pass
through the coil, the bar will become a magnet.
Another curious property of magnetism is that we cannot develop north
magnetism in a bar without developing south magnetism at the same time.
If it were otherwise, important consequences would result. A separate
north pole of a magnet would, if attached to a floating object and
thrown into the ocean, start on a journey towards the north all by
itself. A possible method of bringing this result about may suggest
itself. Let us take an ordinary bar magnet, with a pole at each end,
and break it in the middle; then would not the north end be all ready
to start on its voyage north, and the south end to make its way south?
But, alas! when this experiment is tried it is found that a south pole
instantly develops itself on one side of the break, and a north pole on
the other side, so that the two pieces will simply form two magnets,
each with its north and south pole. There is no possibility of making a
magnet with only one pole.
It was formerly supposed that the central portions of the earth
consisted of an immense magnet directed north and south. Although this
view is found, for reasons which need not be set forth in detail, to be
untenable, it gives us a good general idea of the nature of terrestrial
magnetism. One result that follows from the law of poles already
mentioned is that the magnetism which seems to belong to the north pole
of the earth is what we call south on the magnet, and vice versa.
Careful experiment shows us that the region around every magnet is
filled with magnetic force, strongest near the poles of the magnet, but
diminishing as the inverse square of the distance from the pole. This
force, at each point, acts along a certain line, called a line of
force. These lines are very prettily shown by the familiar experiment
of placing a sheet of paper over a magnet, and then scattering iron
filings on the surface of the paper. It will be noticed that the
filings arrange themselves along a series of curved lines, diverging in
every direction from each pole, but always passing from one pole to the
other. It is a universal law that whenever a magnet is brought into a
region where this force acts, it is attracted into such a position that
it shall have the same direction as the lines of force. Its north pole
will take the direction of the curve leading to the south pole of the
other magnet, and its south pole the opposite one.
The fact of terrestrial magnetism may be expressed by saying that the
space within and around the whole earth is filled by lines of magnetic
force, which we know nothing about until we suspend a magnet so
perfectly balanced that it may point in any direction whatever. Then it
turns and points in the direction of the lines of force, which may thus
be mapped out for all points of the earth.
We commonly say that the pole of the needle points towards the north.
The poets tell us how the needle is true to the pole. Every reader,
however, is now familiar with the general fact of a variation of the
compass. On our eastern seaboard, and all the way across the Atlantic,
the north pointing of the compass varies so far to the west that a ship
going to Europe and making no allowance for this deviation would find
herself making more nearly for the North Cape than for her destination.
The "declination," as it is termed in scientific language, varies from
one region of the earth to another. In some places it is towards the
west, in others towards the east.
The pointing of the needle in various regions of the world is shown by
means of magnetic maps. Such maps are published by the United States
Coast Survey, whose experts make a careful study of the magnetic force
all over the country. It is found that there is a line running nearly
north and south through the Middle States along which there is no
variation of the compass. To the east of it the variation of the north
pole of the magnet is west; to the west of it, east. The most rapid
changes in the pointing of the needle are towards the northeast and
northwest regions. When we travel to the northeastern boundary of Maine
the westerly variation has risen to 20 degrees. Towards the northwest
the easterly variation continually increases, until, in the northern
part of the State of Washington, it amounts to 23 degrees.
When we cross the Atlantic into Europe we find the west variation
diminishing until we reach a certain line passing through central
Russia and western Asia. This is again a line of no variation. Crossing
it, the variation is once more towards the east. This direction
continues over most of the continent of Asia, but varies in a somewhat
irregular manner from one part of the continent to another.
As a general rule, the lines of the earth's magnetic force are not
horizontal, and therefore one end or the other of a perfectly suspended
magnet will dip below the horizontal position. This is called the "dip
of the needle." It is observed by means of a brass circle, of which the
circumference is marked off in degrees. A magnet is attached to this
circle so as to form a diameter, and suspended on a horizontal axis
passing through the centre of gravity, so that the magnet shall be free
to point in the direction indicated by the earth's lines of magnetic
force. Armed with this apparatus, scientific travellers and navigators
have visited various points of the earth in order to determine the dip.
It is thus found that there is a belt passing around the earth near the
equator, but sometimes deviating several degrees from it, in which
there is no dip; that is to say, the lines of magnetic force are
horizontal. Taking any point on this belt and going north, it will be
found that the north pole of the magnet gradually tends downward, the
dip constantly increasing as we go farther north. In the southern part
of the United States the dip is about 60 degrees, and the direction of
the needle is nearly perpendicular to the earth's axis. In the northern
part of the country, including the region of the Great Lakes, the dip
increases to 75 degrees. Noticing that a dip of 90 degrees would mean
that the north end of the magnet points straight downward, it follows
that it would be more nearly correct to say that, throughout the United
States, the magnetic needle points up and down than that it points
north and south.
Going yet farther north, we find the dip still increasing, until at a
certain point in the arctic regions the north pole of the needle points
downward. In this region the compass is of no use to the traveller or
the navigator. The point is called the Magnetic Pole. Its position has
been located several times by scientific observers. The best
determinations made during the last eighty years agree fairly well in
placing it near 70 degrees north latitude and 97 degrees longitude west
from Greenwich. This point is situated on the west shore of the
Boothian Peninsula, which is bounded on the south end by McClintock
Channel. It is about five hundred miles north of the northwest part of
Hudson Bay. There is a corresponding magnetic pole in the Antarctic
Ocean, or rather on Victoria Land, nearly south of Australia. Its
position has not been so exactly located as in the north, but it is
supposed to be at about 74 degrees of south latitude and 147 degrees of
east longitude from Greenwich.
The magnetic poles used to be looked upon as the points towards which
the respective ends of the needle were attracted. And, as a matter of
fact, the magnetic force is stronger near the poles than elsewhere.
When located in this way by strength of force, it is found that there
is a second north pole in northern Siberia. Its location has not,
however, been so well determined as in the case of the American pole,
and it is not yet satisfactorily shown that there is any one point in
Siberia where the direction of the force is exactly downward.
[Illustration with caption: DIP OF THE MAGNETIC NEEDLE IN VARIOUS
LATITUDES. The arrow points show the direction of the north end of the
magnetic needle, which dips downward in north latitudes, while the
south end dips in south latitudes.]
The declination and dip, taken together, show the exact direction of
the magnetic force at any place. But in order to complete the statement
of the force, one more element must be given--its amount. The intensity
of the magnetic force is determined by suspending a magnet in a
horizontal position, and then allowing it to oscillate back and forth
around the suspension. The stronger the force, the less the time it
will take to oscillate. Thus, by carrying a magnet to various parts of
the world, the magnetic force can be determined at every point where a
proper support for the magnet is obtainable. The intensity thus found
is called the horizontal force. This is not really the total force,
because the latter depends upon the dip; the greater the dip, the less
will be the horizontal force which corresponds to a certain total
force. But a very simple computation enables the one to be determined
when the value of the other is known. In this way it is found that, as
a general rule, the magnetic force is least in the earth's equatorial
regions and increases as we approach either of the magnetic poles.