measuring the length of a degree of a meridian, and multiplying this by
three hundred and sixty. This gives the circumference of the earth as
about twenty-five thousand miles, and its diameter as about eight
thousand miles. We know that the two stations between which we measure
are one degree apart when the elevation of the pole at one station is
one degree greater than at the other.
57. _The Earth Flattened at the Poles._--Degrees on the meridian have
been measured in various parts of the earth, and it has been found that
they invariably increase in length as we proceed from the equator
towards the pole: hence the earth must curve less and less rapidly as we
approach the poles; for the less the curvature of a circle, the larger
the degrees on it.
[Illustration: Fig. 68.]
58. _The Earth in Space._--In Fig. 68 we have a view of the earth
suspended in space. The side of the earth turned towards the sun is
illumined, and the other side is in darkness. As the planet rotates on
its axis, successive portions of it will be turned towards the sun. As
viewed from a point in space between it and the sun, it will present
light and dark portions, which will assume different forms according to
the portion which is illumined. These different appearances are shown in
Fig. 69.
[Illustration: Fig. 69.]
Day and Night.
59. _Day and Night._--The succession of day and night is due to _the
rotation of the earth on its axis_, by which a place on the surface of
the earth is carried alternately into the sunshine and out of it. As the
sun moves around the heavens on the ecliptic, it will be on the
celestial equator when at the equinoxes, and 23-1/2° north of the
equator when at the summer solstice, and 23-1/2° south of the equator
when at the winter solstice.
60. _Day and Night when the Sun is at the Equinoxes._--When the sun is
at either equinox, the diurnal circle described by the sun will coincide
with the celestial equator; and therefore half of this diurnal circle
will be above the horizon at every point on the surface of the globe. At
these times _day and night will be equal in every part of the earth_.
[Illustration: Fig. 70.]
[Illustration: Fig. 71.]
The equality of days and nights when the sun is on the celestial
equator is also evident from the following considerations: one-half
of the earth is in sunshine all of the time; when the sun is on the
celestial equator, it is directly over the equator of the earth, and
the illumination extends from pole to pole, as is evident from Figs.
70 and 71, in the former of which the sun is represented as on the
eastern horizon at a place along the central line of the figure, and
in the latter as on the meridian along the same line. In each
diagram it is seen that the illumination extends from pole to pole:
hence, as the earth rotates on its axis, every place on the surface
will be in the sunshine and out of it just half of the time.
61. _Day and Night when the Sun is at the Summer Solstice._--When the
sun is at the summer solstice, it will be 23-1/2° north of the celestial
equator. The diurnal circle described by the sun will then be 23-1/2°
north of the celestial equator; and more than half of this diurnal
circle will be above the horizon at all places north of the equator, and
less than half of it at places south of the equator: hence _the days
will be longer than the nights at places north of the equator, and
shorter than the nights at places south of the equator_. At places
within 23-1/2° of the north pole, the entire diurnal circle described by
the sun will be above the horizon, so that the sun will not set. At
places within 23-1/2° of the south pole of the earth, the entire diurnal
circle will be below the horizon, so that the sun will not rise.
[Illustration: Fig. 72.]
[Illustration: Fig. 73.]
The illumination of the earth at this time is shown in Figs. 72 and
73. In Fig. 72 the sun is represented as on the western horizon
along the middle line of the figure, and in Fig. 73 as on the
meridian. It is seen at once that the illumination extends 23-1/2°
beyond the north pole, and falls 23-1/2° short of the south pole. As
the earth rotates on its axis, places near the north pole will be in
the sunshine all the time, while places near the south pole will be
out of the sunshine all the time. All places north of the equator
will be in the sunshine longer than they are out of it, while all
places south of the equator will be out of the sunshine longer than
they are in it.
62. _Day and Night when the Sun is at the Winter Solstice._--When the
sun is at the winter solstice, it is 23-1/2° south of the celestial
equator. The diurnal circle described by the sun is then 23-1/2° south
of the celestial equator. More than half of this diurnal circle will
therefore be above the horizon at all places south of the equator, and
less than half of it at all places north of the equator: hence _the days
will be longer than the nights south of the equator, and shorter than
the nights at places north of the equator_. At places within 23-1/2° of
the south pole, the diurnal circle described by the sun will be entirely
above the horizon, and the sun will therefore not set. At places within
23-1/2° of the north pole, the diurnal circle described by the sun will
be wholly below the horizon, and therefore the sun will not rise.
The illumination of the earth at this time is shown in Figs. 74 and
75, and is seen to be the reverse of that shown in Figs. 72 and 73.
[Illustration: Fig. 74.]
[Illustration: Fig. 75.]
63. _Variation in the Length of Day and Night._--As long as the sun is
north of the equinoctial, the nights will be longer than the days south
of the equator, and shorter than the days north of the equator. It is
just the reverse when the sun is south of the equator.
The farther the sun is from the equator, the greater is the inequality
of the days and nights.
The farther the place is from the equator, the greater the inequality of
its days and nights.
When the distance of a place from the _north_ pole is less than the
distance of the sun north of the equinoctial, it will have _continuous
day without night_, since the whole of the sun's diurnal circle will be
above the horizon. A place within the same distance of the _south_ pole
will have _continuous night_.
When the distance of a place from the _north_ pole is less than the
distance of the sun south of the equinoctial, it will have _continuous
night_, since the whole of the sun's diurnal circle will then be below
the horizon. A place within the same distance of the _south_ pole will
then have _continuous day_.
At the _equator_ the _days and nights are always equal_; since, no
matter where the sun is in the heavens, half of all the diurnal circles
described by it will be above the horizon, and half of them below it.
64. _The Zones._--It will be seen, from what has been stated above, that
the sun will at some time during the year be directly overhead at every
place within 23-1/2° of the equator on either side. This belt of the
earth is called the _torrid zone_. The torrid zone is bounded by circles
called the _tropics_; that of _Cancer_ on the north, and that of
_Capricorn_ on the south.
It will also be seen, that, at every place within 23-1/2° of either
pole, there will be, some time during the year, a day during which the
sun will not rise, or on which it will not set. These two belts of the
earth's surface are called the _frigid zones_. These zones are bounded
by the _arctic_ circles. The nearer a place is to the poles, the greater
the number of days on which the sun does not rise or set.
Between the frigid zones and the torrid zones, there are two belts on
the earth which are called the _temperate zones_. The sun is never
overhead at any place in these two zones, but it rises and sets every
day at every place within their limits.
65. _The Width of the Zones._--The distance the frigid zones extend from
the poles, and the torrid zones from the equator, is exactly equal to
_the obliquity of the ecliptic_, or the deviation of the axis of the
earth from the perpendicular to the plane of its orbit. Were this
deviation forty-five degrees, the obliquity of the ecliptic would be
forty-five degrees, the torrid zone would extend forty-five degrees from
the equator, and the frigid zones forty-five degrees from the poles. In
this case there would be no temperate zones. Were this deviation fifty
degrees, the torrid and frigid zones would overlap ten degrees, and
there would be two belts of ten degrees on the earth, which would
experience alternately during the year a torrid and a frigid climate.
Were the axis of the earth perpendicular to the plane of the earth's
orbit, there would be no zones on the earth, and no variation in the
length of day and night.
66. _Twilight._--Were it not for the atmosphere, the darkness of
midnight would begin the moment the sun sank below the horizon, and
would continue till he rose again above the horizon in the east, when
the darkness of the night would be suddenly succeeded by the full light
of day. The gradual transition from the light of day to the darkness of
the night, and from the darkness of the night to the light of day, is
called _twilight_, and is due to the _diffusion of light from the upper
layers of the atmosphere_ after the sun has ceased to shine on the lower
layers at night, or before it has begun to shine on them in the morning.
[Illustration: Fig. 76.]
Let _ABCD_ (Fig. 76) represent a portion of the earth, _A_ a point on
its surface where the sun _S_ is setting; and let _SAH_ be a ray of
light just grazing the earth at _A_, and leaving the atmosphere at the
point _H_. The point _A_ is illuminated by the whole reflective
atmosphere _HGFE_. The point _B_, to which the sun has set, receives no
direct solar light, nor any reflected from that part of the atmosphere
which is below _ALH_; but it receives a twilight from the portion _HLF_,
which lies above the visible horizon _BF_. The point _C_ receives a
twilight only from the small portion of the atmosphere; while at _D_ the
twilight has ceased altogether.
67. _Duration of Twilight._--The astronomical limit of twilight is
generally understood to be the instant when stars of the sixth magnitude
begin to be visible in the zenith at evening, or disappear in the
morning.
Twilight is usually reckoned to last until the sun's depression
below the horizon amounts to eighteen degrees: this, however,
varies; in the tropics a depression of sixteen or seventeen degrees
being sufficient to put an end to the phenomenon, while in England a
depression of seventeen to twenty-one degrees is required. The
duration of twilight differs in different latitudes; it varies also
in the same latitude at different seasons of the year, and depends,
in some measure, on the meteorological condition of the atmosphere.
When the sky is of a pale color, indicating the presence of an
unusual amount of condensed vapor, twilight is of longer duration.
This happens habitually in the polar regions. On the contrary,
within the tropics, where the air is pure and dry, twilight
sometimes lasts only fifteen minutes. Strictly speaking, in the
latitude of Greenwich there is no true night from May 22 to July 21,
but constant twilight from sunset to sunrise. Twilight reaches its
minimum three weeks before the vernal equinox, and three weeks after
the autumnal equinox, when its duration is an hour and fifty
minutes. At midwinter it is longer by about seventeen minutes; but
the augmentation is frequently not perceptible, owing to the greater
prevalence of clouds and haze at that season of the year, which
intercept the light, and hinder it from reaching the earth. The
duration is least at the equator (an hour and twelve minutes), and
increases as we approach the poles; for at the former there are two
twilights every twenty-four hours, but at the latter only two in a
year, each lasting about fifty days. At the north pole the sun is
below the horizon for six months, but from Jan. 29 to the vernal
equinox, and from the autumnal equinox to Nov. 12, the sun is less
than eighteen degrees below the horizon; so that there is twilight
during the whole of these intervals, and thus the length of the
actual night is reduced to two months and a half. The length of the
day in these regions is about six months, during the whole of which
time the sun is constantly above the horizon. The general rule is,
_that to the inhabitants of an oblique sphere the twilight is longer
in proportion as the place is nearer the elevated pole, and the sun
is farther from the equator on the side of the elevated pole_.
The Seasons.
68. _The Seasons._--While the sun is north of the celestial equator,
places north of the equator are receiving heat from the sun by day
longer than they are losing it by radiation at night, while places south
of the equator are losing heat by radiation at night longer than they
are receiving it from the sun by day. When, therefore, the sun passes
north of the equator, the temperature begins to rise at places north of
the equator, and to fall at places south of it. The rise of temperature
is most rapid north of the equator when the sun is at the summer
solstice; but, for some time after this, the earth continues to receive
more heat by day than it loses by night, and therefore the temperature
continues to rise. For this reason, the heat is more excessive after the
sun passes the summer solstice than before it reaches it.
69. _The Duration of the Seasons._--Summer is counted as beginning in
June, when the sun is at the summer solstice, and as continuing until
the sun reaches the autumnal equinox, in September. Autumn then begins,
and continues until the sun is at the winter solstice, in December.
Winter follows, continuing until the sun comes to the vernal equinox, in
March, when spring begins, and continues to the summer solstice. In
popular reckoning the seasons begin with the first day of June,
September, December, and March.
The reason why winter is counted as occurring after the winter solstice
is similar to the reason why the summer is placed after the summer
solstice. The earth north of the equator is losing heat most rapidly at
the time of the winter solstice; but for some time after this it loses
more heat by night than it receives by day: hence for some time the
temperature continues to fall, and the cold is more intense after the
winter solstice than before it.
[Illustration: Fig. 77.]
Of course, when it is summer in the northern hemisphere, it is winter in
the southern hemisphere, and the reverse. Fig. 77 shows the portion of
the earth's orbit included in each season. It will be seen that the
earth is at perihelion in the winter season for places north of the
equator, and at aphelion in the summer season. This tends to mitigate
somewhat the extreme temperatures of our winters and summers.
[Illustration: Fig. 78.]
70. _The Illumination of the Earth at the different Seasons._--Fig. 78
shows the earth as it would appear to an observer at the sun during each
of the four seasons; that is to say, the portion of the earth that is
receiving the sun's rays. Figs. 79, 80, 81, and 82 are enlarged views of
the earth, as seen from the sun at the time of the summer solstice, of
the autumnal equinox, of the winter solstice, and of the vernal equinox.
[Illustration: Fig. 79.]
[Illustration: Fig. 80.]
[Illustration: Fig. 81.]
[Illustration: Fig. 82.]
[Illustration: Fig. 83.]
Fig. 83 is, so to speak, a side view of the earth, showing the limit of
sunshine on the earth when the sun is at the summer solstice; and Fig.
84, showing the limit of sunshine when the sun is at the autumnal
equinox.
[Illustration: Fig. 84.]
71. _Cause of the Change of Seasons._--Variety in the length of day and
night, and diversity in the seasons, depend upon _the obliquity of the
ecliptic_. Were there no obliquity of the ecliptic, there would be no
inequality in the length of day and night, and but slight diversity of
seasons. The greater the obliquity of the ecliptic, the greater would be
the variation in the length of the days and nights, and the more extreme
the changes of the seasons.
Tides.
72. _Tides._--The alternate rise and fall of the surface of the sea
twice in the course of a lunar day, or of twenty-four hours and
fifty-one minutes, is known as the _tides_. When the water is rising, it
is said to be _flood_ tide; and when it is falling, _ebb_ tide. When the
water is at its greatest height, it is said to be _high_ water; and when
at its least height, _low_ water.
73. _Cause of the Tides._--It has been known to seafaring nations
from a remote antiquity that there is a singular connection between
the ebb and flow of the tides and the diurnal motion of the moon.
[Illustration: Fig. 85.]
This tidal movement in seeming obedience to the moon was a mystery
until the study of the law of gravitation showed it to be due to
_the attraction of the moon on the waters of the ocean_. The reason
why there are two tides a day will appear from Fig. 85. Let _M_ be
the moon, _E_ the earth, and _EM_ the line joining their centres.
Now, strictly speaking, the moon does not revolve around the earth
any more than the earth around the moon; but the centre of each body
moves around the common centre of gravity of the two bodies. The
earth being eighty times as heavy as the moon, this centre is
situated within the former, about three-quarters of the way from its
centre to its surface, at the point _G_. The body of the earth
itself being solid, every part of it, in consequence of the moon's
attraction, may be considered as describing a circle once in a
month, with a radius equal to _EG_. The centrifugal force caused by
this rotation is just balanced by the mean attraction of the moon
upon the earth. If this attraction were the same on every part of
the earth, there would be everywhere an exact balance between it and
the centrifugal force. But as we pass from _E_ to _D_ the attraction
of the moon diminishes, owing to the increased distance: hence at
_D_ the centrifugal force predominates, and the water therefore
tends to move away from the centre _E_. As we pass from _E_ towards
_C_, the attraction of the moon increases, and therefore exceeds the
centrifugal force: consequently at _C_ there is a tendency to draw
the water towards the moon, but still away from the centre _E_. At
_A_ and _B_ the attraction of the moon increases the gravity of the
water, owing to the convergence of the lines _BM_ and _AM_, along
which it acts: hence the action of the moon tends to make the waters
rise at _D_ and _C_, and to fall at _A_ and _B_, causing two tides
to each apparent diurnal revolution of the moon.
74. _The Lagging of the Tides._--If the waters everywhere yielded
immediately to the attractive force of the moon, it would always be
high water when the moon was on the meridian, low water when she was
rising or setting, and high water again when she was on the meridian
below the horizon. But, owing to the inertia of the water, some time
is necessary for so slight a force to set it in motion; and, once in
motion, it continues so after the force has ceased, and until it has
acted some time in the opposite direction. Therefore, if the motion
of the water were unimpeded, it would not be high water until some
hours after the moon had passed the meridian. The free motion of the
water is also impeded by the islands and continents. These deflect
the tidal wave from its course in such a way that it may, in some
cases, be many hours, or even a whole day, behind its time.
Sometimes two waves meet each other, and raise a very high tide. In
some places the tides run up a long bay, where the motion of a large
mass of water will cause an enormous tide to be raised. In the Bay
of Fundy both of these causes are combined. A tidal wave coming up
the Atlantic coast meets the ocean wave from the east, and, entering
the bay with their combined force, they raise the water at the head
of it to the height of sixty or seventy feet.
75. _Spring-Tides and Neap-Tides._--The sun produces a tide as well as
the moon; but the tide-producing force of the sun is only about
four-tenths of that of the moon. At new and full moon the two bodies
unite their forces, the ebb and flow become greater than the average,
and we have the _spring-tides_. When the moon is in her first or third
quarter, the two forces act against each other; the tide-producing force
is the difference of the two; the ebb and flow are less than the
average; and we have the _neap-tides_.
[Illustration: Fig. 86.]
[Illustration: Fig. 87.]
[Illustration: Fig. 88.]
Fig. 86 shows the tide that would be produced by the moon alone; Fig.
87, the tide produced by the combined action of the sun and moon; and
Fig. 88, by the sun and moon acting at right angles to each other.
The tide is affected by the distance of the moon from the earth, being
highest near the time when the moon is in perigee, and lowest near the
time when she is in apogee. When the moon is in perigee, at or near the
time of a new or full moon, unusually high tides occur.
76. _Diurnal Inequality of Tides._--The height of the tide at a
given place is influenced by the declination of the moon. When the
moon has no declination, the highest tides should occur along the
equator, and the heights should diminish from thence toward the
north and south; but the two daily tides at any place should have
the same height. When the moon has north declination, as shown in
Fig. 89, the highest tides on the side of the earth next the moon
will be at places having a corresponding north latitude, as at _B_,
and on the opposite side at those which have an equal south
latitude. Of the two daily tides at any place, that which occurs
when the moon is nearest the zenith should be the greatest: hence,
when the moon's declination is north, the height of the tide at a
place in north latitude should be greater when the moon is above the
horizon than when she is below it. At the same time, places south of
the equator have the highest tides when the moon is below the
horizon, and the least when she is above it. This is called the
_diurnal inequality_, because its cycle is one day; but it varies
greatly in amount at different places.
[Illustration: Fig. 89.]
77. _Height of Tides._--At small islands in mid-ocean the tides never
rise to a great height, sometimes even less than one foot; and the
average height of the tides for the islands of the Atlantic and Pacific
Oceans is only three feet and a half. Upon approaching an extensive
coast where the water is shallow, the height of the tide is increased;
so that, while in mid-ocean the average height does not exceed three
feet and a half, the average in the neighborhood of continents is not
less than four or five feet.
The Day and Time.
78. _The Day._--By the term _day_ we sometimes denote the period of
sunshine as contrasted with that of the absence of sunshine, which we
call _night_, and sometimes the period of the earth's rotation on its
axis. It is with the latter signification that the term is used in this
section. As the earth rotates on its axis, it carries the meridian of a
place with it; so that, during each complete rotation of the earth, the
portion of the meridian which passes overhead from pole to pole sweeps
past every star in the heavens from west to east. The _interval between
two successive passages of this portion of the meridian across the same
star_ is the exact period of the complete rotation of the earth. This
period is called a _sidereal day_. The sidereal day may also be defined
as _the interval between two successive passages of the same star across
the meridian_; the passage of the meridian across the star, and the
passage or _transit_ of the star across the meridian, being the same
thing looked at from a different point of view. The interval _between
two successive passages of the meridian across the sun_, or _of the sun
across the meridian_, is called a _solar day_.