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```THE LIBRARY

OF

THE UNIVERSITY
OF CALIFORNIA

LOS ANGELES

2i 'K

AN ANGULAR TOUR OF THE WORLD

OR

THE CURIOSITIES

OF

Latitude and Longitude

A BOOK FOR TEACHERS

BY

EDWARD R. E. COWELL
Member of the Chicago Academy of Sciences

THOMAS CHARLES CO
CHICAGO

BY
E. R. E. COWELL

Engineering \$
Mathematical
Sciences & 3 /

"*"> C33

TO THE TEACHER.

^ I A HE object of this little work is to make the sub-
A. ject clear, so that it may be intelligently pre-
sented to your classes. A clear understanding of the
earth's motions and the relation of the earth to the
other heavenly bodies is necessary in teaching mathe-
matical geography.

Facts belong to the physical world and truths to
the moral and spiritual world. A teacher who has
the best and highest development of the scholar in
view will combine facts and truths in teaching.

L/et me explain. ' ' The world rotates on its axis
once in twenty-four hours." That is a physical fact.
' ' We must always have a cause adequate to produce
an effect." That is a moral truth. "The earth's
axis is inclined sixty-six and one-half degrees to the
sun's path." That is a fact. " The wisdom of this
arrangement is evident. ' ' That is a truth.

I believe in the concrete idea in teaching. In
order to present a fact so that it may be readily seen,
it should be given in a concrete form. I believe the

4 TO THE TEACHER.

truth can be arrived at without wasting the mental
powers in mere mathematical gymnastics.

We must understand the principles involved in a
problem, get a bird's-eye view of it, get down to the
roots of it and out to the twigs of it grasp it. It is
of no use to work out a problem by rule unless the
student understands the reason for the rule.

I believe in fulness of explanation and in variety
of illustration, and in arriving at knowledge by
inductive reasoning; and let us forever bear in mind
this truth, that " we must always have a cause ade-
quate to produce an effect. ' '

STATE NORMAL SCHOOL,

ItOS AfiCEIlES, GRU.

CONTENTS.

PAGK.

Accurate Clocks 45

Altitude , .,... 25

Angular Distances 41

Angular Tour of the World. ., 10

Antipodal Meridian 20-5(5

Antipodes 20

Apparent Sun Time 64

Apparition ... 18

Astronomical Geography &

A Wonderful Clock 45

Axis of Rotation 14

Belts (Zone) 15

Beginning of a Day 51

Celestial Pole 36

Center of Gravity 34

Changes in Appearance of the Heavens 37

Circumnavigating the Globe 60

Climate 22

Clocks Agree 21

Clocks Differ 21

Clock The Earth 42-44

Co-Latitude 25

Co-Incident Phenomena :'> - J

Compensation Balance 30

Concentric Zone Boundaries.... .. 14

CONTENTS.

Concrete Teaching 3

Cone of Rotation 43

Date Line 53

Dawn and Twilight 36

Day 42

Declination 25

Direction of Rotation and Revolution. ... 13

Diurnal Rotation 34

East and West 35

Equator 39

Equinoxes 12

Facts and Truths 3

Gain or Loss of Time; 57

Gravity 39

Greenland 17

Greenwich Mean Time 63

Gyroscope 43

Heat 31

Inclination of Axis 12

International Date Line 53

Land of the Midnight Sun 17

Latitude and the Sun's Meridian Altitude 23

Defined 33

How to Obtain 26

Of Cities 76

Law of Compensation 30

London 51

Longest Day 18

Longitude Defined 41

How Obtained at Sea 63

Of Cities.... 76

CONTENTS. 7

Longitude Proof of Earth's Rotundity '. 10

'Longitudinal Quadrants of the Earth 54

Magnetic Pole 34

Making of a Zone 13

Mathematical Geography 40

Mean Sun Titne 65

Meridian 180 53

Meridians 41

Midnight 56

Motions of a Steam Engine 11

Mountain-top Temperatures 22

Night 23

Noon 22

North Polar Star 33

Norway 17

Occupation 18

Parallels 15

Parallelism of the Axis 12

Pendulum , 39

Phenomena of Day and Night 29

Place of Sun's Rising and Setting 28

Polaris 43

Poles 36

Precession 43

Proofs of Earth's Rotundity 10

Revolution 13

Rising and Setting Stars 39

Rotation 13

Sidereal Time 44

Sidereal Clock.... .. 44

8 CONTENTS.

Sea Level Temperatures . 22

Seasons. 1*

Sextant 64

Shape of the Earth 32-72

Standard Time 67

Succession of Days 49

Sun's Declination 19

Sun's Meridian Altitude 23

Sun-DialTime 23

Telegrams from Distant Points ... 10

The Midnight Sun 17

Time .". 42

Value of a Degree

Latitude 72

Longitude 70

Watches ., 45

Where does the Day Begin? .'., 51

Width of the Zones 15

Yesterday and Today 55

ILLUSTRATIONS.

1. The Earth 6ti

2. Rotation of the Northern Heavens 35

3. Twilight Projection 37

4. The Hour Angle 47

6. Direction of Rotation, etc 13

7. Sunrise and Sunset Points .'. 28

8. Sun's Meridian Altitude 24

9. Angle of the Sun's Rays ... 25

AN ANGULAR TOUR OF THE WORLD;

The Curiosities of Latitude and Longitude

LONGITUDE... ...LENGTH.

HT^HERE is no latitude at the equator and no longi-
-* tude at London (or Greenwich), these being the
initial or starting-points from which latitude and
longitude are measured. We may define the position
of any place on the earth very accurately by giving
its latitude and longitude.

The City Hall. New York, for instance, is 40 42'
44" north latitude and 74 o' 24" west longitude.

Yale College, New Haven, is 41 18' 28" north
latitude and 72 55' 45" west longitude.

The State House, Boston, is 42 21' 28" north
latitude and 71 3' 50" west longitude.

The Auditorium, Chicago, 1541 53' north latitude
and 87 37' west longitude.

10 CURIOSITIES OF LATITUDE AND LONGITUDE.

One of the simplest and most self-evident proofs
of the rotundity or sphericity of our earth is in con-
nection with longitude.

If the earth were flat, the sun at rising would
appear at the same instant to every one west of it, say
at Yokohama, Athens, London, New York, Chicago
and San Francisco.

Now the fact is, that when the sun is rising in
Australia it is setting in England, and it is on the
meridian of (or noon at) Chicago, all at the same
instant.

If we were to send a telegram from Melbourne in
the early morning (sunrise) of Sunday, July i, it
would reach Chicago Saturday noon, June 30, the
previous day.

L/et me take you on a personally conducted tour
around the world. We will travel around the earth
obliquely, at an angle of 66^ degrees to the equator,
crossing every meridian and every parallel as far as
the two circles. This might be called "An Angular
Tour of the World. ' ' We shall witness some very
interesting phenomena.

The curiosities of latitude and longitude are simply
those phenomena we experience by change of posi-
tion. If a person living on the equator and used to
seeing the sun rise and set at six o'clock every day

CURIOSITIES OF LATITUDE AND LONGITUDE. II

throughout the year were to go to latitude 66^3 north
(on June 21), he would see the sun at midnight. This
to him would be a curiosity; it is a phenomenon of
latitude.

Suppose a person living, say, at San Francisco,
saw the sun set at 5 p. M., and could travel rapidly
around the earth on that parallel, the sun would set
at 5 P. M. for him at Pekin, China, and every other
watch to the local time of the place. That is a phe-
nomenon of longitude and latitude.

Now, suppose a person lived at the Arctic Circle,
on, say, meridian 75 west longitude, another at the
Equator, and another at the Antarctic Circle, on the
same meridian ; all three would have exactly the
same time their clocks would all agree.

L/et me give you an analysis of the strange and
complex phenomena which I call the " Curiosities of
Latitude and Longitude.'' Three causes combine to
produce these results:

First The axial rotation of the earth (diurnal).

Second The inclination of the axis of rotation.

Third The earth's yearly revolution around the
sun.

Did you ever watch the motions of the separate
parts of a steam engine valve, piston and valve-

12 CURIOSITIES OF LATITUDE AND LONGITUDE.

gear? The motion of each is simple; each part
works in harmony with, and in relation to, the other
parts; the result looks complex. Just so in regard to
the several motions of the earth.

Note, now, the effect of the inclination of the
earth's axis, 66^ degrees, to the plane of its orbit,
or 23^* to a perpendicular to the plane of the earth's
orbit. The equator is inclined 23 ^ degrees to the
apparent path of the sun, or the ecliptic. The par-
'allelism of the axis to itself in the yearly journey is
strictly maintained.

The rotation of the seasons spring, summer,
autumn and winter is one result of this inclina-
tion, and the belting of the earth with zones is
another.

In the rotation of seasons it will be observed that
in both spring and fall (or autumn) seasons days and
nights are equal\ all over the globe. The night
shadow is then perpendicular, whereas in the summer
and winter seasons the greatest possible variation
takes place in the length of day and night and in the
' position of the night shadow.

The plane of the ecliptic, or sun's path, is the
the plane of the earth's orbit. This crosses the
equator at an angle of

* 23-28 / . f Equinox Vernal March 21, and Autumnal Sept. 21 .

CURIOSITIE

ES OF LA

TITUDE AND LONGITUDE. 13

The inclination of the axis to the plane of the
earth's orbit is 66^ or 23^ to a perpendicular to
the plane. The following diagram shows the direc-
tion of revolution and rotation, also the fixed axis of
rotation :

What makes a zone ?

Did you ever watch a wood-turner at his lathe?
Let him touch any point on a revolving cylinder or
globe with the point of his instrument and instantly
that point becomes a circle by the rotation of the
cylinder on its axis, and the fixed position of the axis.

Now, if the rays of the sun touch a point north or
south, say, for instance, the Arctic Circle, the diurnal

14 CURIOSITIES OF LATITUDE AND LONGITUDE.

rotation of our globe makes that point a circle. As
compared to the (apparent) moving sun in his yearly
path, the earth's rotation is rapid.

Here is another point, say 23 28' nortri of the
equator, over which the sun is vertical; the daily
rotation makes this a circle again, and that circle is
the Tropic of Cancer. Now, if the sun is vertical (in
the zenith) at any point on the Tropic of Cancer, he
is vertical at every point on that parallel; for the time
being the "sun stands still," while the earth keeps
on rotating, and, as the Tropic of Cancer is the limit
of the sun's path north of the equator, of course it is
the limit of verticality, hence marks the northern
boundary of the Torrid Zone.

Observe that these circles are all concentric, paral-
lel to each other, because of the fixed position of the
axis of rotation. No matter how many points may
be touched by the wood-turner in his work, these
all become concentric circles, because of the fixed axis
of rotation.

This explains why the same series of phenomena
takes place at all points "on a parallel. It is due to
the stationary sun (for the time) and the rapidly
rotating earth. Were the rotation slower (say a
month), there would be quite an appreciable difference
in the phenomena at different places on, a parallel.

CURIOSITIES OF LATITUDE AND LONGITUDE. 15

A parallel is a circle running around the earth, east
and west, smaller than the equator, all points of
which are equally distant from the equator. It is a
circle parallel to the equator.

From what has been said, it will readily be seen
that the zones are made practically by the sun,
in combination with the rotating earth and the fixed
axis of rotation.

There are five zones, as there are five races of men,
and five great continents and five large oceans. As
the Arctic and Antarctic, or Frigid Zones, bound the
limit of the sun's rays at the winter solstice, so the
Torrid Zone bounds the limit of his verticality at the
summer solstice.

The width of the zones, therefore, corresponds
with the apparent movements of the sun, the inclina-
tion of the earth's axis to a perpendicular to the
ecliptic, or sun's path, being 23 degrees and 28 min-
utes. So we have the widths of the zones as follows:

Arctic 23 28'

North Temperate 43 04'

Torrid 46 56', or twice 23 28'

South Temperate 43 04'

Antarctic 23 28'

1 80 oo'

1 6 CURIOSITIES OF LATITUDE AND LONGITUDE.

It will be observed by this arrangement that the
greatest possible width is given to that portion of the
earth best adapted to man and his needs, /. e. , best
adapted for his occupation, namely, the two temperate
s zones a belt 86 8' wide, or nearly half of the total
of 1 80 degrees.

The proportion is very much larger than this when
we consider the area of this belt. The value of a
degree of longitude rapidly diminishes as we approach
the poles so that the area of the Frigid Zones is much
smaller in proportion to their width than the Temper-
ate or Torrid Zones.

If the earth's equator were not inclined 23 28' to
the ecliptic or sun's path, that is, if the sun moved
in the equator instead of the ecliptic, eternal cold
and darkness would prevail at some places, and eter-
nal heat and light at others. It is the inclination of
the axis plus the rotation of that axis, together with
the yearly path of the sun, that produces the compen-
satory balance of the alternate and equal distribution of
heat and cold, light and darkness for the whole earth.
I believe the earth is adapted to man and his needs.
The wisdom of the inclination, rotation and revolution
is evident; nothing in Nature is accidental. When
the " Heavens and the Earth were finished" they were
finished in the sense of perfection and completeness.

CURIOSITIES OF LATITUDE AND LONGITUDE. IJ

Suppose the axis of the earth were inclined 56^
instead of 66 y> to the plane of its orbit. New Orleans
would then be in the Torrid Zone, and Edinburgh
would be in the Arctic Zone.

Suppose the inclination were 76^, Greenland
would then be in the North Temperate Zone, and
Bombay, which is now in the Torrid, would be in the
North Temperate Zone.

Now suppose the angle of the ecliptic to the equa-
tor was 30 instead of 23 28'. The width of the
zones would be as follows: Torrid, 60; the two Frigid
Zones, 30 each; the Temperate Zones, 30 each,
and England would then be in the Arctic Zone and in
winter would have no sun at all.

Travelers call Norway the land of the midnight
sun, but this is true of any land beyond the 665^ par-
allel of latitude. On the 2ist of June the sun does
not set at all from the Arctic Circle to the North Pole,
and on the 2ist of December he does not set from the
Antarctic Circle to the South Pole.

I suppose that the reason why Norway is especially
designated as the " Land of the Midnight Sun" is,
that Norway is accessible to travelers and is in the
regular route of excursion travel, but Greenland,
being within the Arctic regions, is getting to
be quite as accessible, and is just as much the

1 8 CURIOSITIES OF LATITUDE AND LONGITUDE.

"Land of the Midnight Sun" as are Sweden and
Norway.

The two polar circles are the farthest limits north
and south where a day can consist of just twenty-four
hours (on June 21 and December 21) with no night.
Less than these two points the day can never be
twenty-four hours long. Beyond these circles the day
may be anywhere from 24 hours to six months long.
The two circles, therefore, mark the maximum twenty-
four-hour day, or a period of twenty-four hours when
the sun is above the horizon.

Let me explain this phenomenon of latitude.

The greatest length of the day for all latitudes
north of the equator, occurs on June 21. The night
shadow then extends in a diagonal line from one edge
of the Arctic Circle, to the opposite edge of the Ant-
arctic Circle, thus uncovering (or exposing to the sun's
rays) the northern Frigid Zone, and completely cov-
ering the southern. The cut on page 28 shows the
position of the night shadow for June 21. This
diagonal line cuts the equator at an angle of 66 ]/ 2
and is 23}^ from the meridian or perpendicular.

At the equator the day would be just 12 hours
long, the sun would rise at 6 and set at 6; at the 55th
parallel the day would be 18 hours long; sun rises at
3 and sets at 9; at the 66 ^< parallel, the day is 24

CURIOSITIES OF LATITUDE AND LONGITUDE. 19

hours long and the sun neither rises nor sets, but at
noon he is 47 high and at midnight on the horizon,
and due north. At the 55th parallel south, the day
would be now, only six hours long; sun rises at 9 and
sets at 3. At the 66^4 parallel south, there would
be no day; sun does not rise at all. The night is 24
hours long.

Now as the line of the night shadow forms an angle
with the meridian, equal to the angle of the sun with
the equator, the greater the angle the greater will be
the difference in lengths of the day and night at vari-
ous latitudes, and, as the greatest angle is 23^ and
the greatest difference 12 hours (at the Polar Circles)
each degree would represent about 30 minutes. If,
therefore, the sun were 4 north declination, there
would be a difference of about two hours between the
length of the day at the equator and at the Polar Cir-
cles; that is, the day would be two hours in excess of
12 at the Arctic Circle, and two hours less than 12 at
the Antarctic Circle. Four degrees south declination
would reverse this. Of course, at the very poles
themselves a very slight angle would produce a day of
24 hours long and as the angle increased, the region
of perpetual sunshine would increase in the one Polar
Zone and correspondingly decrease in the other.

People who live on opposite sides of the earth, or

20 CURIOSITIES OF LATITUDE AND LONGITUDE.

the Antipodes, have opposite latitudes, longitudes,
days, nights and seasons. The Antipodal Meridian
Antipodes, the point on that meridian in opposite lat-

People living in the same longitude have the same
NOON, and, in fact, all hours of the day alike. Their
clocks will all agree, but the times of their sunrise
and sunset depends on the declination of the sun and
their latitude. People living on the same parallel of
latitude have sunrise and sunset at the same hours rel-
atively, but their clocks will all differ. The relative
time of sunrise, for instance, on the 42d parallel,
would be the same to all places on that parallel,
although in absolute time they might be hours apart.
Sunrise would be at about the same hour to people
living in Boston, Albany, Buffalo, Chicago, Omaha>
Pekin, Constantinople, Rome and Madrid, although
these places are widely apart in absolute time.

CURIOSITIES OF LATITUDE AND LONGITUDE. 21

CLOCKS ALL AGREE. CLOCKS ALL DIFFER.

\\

^ 'd ~

j i.

A Parallel of Latitude.

Longitude is measured
on this line east and west.

On this line the lengths
of the day, time of sunrise
and sunset all differ (ex-
cept twice a year).

The time at any point on
this line agrees with the
time at any other point If
it is XII (noon) at 66}^
north, it is XII (noon) at
66^ south.

On this line the lengths
of the day and time of sun-
rise arid sunset are the
same at all points,

On this line time differs
at every point. No two
points have the same time,
but the relative time of
sunrise and sunset would
be the same at every point.

I have stated that all places in the same latitude
have the same seasons, length of day and night,
hours of sunrise and sunset, etc., but they may not
have the same climatic conditions, on account of

22 CURIOSITIES OF LATITUDE AND LONGITUDE.

various physical causes, mountain ranges, ocean cur-
rents, etc. For instance, England and Labrador are
nearly in the same latitude, but the equatorial cur-
rents that reach England make a mild and soft cli-
mate, while Labrador is cold and sterile.

Sea level temperatures are quite different from
those of mountain tops. A mountain 15,000 feet
high, even at the equator, would have a temperature
about equal to that of the sea level at the Arctic
Circle.

There is a great difference in the United States in
the climate of the Pacific slope and that of the inte-
rior of the same latitude.

So that, although the zones are bounded by mathe-
matically concentric circles, made practically by the
sun's path, the isothermal or heat lines curve accord-
ing to the modifying conditions mentioned.

NOON.

When the sun is on the meridian of a place (i.e.,
when it has attained its highest altitude), it is NOON
at that meridian, and at that meridian only. Only
one meridian can have noon at the same instant; all
others are either in A. M. or p. M. Bear in mind that
a meridian runs from pole to pole, or half around the

CURIOSITIES OF LATITUDE AND LONGITUDE. 23

earth; consequently the antipodal or opposite meridian
must be a midnight meridian. Now, noon is a point
exactly half way (sun-dial time) between sunrise and
sunset, and midnight a point exactly opposite noon.

Of course, in average or mean sun time the fore-
noon may be longer or shorter than the afternoon.

The earth turns uniformly on its axis. Noon is
marching around the world with measured tread.
One meridian after another is brought opposite the
sun.

The period of the rotation is twenty-four hours,
not a second more or less.

LATITUDE AND THE SUN'S MERIDIAN
ALTITUDE.

Latitude will, of course, affect the sun's meridian
altitude. Note the height of the sun in the diagram
on page 24.

It is arranged for March and September; the sun
is vertical on the equator; the angle diminishes from
this (90) to zero at either pole. At the two tropics
the altitude is 66>< and at the two circles 23^ at
noon.

The angle for June, the highest limit north, when
the sun is vertical on the Tropic of Cancer, will

24 CURIOSITIES OF LATITUDE AND LONGITUDE.

extend 23^ beyond the North Pole, so that at the
North Pole the meridian altitude would be 23^.
The angle for December would just touch the Arctic

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LATITUDE NORTH.

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September 21.

Circle; consequently the sun would not appear above
the horizon from that point to the North Pole.

March 21 and September 21 the angle would just

CURIOSITIES OF LATITUDE AND LONGITUDE. 25

touch either pole. The sun would, therefore, be on
the horizon at midday at those points.

The sun's declination- is its distance north or south
of the equator.

To find the sun's meridian altitude, add its declina-
tion for that day to the . co-latitude of the place (the
co-latitude of a place is its latitude deducted from
90); that is, if the latitude and declination are both
of the same name; but if one is north and the other
instance, we have stated that the sun's meridian alti-
tude for the Arctic Circle (66>< north) for the 2ist
of June would be 47. ' The declination of the sun
for this da}- is 23^2 north, and the co-latitude of
66^ would be 23><; this added to the declination
equals 47, which is the meridian altitude of the sun
for that date. When the sun is at a meridian alti-
tude of 45, his rays would fall perpendicularly on
the side of a hill facing the south at an angle of 45.

26 CURIOSITIES OF LATITUDE A;ND LONGITUDE.

Latitude does not affect TIME, except, as we have
stated, the times of sunrise and sunset. I have
explained how the meridian altitude of the sun can
be found from the latitude and the sun's declination.
Here is a simple rule for finding latitude:

LATITUDE HOW OBTAINED.

From 90 (corrected 89 48') deduct the sun's ob-
served altitude, which will equal the zenith distance
(make Z. D. north if sun bears south, or south if the
sun bears north). Add to zenith distance the sun's
declination, if both same name, and the sum will be
the latitude. If one is north and the other is south,
deduct; the latitude will then be the same name as the
greater number. June 2ist the sun's meridian alti-
tude at the Arctic Circle is 47; 90 47 43 (its
Z. D.) added to 23^ (Sun's N. Dec.) = 66}^, or the
latitude.

On the 2ist of December the conditions we have
stated for June in regard to meridian altitude north "and
south would be reversed. The sun is vertical on the
earth only at places between the tropics. The mer-
idian altitude of the sun is therefore never 90 or
vertical (in the zenith) at any place outside of the
Torrid Zone. (Never vertical in the United States. )

CURIOSITIES OF LATITUDE AND LONGITUDE. 27

The sun is vertical on the equator only on the 2ist of
March and 2ist of September; on the Tropic of
Cancer on the 2ist of June and on the Tropic of
Capricorn on the 2ist of December. On March 21
and September 21 the sun's meridian altitude equals
the co-latitude of a place; for instance, the latitude
of Chicago is 42 N. ; the co-latitude is 90 42=
48, the meridian altitude at that date.

90 minus the altitude of a heavenly body equals its
zenith distance.

90 minus the latitude of a place, equals its co-lati-
tude or complement.

90 minus the sun's declination equals its polar
distance. >

Latitude affects the apparent place of the rising
and setting of the sun. In March and September, or
at the two equinoxes, the sun rises due east and sets
due west, but as he advances northward or southward
his rising and setting points advance northward or
southward. On the 2ist of June the sun rises 23^
degrees north of east, but for all places north of the
Tropic of Cancer the sun will be south of the observer
at noon. If the sun is due south at noon, he will be
due north at midnight.

In summer, in the higher latitudes, the sun rises

28 CURIOSITIES OF LATITUDE AND LONGITUDE.

and sets farther and farther from the east and west
points until it is due north.

MIDNIGHT

DIAGRAM SHOWING THE POINTS OF SUN'S RISING AND
SETTING JUNE 21.

CURIOSITIES OF LATITUDE AND LONGITUDE. 29

'THE PHENOMENA OF DAY AND NIGHT.

The phenomena of day and night are phenomena
belonging to both latitude and longitude. On the
2ist of June, two-thirds of the night shadow on the
earth is below the equator and one-third of the night
shadow is above it. On the 2ist of December these
conditions are reversed. The shadow of night on the
earth and the illuminated portions are always exactly
half and half (the shadow, however, includes dawn
and twilight), but the position of the shadow is depen-
dent upon the time of year and latitude. The shadow
is always pivoted at the equator, consequently day
and night at this place are always equal. Twice a
year, March and September, the shadow is perpen-
dicular to the equator; that is, the line of the shadow
is co-incident with the meridian line to which it may
be pivoted. The shadow is always at a right angle
to the sun, so that if the sun is north the shadow is
south; and if the sun is south the shadow is north.
Whatever angle the sun makes with the equator, a
with the meridian. On the 2ist of June and the 2ist
of December the line of the shadow cuts the Arctic
Circle on the one hand and the Antarctic Circle on
the other, and the angle is 23^. At all other times

30 CURIOSITIES OF LATITUDE AND LONGITUDE.

of the year the shadow encroaches upon the polar
regions until the shadow becomes perpendicular, as
stated, March 21 and September 21; so that every
portion of the earth has an equal amount of shadow
and sunshine at some time of the year from pole to
pole.

There is a wonderful compensation balance in the
earth. There is not a spot on its surface that does
not enjoy, at some time, its equal share of the oppo-
sites of night and day, or sunshine and shadow, heat
and cold, summer and winter, etc. This is especially
true of sunshine. All parts of the earth have an
equal amount of sunshine in the yearly distribution
of sunshine.

Take, for instance, the latitude of New York at
the summer solstice, June 21; New York has fifteen
hours of sunshine and nine hours of shadow. The
opposite latitude south, say a place in New Zealand,
has nine hours of sunshine and fifteen hours of shadow.
Now, take December 21; the winter solstice: New
York has nine hours of sunshine and fifteen of shadow,
while New Zealand has fifteen of sunshine and nine

The law ol compensation is exemplified in the
distribution of heat and cold. The greatest heat is
of course in the Torrid Zone, where the rays of the

CURIOSITIES OF LATITUDE AND LONGITUDE. 31

sun fall perpendicularly, and the greatest cold is in the
Frigid Zones, where the rays of the sun fall obliquely
upon the earth. But here comes in the wonderful
compensator}- balance of unequal day and night,
thus in a measure equalizing the heat.

Heat is cumulative. If more heat is received by
day than can be radiated away at night, it grows and
accumulates.

Thus, in the Northern Hemisphere, though the
longest day is reached in June, the hottest days are
in July and August.

At the equator, or in the hot-belt, days and nights
are about equal in length, so that when the sun sets
at b o'clock the earth begins to cool and the heat
gathered during the day is radiated away during the
twelve hours of the night.

Travelers who go to southern states in summer re-
mark upon the coolness of the nights, notwithstand-
ing the hot days.

Thus, this law of compensation (owing to the diur-
nal rotation and the inclination of the axis of rota-
tion), makes all parts of our earth habitable and adapted
to the needs of man.

Day and night must always together equal 24
hours. If the day exceeds 12 hours, the night is
less than 12 hours in exact proportion. Day and night

32 CURIOSITIES OF LATITUDE AND LONGITUDE.

are differential for all latitudes and 24 hours is trie
total.

Knowing the length of either the day or night (by
day and night I mean the time between the rising
and setting, or the setting and the rising sun) it is
easy to get the hours of sunrise or sunset; or, know-
ing the hours of sunrise and sunset, it is easy to get
the length of the day or night.

Double the hour of sunrise for the length of the

night,
And double the hour of sunset for the length of

the day;
Or take half the length of the day for the hour

of sunset,

And half the length of the night for the hour of
sunrise.

CO-INCIDENT PHENOMENA.

The same latitude phenomena occurs in the co-iu-
cident months as follows:

May and July,

April and August,

February and October,
January and November.

In shape the earth is an oblate spheroid, i. e., a
sphere slightly flattened at the poles, with an excess

CURIOSITIES OF LATITUDE AND LONGITUDE. 33

of matter at the equator. Its polar diameter is 7,899
and its equatorial diameter 7,925 statute miles; the
value of a degree therefore at the poles is 0.7 of a
mile greater than at the equator. Its circumference
is 24,897 statute miles. Latitude is measured north
and south from the equator, and the latitude of a
place is its distance in degrees north or south of the
equator. Probably sea levels in corresponding lati-
tudes north or south of the equator are equi-distant
from the earth's center.

THE NORTH POLAR STAR.

Latitude affects the height of the Pole Star, which is
always at an altitude equal to the observer's latitude.
The farther we go north, the higher the Pole Star
appears above our horizon.

To an observer at the equator, the Pole Star will be
on his horizon. Standing at the North Pole this star
would be in his zenith. At any latitude between
these two places the star will appear at a correspond-
ing altitude. At New York, for instance, the star
will appear about 41 degrees above the horizon.
At the latitude of Chicago, 42 degrees.

At London it would be 52, and at Christiania, Nor-

34 CURIOSITIES OF LATITUDE AND LONGITUDE.

way, the star would appear about 60 degrees above
the horizon.

Every degree we move north, the North Star moves
a degree higher in the heavens. It is easy to find
the value of a degree of latitude, for if a ship sails
about 69 miles north or south the Pole Star would
move a degree north or south ; hence 69 miles must be
about the value of a degree of latitude. Note the
table on pp. 72-73. This will show the exact value
of a degree of latitude; it varies from 68.698 to
69.392, i. e., expressed in English statute miles.

The diurnal (daily) rotation (apparent) of the north-
ern heavens is contrary to the hands of a watch.

The earth is our observatory, but bear in mind it is
a movable observatory. The apparent movements of
the celestial bodies are due solely to the movements
of our earth. The center of gravity possibly may not
lie in the center of our earth. The greater land por-
tion of the earth is in the Northern Hemisphere, and
the greater part of this land portion is in the eastern
half, between 15 W. and 160 E. Long.

The magnetic pole is not the North pole, but is in
about 105 West Long, and 75 North Lat.; the com-
pass will not therefore always point North. The
variation must be known and corrected by the navi-
gator.

CURIOSITIES OF LATITUDE AND LONGITUDE. 35

As regards the moving circle of rotation, East and
West are arbitrary terms. There is no East or West
in a circle.

DIRECTION OF DIURNAL ROTATION.

The diurnal rotation of the earth causes an appar-
ent diurnal rotation of the heavens. In the northern

36 CURIOSITIES OF LATITUDE AND LONGITUDE.

hemisphere it will be seen that the north celestial
pole is the point about which the heavens revolve.
Here a star has no diurnal motion. The north celes-
tial pole is in a line with the axis of the earth. A
prolonged exposure photograph of the circumpolar
stars (i. e., those stars which are above the observer's
horizon) show concentric rings of light. Even the
Pole Star itself leaves a little trail of light as it revolves
around the true pole, about a degree and a half from
it. The true celestial pole is that point in the heav-
ens where the axis of the earth, if prolonged, would
pierce the heavens.

Although the diurnal rotation of the earth is unvary-
ing, this great clock having kept time through all
the ages without the loss of a second, yet the axis
of the earth is not (according to recent investiga-
tions and experiments) a rigid or fixed line in
the earth; i. e., the North Pole does not maintain an
absolutely fixed position. This, of course, affects lat-
itudes.

CURIOSITIES OF LATITUDE AND LONGITUDE. 37

DAWN AND TWILIGHT.

Latitude affects the amount and duration of twi-
light; the duration varies with the season and the
latitude, the longer twilights existing in the north-

TWILIGHT PROJECTION.

38 CURIOSITIES OF LATITUDE AND LONGITUDE.

ern latitudes (in summer), and in the southern latitudes
(in winter).*

The reason for this is that the greater the distance
from the equator north and south, the more oblique is
the line of the setting or rising sun with the horizon;
consequently the greater length of time occupied in
reaching the 18 limit of reflection. The sun ap-
proaching the horizon vertically, reflection would dis-
appear much sooner than if he approached it at an
oblique angle.

Dawn and twilight are of equal duration. They
are both included between the setting and rising of
the sun. Twilight continues until the sun is 18 be-
low the horizon. Dawn begins when the sun is 18
from rising.

CHANGES IN THE APPEARANCE OF THE
HEAVENS.

Another curiosity of latitude is the change in the
appearance of the heavens at different points.

*It should be borne in mind that in speaking of summer and
winter, we mean that portion of the year representing the summer
and winter of the Northern Hemisphere. December is the sum-
mer of the Southern Hemisphere and June the winter season.

CURIOSITIES OF LATITUDE AND LONGITUDE. 39

On the equator at latitude zero, stars will rise and
set vertically, cutting the horizon at right angles. At
the poles or latitude 90, the stars would neither
rise nor set, but would revolve around the pole
in concentric circles at altitudes corresponding to their
declinations. The moon would be visible for about
two weeks, and the sun for six months at a time.

At any latitude between the equator and the poles,
the stars would rise and set obliquely.

LATITUDE AFFECTS GRAVITY.

A body would weigh more at the poles than at the
equator, but if weighed with ordinary weight balances
the difference would not show, as the weights them-
selves would be affected as well as that which is
weighed.

A pendulum swings faster at the poles than at the
equator. A pendulum clock that would keep accu-
rate time at the equator, would gain 3 y z minutes a
day at the poles; moreover, as a pendulum would
swing in a true plane, the rotation of the earth would
cause it to form a star marked upon the surface of the
globe could it swing about the pole.

Such are some of the curiosities of latitude. We
might recapitulate some of the effects, as follows:

40 CURIOSITIES OF LATITUDE AND LONGITUDE.

1. Varying lengths of day and night.

2. The hours of sunrise and sunset.

3. The angle of the sun.

4. The place of the sun's rising and setting.

5. The peculiar angles of the rising and setting

of stars.

6. The position of the night shadow.

7. Variation in length of degrees.

8. Height of the Pole Star.

9. The circles of perpetual apparition and occul-

tation.

10. Twilight and dawn.

11. Gravity.

12. The pendulum.

The curiosities of latitude mentioned are those
which are due solely to the motions of the earth. I
have not touched on the physical aspects of latitude
except incidentally.

The work is intended to show those phenomena
which come within the reach and scope of Mathemat-
ical Geography.

CURIOSITIES OF LATITUDE AND LONGITUDE. 41

LONGITUDE AND TIME.

LONGITUDE

is the angular distance between any two meridians.
It is reckoned, east or west, from any given meridian,
called a first or prime meridian. Meridian circles
run around the earth north and south, and a meridian
reaches from pole to pole. Meridian lines all con-
verge at the poles, and cut the equator at right
angles. The greatest longitude any place can have
is 1 80, or half around the globe. Longitude is ex-
pressed in degrees, minutes and seconds.

WHAT IS TIME ?

A part of duration.

The system of those relations which any event has
to any other, past, present or future; an arc cut out
of the circle of eternity.

Time is personified as an old man, bald-headed,
but having a forelock, and carrying a scythe and
hour-glass.

42 CURIOSITIES OF LATITUDE AND LONGITUDE.

Tempus (L.), Temps (P.), Tempo (P. I.), whence
temporal, temporary, etc. Cent. Die.

Chronos Time. Chronology Reckoning of time.

Time has been compared to a stream, or the flow of
a river; the part that goes by now will never pass
again.

Time is a procession of seconds, minutes, hours
and days, months, years and centuries, ever march-
ing on.

How is time measured ? What is our chronometric
register? What is the standard unit?

THE EARTH OUR CLOCK.

The axial rotation of the earth once in 24 hours,
or one day, gives us our exact standard of measure-
ment.

By the word day, we mean the whole 24 hours, or
the period of one rotation of the earth upon its axis.
From dial, dies, come diary, diurnal, day. Cent.
Die.

Day and night must always equal 24.
60 seconds i minute.
60 miriutes=i hour.
24 hours =i day, or period of the Earth's

rotation.
24 hours=i44o minutes, or 86,400 seconds.

CURIOSITIES OF LATITUDE AND LONGITUDE. 4.3

The earth, in its rotation, obeys an original im-
pulse. This movement of the earth does not come
under the law of universal gravitation. When a body
turns upon a true and symmetrical axis and gravity
is not brought into play, the axis will maintain its
unvarying position.

A gyroscope top illustrates this. When set in
motion, the axis always maintains the direction in
which it is placed. There may be two movements
of the gyroscope top the one a rapid rotation on its
axis, the other a slow, conical movement of its axis,
owing to a rotation of the top, frame and all.

The earth was set spinning with the northern end
of its axis pointing to the north celestial pole, and
that position it still maintains.

It is true there is a slow circular motion of the pole
of the earth around the pole of the ecliptic, causing
the precession of the equinoxes, i.e., the zenith of the
poles change about 20" annually. In time, therefore,
Polaris will cease to be the Pole Star. There is also
a slight oscillation of the pole itself, but practically
the axis maintains its true position.

Polaris, the bright polar star, is the jewel in which
the axis is pivoted, though at present Polaris, strictly
speaking, is i 16' from the true north celestial pole.
The earth turns upon its axis, or polar diameter, in

44 CURIOSITIES OF LATITUDE AND LONGITUDE.

an inclined position of 23^, in exactly 23 hours, 56
minutes, 4^ seconds, expressed in mean solar time,
from west to east, as do all the planets.

A SIDEREAL DAY.

This is a sidereal day. It is the length of time
that elapses between two successive transits of the
same fixed star across a meridian.

Let not the student be confused because a sidereal
day is shorter than a mean solar day.

There are exactly 24 sidereal hours in a sidereal day,
and exactly 24 mean solar hours in a mean solar day,
but a sidereal day expressed in mean solar time is 4
minutes shorter than a mean solar day. As regards
the earth, the sun moves, while the stars do not.

The gain of mean solar over a sidereal day of 4 min-
utes a day, amounts to 2 hours a month, or i day a
year. A sidereal clock (such as are used in observa-
tories) and a mean solar clock, therefore, do not
coincide, except on the 2ist of March. The hands
would then agree. The difference of 24 hours would
not appear. Like the hands of a watch, they are not
together at any hour except 12 o'clock.

The earth, in its diurnal rotation sweeps the entire
circle of the heavens. All circles contain exactly

CURIOSITIES OF LATITUDE AND LONGITUDE. 45

360. The 360 of this circle are traversed in exactly
24 hours, and as 360-^24=15, it is evident that each
hour of the 24, the earth passes through just 15.

Now the day contains 24 hours, 1440 minutes or
86,400 seconds, and the 360 contains 21,600 minutes
or i, 296,000 seconds ; hence the earth will pass through
15 in one hour, 15' in one minute, and 15" of arc in
one second.

The accuracy and steadiness of the turning of the
earth are so remarkable that each fractional part of
the 24 hours will show an exact proportionate num-
ber of degrees, minutes and seconds of arc passed
over; in fact, when the last second of the 24 hours is
passed, the last second of the 1,296,000 seconds of
arc is also finished.

A WONDERFUL CLOCK.

The next beat of the clock begins the first 15" of
the circle again, and every beat of the pendulum
thereafter carries the earth through 15" of arc.

When we consider the accuracy of this magnificent
clock, we are astonished. The best time-keepers are
lever escapements and chronometer balances; watches
of high-class makes, with care in wearing, will run
within one second per week. Tiffany of New York

46 CURIOSITIES OF LATITUDE AND LONGITUDE.

has records of watches running ten months with a
variation of only seven seconds.

Full chronometers are not in use for pocket wear;
they are liable to be affected by any sudden motion
of the wearer.

Our chronometer is liable to no accidents; it needs
no oiling or cleaning; it never runs down. No clock
that was ever constructed can ' ' keep time' ' with the
earth. This clock is adjusted to heat, cold and posi-
tion. It is self-winding, never gets out of order, and
is synchronized -to beat with the stars. It has not lost
a beat through all the ages; that is, the time of its
rotation has not varied in thousands of years.

The star that is cut in two by the line in the field
of the transit telescope at 8 o'clock, sidereal time,
tonight, will be cut in two by the same line at pre-
cisely 8 o'clock, sidereal time, tomorrow night, and
the next night, and so on through the years and ages.

The figures on p. 47 represent two sections cut from
a globe and a Mercator map, respectively. The
space represents one hour or 15. It will be seen
that all the parallel horizontal lines and spaces have
the same value, both in time and degrees.

Time and longitude are synonymous.

It will be observed that a point at u ^4" moves very
slowly compared with a point at "/)," yet the time

CURIOSITIES OF LATITUDE AND LONGITUDE. 47

occupied will be precisely the same. "Z>" represents
the equator.

POLE

EQUATOR

A point on the earth's surface at the equator moves
toward the east at the rate of about 1,000 miles an
hour, because the earth's equatorial circumference is
about 25,000 miles, and as it takes 24 hours for one
complete rotation, a point here would move, in one
hour, one twenty-fourth of the circumference, or
about 1,000 miles. This motion is reduced to noth-
ing at the poles.

48 CURIOSITIES OF LATITUDE AND LONGITUDE.

At the latitude of New York, the motion is about
800 miles per hour, and at the latitude of Christiania,
it is reduced to 500 miles per hour; but a point on
the equator passes over 15 in one hour; so does a
point at the 6oth parallel.

The hare at the equator will arrive at his destina-
tion at the same instant as the tortoise at the 6oth
parallel. All hour circles have the same value,
whether they contain 60 miles or one mile to a
degree.

Longitude is not synonymous with miles. It is
not measured in miles, but in degrees. An hour
angle contains 15, whether it contains 900 miles (as
at the equator), or one mile (as at the 8gih parallel).

See table on page 70.

CURIOSITIES OF LATITUDE AND LONGITUDE. 49

THE SUCCESSION OF DAYS.

Now let us see how the days follow each other.
When and where does a day begin? Where does
Saturday or Sunday begin? Is Sunday universal
over the earth, or is it partly Sunday and partly
Saturday or Monday or some other day? Is today
the same day of the month at New York and New
Zealand, at Bombay and at San Francisco?

Let me say that there is always day and night on
the globe that is to say, somewhere it is always per-
petual day and somewhere perpetual night around
the world. The sun is always waking up the morn-
ing and chasing away the shadows of night.

"Somewhere the glorious morning hues,

Somewhere upon this earth of ours

You'll find 'tis always morning."

And night is always following up the day. Where,
then, does the day begin? Now suppose we begin
our investigation of this subject at Chicago, near the

50 CURIOSITIES OF LATITUDE AND LONGITUDE.

9oth meridian of west longitude, on, say Saturday
morning at 6 o'clock, we shall find the local time of
New York to be 7 o'clock A. M.; 10 A. M. at the
Azores in mid- Atlantic, noon at London, 7.30 P. M.
at Pekin, China, while at New Zealand the day is
drawing to a close. Thus it is early morning at
Chicago, breakfast time in New York, dinner time in
London, and supper time in Pekin all in the same
day.

Suppose now we take a step to the westward of
Chicago. It is 4 A. M. at San Francisco, and 1.30
A. M. at Honolulu. But all this is Saturday, a civil
day twenty-four hours long, and as the civil day
begins at midnight, it is evident that this particular
day was born a little to the west of Honolulu. Civil
days are divided into periods of twelve hours each;
hence all clock dials are divided into twelve spaces of
one hour each.

To a person living at Honolulu, then, Saturday
has just begun; to one living in London it is noon of
Saturday; to one living in New Zealand Saturday is
nearly over and he is sleeping into Sunday morning;
to a resident of Chicago, Sunday is eighteen hours
away, while to a Londoner, it is but twelve hours
away. Now it is clear that by the time Sunday gets
to Honolulu, it is Monday morning at "New Zealand.

CURIOSITIES OF LATITUDE AND LONGITUDE. 51

Though Honolulu and New Zealand are not far apart
in longitude, they are widely apart as regards lati-
tude, the one being in north and the other in south
latitude. But latitude does not affect time.

People who live on the opposite side of the earth,
or Antipodes, have opposite latitudes, longitudes,
days, nights and seasons.

The people of Europe have observed their Sunday
while the people of the United States are sleeping,
and while the people of the United States are observ-
ing their Sunday, the people of Europe are sleeping
into Monday morning. It is evident, therefore, that
for purposes of commerce and navigation, there must
be a beginning somewhere of a day, at some point on
the earth a day must begin and end, that is, the com-
mercial civil day; Saturday, for instance, the day we
have just been describing.

WHERE DOES THE DAY BEGIN?

The point opposite noon would evidently be the
best TIME point, and a point farthest removed from
land and civilization, the best GEOGRAPHICAL point
with which to begin a new day. I/mdon being the
metropolitan city of the earth, the geographical center
of the land portion and the commercial center, it is

52 CURIOSITIES OF LATITUDE AND LONGITUDE.

fitting also that it be the time center, and that the
meridian of London should be the first meridian. A
point opposite London in the Pacific ocean is a point
farthest removed from this center of the world's
civilization; it is therefore the best point to begin the
day.

The maritime powers of the world have agreed
to regard this iSoth degree of longitude from
London (or Greenwich) as the point where the day
changes. This meridian therefore leads the day.
Its passage under the iSoth or midnight celestial
meridian marks the beginning of a new day for the
earth ; here today becomes tomorrow. We have a new
date for the month, and a new day for. the week in
the transition. It is here that Saturday ends and
Sunday begins.

It is here, then, that Sunday was born, just to the
west of Honolulu, but bear in mind that the day
travels westward, therefore this new born day does
not visit Honolulu until it has made the circuit of
the round globe. Sunday travels west via New
Zealand.

Honolulu and New Zealand are only about 30
apart in longitude, but they are a whole day apart as
regards any particular day, because the point at which
the day changes lies between them. Again, it is

CURIOSITIES OF LATITUDE AND LONGITUDE. 53

evident that Sunday is a long way off from Honolulu,
because that place has only just passed out of Friday
into Saturday, whereas New Zealand is passing out
of Saturday into Sunday.

Sunday travels west, because the earth travels east.
Sunday must visit China, Russia, India and all of
Europe, must cross the Atlantic and the United
States before it can reach the Pacific and Honolulu,
and no sooner does Honolulu get out of Saturday into
Sunday, than Monday morning appears at New Zea-
land.

THE INTERNATIONAL DATE LINE.

The international date line, though practically the
iSoth meridian, is a line drawn irregularly through
the Pacific ocean, south through Behring- sea; south-
west past the Aleutian islands; south from Attu island
on meridian 172 south, to parallel 15 north; east on
1 5th parallel to i5Oth meridian west; south on i5Oth
meridian to parallel 15 south; west, clearing Society
islands, to meridian 155 west; south to Tropic of
Capricorn; southwest by south indefinitely.

The day begins here, at the iSoth meridian and
travels west, because the earth travels east. When it
arrives at London it is about 12 hours old, at New

54 CURIOSITIES OF LATITUDE AND LONGITUDE.

20 hours old.

When the day arrives here at the iSoth meridian,
it is 24 hours old; it gradually grows less and less,
with the new day following, the old day diminishes and
the new day increases. When noon arrives here, the
end of the day is at London, with the new day
following close.

The preceding day is west of the line, the succeed-
ing day is east of it.

The longitudinal quadrants of the earth are as
follows :

XII NOON The initial meridian London.
VI A.M. The goth meridian of W. L. Chicaj

CURIOSITIES OF LATITUDE AND LONGITUDE. 55
MIDNIGHT The iSoth meridian Pacific

Oceaff.

VI P.M. Tr^oth meridian of E. L. Calcutta.

These are the four cardinal points of the circle.

In studying the above diagram, it is necessary to
bear in mind the point of view, which is the iSoth
meridian, looking through the globe to London. It
does not represent the plane of any parallel, but is
designed to show longitude. When XII (noon) is at
London, one day and date prevail over the entire
earth. If' noon is either east or west of London, parts
of two days are in operation. When noon is at London,
there is only "a today" upon the earth. When noon
leaves London, there is "a today," "a yesterday"
and "a tomorrow" in operation.

Suppose, for instance, noon had arrived at Chicago-
Chicago's antipodal meridian is the meridian which
passes through Calcutta. Therefore, if it is noon at
Chicago it is midnight at Calcutta. All of that portion
of the earth east of Calcutta is therefore in tomorrow,
and there people could say of that portion of the earth
west of Calcutta (which would include of course Chi-
cago) "that is in yesterday,"- and everyone has "a
today. ' ' When it is noon at London only one day occu-
pies the earth simply because there are 1 2 hours either
side of noon, and 12 hours in either direction would

56 CURIOSITIES OF LATITUDE AND LONGITUDE.

produce midnight. The opposite meridian from Lon-
don being the iSoth degree, of course, there it would
be midnight. The antipodal meridian of any place
is the one removed from it by 12 hours, or 180 degrees.

To find your antipodal meridian, deduct from 180
in opposite longitude. For instance, what is the
opposite (or antipodal) meridian to New York (75th
W. L.) 180 75=105; 105 E. L. is the antipodal meri-
dian to New York.

When noon leaves London on its travels west (every-
thing goes west) and arrives at the i5th degree of
west longitude, or, in other words, has advanced one
hour to the west, the new day starting at the iSoth
meridian is one hour old and has advanced to the
i65th degree of east longitude.

We have explained how the two places, Honolulu
and New Zealand, are near together and yet practic-
ally a whole day apart, Honolulu being, just east of
the line and New Zealand just to the west of it We
have explained that the day travels west, so New
Zealand is the first to see the new-born day. It is
clear, then, if it is Friday (near midnight) at Hono-
lulu to the east of the line and Sunday (near i A. M.)
to the west of it, that a ship which sails from Honolulu
to New Zealand, or from east to west, must sail out of

CURIOSITIES OF LATITUDE AND LOXGITUDE. 57

Friday into Sunday, and thereby skips the interven-
ing day of Saturday, and gains a day, while vice versa,
a ship which sails from New Zealand (where Sunday
has begun) to Honolulu, where Friday has just ended
and Saturday begun, or from west to east, must lose
a day, because it has to go back into Friday. Now
this change of date at the i8oth meridian must npt be
confounded with the gain or loss of time in trawling
east or west with or against the rotation of the Barth.
To gain or lose on the sun we must move our noon
point. The moment we leave our position, i. e. , our
meridian, we gain or lose, just in proportion to the
number of degrees passed over.

GAIN OR LOSS OF TIME.

For instance, if we leave New York at the 75th
meridian and sail east to London, we have gained as
many hours as fifteen is contained in seventy-five, or
five hours, i. e., our noon in New York is five hours
back of the noon we are now experiencing; or, in
other words, noon of London is 7 A. M. at New York,
and noon of New York is 5 p. M. of London. Here
we gain absolute time, and this time is in exact pro-
portion to the number of degrees passed over. In the
other case an arbitrary line changed our date and put

58 CURIOSITIES OF LATITUDE AND LONGITUDE.

us backward or forward in our dates. Moreover the
crossing of this iSoth meridian makes us gain the
day as we go west and lose as we go east. In sailing,
as regards the sun, just the reverse of this is true.
We gain time in sailing east and lose time in sailing
west, and in the latter case the time bears an exact
proportion to the number of degrees passed over,
while in the former we jump a whole day.

Every 15 passed over east or west is one hour of
time, and as there are 360 in the entire circuit we
should gain or lose in making the entire circuit just
twenty-four hours, or one day, because 360 -f- 15= 24.

Now we may creep over the 15 or fly over them
the result is just the same. With Jules Verne we may
circumnavigate the globe in eighty days, or we may
take eighty years to do it. We shall in either case
lose or gain but twenty-four hours.

How shall we reconcile this gain in traveling east-
ward with the loss in covering the i Both meridian?

Now in sailing, say from 30 west of New Zealand
to 30 east of Honolulu (for purpose of illustration let
us imagine these two places to be on the iSoth meri-
dian), we have passed to the east 60, a four hours'
&ain in time, but in doing this we crossed the line
going east, so we lost a day. What have we lost
or gained? Well, we have lost a day and gained

CURIOSITIES OF LATITUDE AND LONGITUDE. 59

four hours. In other words we have lost twenty
hours.

Suppose it was 10 A. M. of Sunday 30 west of the
line, 30 east of it is 2 P. M. of Saturday. If Sunday
was July 31, then we shall find our date to be Satur-
day, July 30, at 2 P. M., because we count back
twenty hours from 10 A. M. Sunday.

So a ship which sails east from London around the
world crossing this meridian, will lose a day and gain
half a day. That is to say if it is noon Saturday, July
31, at London, it is midnight of Saturday, July 31,
at this meridian.

Now at this arbitrary line or the iSoth meridian,
we have practically parts of two days in operation,
while at all other places on the Earth there is but one
day. On the line we have the midnight hours of
Friday and the early hours of Sunday, the rest of the
globe being occupied by Saturday. Saturday is
flanked on the one side by Friday and on the other
by Sunday/

I have stated that Honolulu and New Zealand were
a whole day apart practically they are yet this is
not strictly correct. The difference is not exactly a
whole day, by putting it thus the student at once
grasps the idea that one place is in one day of the
week and the other in another day of the week.

60 CURIOSITIES OF LATITUDE AND LONGITUDE.

The aim is to make it perfectly clear why it is
Saturday in one place and Sunday in another on the
earth.

CIRCUMNAVIGATING THE GLOBE.

If a ship were to circumnavigate the globe on the
equator, at the rate of 900 geographical miles a day,
it would take just twenty-four days to do it, because
15 multiplied by sixty, the number of miles in a
degree at the equator, would produce 900, and as 15
is one twenty-fourth of the circumference it would
take just twenty-four days to sail the 360. Now as
the meridians converge at the poles, the number of
miles to a degree grows less and less as we approach
the poles. At 60 north latitude, for instance, there
are only thirty miles to a degree, consequently a ship
sailing 900 miles a day will take but twelve days to
circumnavigate the globe on this parallel.

Time and longitude are synonymous, but not time
and distance.

We cannot measure miles east or west without
knowing on what parallel they are to be measured.
There is no time and longitude at the absolute poles.
Nor is it needed. We cannot sail much nearer than
10 of the poles. The moment, however, we leave

CURIOSITIES OF LATITUDE AND LONGITUDE. 6 1

the pole, the meridian lines have an appreciable
angle, therefore, longitude can be computed.

Now the earth performs a complete rotation on its
axis in exactly twenty-four hours, and in doing this
goes through exactly 360, and each fractional part of
the twenty-four hours will show an exact correspond-
ing number of degrees (of arc) passed over. It is
evident from this that degrees of longitude and
hours of time are convertible and interchangeable
terms. Longitude means length as latitude means
breadth, though latitude has nothing to do with
time.

There are 21,600 minutes, or 1,296,000 seconds of
arc in 360. Also there are 1440 minutes, or 86,400
seconds of time in twenty-four hours. Now by divid-
ing degrees by hours, or minutes by minutes, or
seconds by seconds, we shall see that fifteen degrees of
longitude will equal one hour of time, fifteen minutes
of longitude one minute of time, and fifteen seconds
of longitude one second of time.

The difference in longitude between any two places
is the angular distance between their meridians, and
is expressed in degrees and fractions.

Now if we knew the local time of two places, we
could easily reduce this time to degrees of longitude
by multiplying the number of hours by fifteen, which

62 CURIOSITIES OF LATITUDE AND LONGITUDE.

would give degrees, or by adding four minutes for
each degree.

On land it is easy to get simultaneous times by
telegraph, but at sea this could not be done, except in
some instances, as, for instance, when the Atlantic
cable was laid, the time was transmitted daily from
the land to the ship.

Knowing the difference in time, and consequently
the longitude, it is easy to get the distance, i. e. ,
taking into account the number of miles to a degree
on a given parallel. With each degree of latitude,
however, the miles in a degree of longitude decrease
from the equator to the pole. This is easily understood
by observing how the meridian lines converge towards
one another at the poles, on a globe, as we have ex-
plained.

The greatest longitude a place can have, east or
west, is 1 80, though sometimes it is reckoned clear
around the globe from a given meridian.

CURIOSITIES OF LATITUDE AND LONGITUDE. 63

THE FINDING OF LONGITUDE,

London (or Greenwich) time is the standard for
navigators all over the world. It is the universal time
meridian. Every ship, therefore, carries a chronom-
compensation balance, hung and balanced so as to be
affected as little as possible by the motion of the ship,
and this chronometer is set to

Greenwich Mean Time.

To find his longitude, the navigator must know the
mean time of the ship, and Greenwich mean time.
This latter should be kept by the ship's chronom-
eter (and the error of rate known, to be cor-
rected in calculation). His own observations must
be corrected for dip (distance from the sea level), re-
fraction, parallax, and also for the semi-diameter of
the sun (if he observes the sun). In other words, the
navigator must know the hour angle of the sun. In
order to get this he must know

64 CURIOSTTIES OF LATITUDE AND LONGITUDE.

1. His Tatitude.

2. The ?tm's altitude, and

3. The sun's declination for that day.

And when he has found apparent sun time, it must
be corrected (by equation) to mean sun time; then
having found the mean sun time of the ship, and
noted the difference between it and Greenwich mean
time, longitude is easily ascertained by converting
the difference in time found into longitude.

Latitude is taken at noon, when the sun is near the
meridian, but longitude observations are taken morn-
ing or evening when the sun is a few degrees above
the horizon.

The instrument used is called a sextant, because it
represents the sixth part of a circle.

If the navigator finds the local time of the ship to be
later in the day, then he is in east longitude. If he
finds it to be earlier in the day, he is in west longitude,
because as the earth travels towards the east, places to
the east of us will be later in the day, while those west
of us will be earlier in the day. For instance,
if the time of the ship be noon, and the captain finds
that his chronometer says 8 A. M., then he is in 60
east longitude. But if his chronometer says 4 p. M.,
then he is in 60 west longitude.

We have shown how time is kept by the rotation of

CURIOSITIES OF LATITUDE AND LONGITUDE. 65

the earth. Now the solar or sun day is variable, but
bear in mind that it is the length of the day, plus the
length of the night, that makes the whole day.

The solar day is variable. Not so the rotation of
the earth. That is forever the same. It is the mean
sun, or average sun, that makes the true day.

The time as kept by clocks is mean sun time. It is
the time representing the 24 hours of the earth's ro-
tation.

Sidereal time is time as referred to the stars. A
sidereal day, expressed in sidereal hours, is the same
as a mean solar day expressed in mean solar hours.

The sun travels in the ecliptic or obliquely across
the earth; if he traveled in the equater, he would move
uniformly, and his path could be divided into 24
equal parts, but as he moves obliquely we are obliged
to make an average sun (or mean sun). Apparent,
or real sun time, therefore, is not the same as mean sun
time. The difference varies from o to 15 minutes.

In speaking of noon being exactly half way be-
tween sunrise and sunset, we mean apparent noon.

In closing let me say that a great many cobwebs
will be brushed away by bearing in mind two facts:
First, that the earth rotates in exactly twenty-four
hours. Second, that it sweeps through the grand
circle of 360 in just that period. And when we

66 CURIOSITIES OF LATITUDE AND LONGITUDE.

come to understand that it has done this for ages
without appreciable loss, we are simply astonished at
the accuracy of this magnificent clock, and the wis-
dom that planned it.

CURIOSITIES OF LATITUDE AND LONGITUDE. 69

Not only would they cut through cities, but streets
and even houses, so that possibly it might be six
o'clock in the parlor and seven o'clock in the kitchen
of a house.

Moreover, as Captain Parker states in his ' ' Fa-
miliar Talks on Astronomy," "standard time is
not natural, and it would produce in some instances
curious anomalies ; for instance, suppose standard time
was 30 minutes later than real sun time at a given
place. On March 2ist the sun would then rise at 6:30
standard time, and set at 6:30 standard time at that
place; that would make the morning 5^ hours long
and the afternoon 6^ hours long." Nevertheless, I
am an advocate for a system of universal standard
time for the earth, because it is of great benefit to
travelers. And I hope all the nations of the earth
will soon adopt it for all railway and steamer lines.

70 CURIOSITIES OF LATITUDE AND LONGITUDE.

LONGITUDE.

The following table gives the number of miles in
a degree at each parallel from the equator to the pole:

LENGTH OF A DEGREE OF LONGITUDE AT EACH
PARALLEL OF LATITUDE.

STATUTE

NAUT.

STATUTE

NAUT.

LAT.

MILE.

MILE.

LAT.

MILE.

MILE.

O

69.160

60.000

45

48. 986

42.498

I

69.150

59-991

46

48.126

4I-752

2

69.119

59-964

47

47-25I

40.992

3

69.066

59-9I9

48

46.362

40.223

4

68.992

59.855

49

45-459

39-439

5

68.898

59-773

50

44.542

38-643

6

68. 783

59-673

5 1

43.611

37-835

7

68. 647

59-555

52

42.667

37.016

8

68.491

59-4I9

53

41.710

36.186

9

68.314

59-265

54

40.740

35-344

10

68.116

59-093

55

39-758

34-491

ii

67.898

58.904

56

38.763

33.628

12

67.659

58.697

57

37-756

32.755

13

67.400

58.472

58

36.737

31.872

H

67.120

58.229

59

35-707

30.979

15

66.820

57.968

60

34-666

30.076

16

66.499

57.690

61

33-6i5

29.164

17

66.158

57-394

62

32.553

28.242

18

65.797

57.081

63

31.481

27.311

19

65.416

56.751

64

30-399

26.372

20

65-015

56.404

65

29.308

25-425

CURIOSITIES OF LATITUDE AND LONGITUDE. 7 I

STATUTE

NAUT.

STATUTE

NAUT.

LAT.

MILE.

MILE.

LAT.

MILE.

MILE.

21

64.594

56.039

66

28. 208

24.471

22

64.154

55-657

67

27.100

23-509

23

63-695

55.258

68

25-983

22.540

24

63.216

54-843

69

24-857

21.564

25

62.718

54'4H

70

23.723

20.582

26

62.201

53-962

7i

22.582

19-593

27

61.665

53-497

72

21-435

18.598

28

61. no

53-oi6

73

20.282

17-597

2 9

60.536

52.518

74

19.122

16.590

30

59-944

52.005

75

!7-95 6

I5-578

3 1

59-334

5*-476

76

16.784

14.561

32

58.706

50-931

77

15.607

13-539

33

58.060

50-370

78

14.425

12.513

34

57-396

49-794

79

13-238

11.484

35

56.715

49-203

80

12.047

10.452

36

56.016

48.597

81

10.853

9.417

37

55- 3

47.976

82

9-656

8-379

38

54-568

47-340

83

8.456

7-338

39

53- 8l 9

46.690

84

7-253

6.294

40

53-053

46.026

85

6.048

5.248

4i

52.271

45-348

86

4.841

4-200

42

51-473

44-656

87

3-632

3-!5i

43

50-659

43-950

88

2.422

2. 101

44

49.830

43-231

89

1. 211

1.050

72 CURIOSITIES OF LATITUDE AND LONGITUDE.

LATITUDE.

The earth is an oblate spheroid, i. e. , its Polar
diameter is about 26^/2 miles shorter than its Equa-
torial diameter.

Were the earth a perfect sphere, the miles in a
degree of latitude would be the same at each parallel.
They do not vary much, however, as the following
table will show:

LENGTH OF A DEGREE OF LATITUDE AT EACH
PARALLEL.

STATUTE

NAUT.

LAT.

MILE.

MILE.

O

68.698

59.600

I

68.698

59.600

2

68.699

59.601

3

68.700

59.602

4

68. 702

59-603

5

68. 704

59-605

6

68.706

59.607

7

68. 709

59.609

8

68.712

59.612

9

68.715

59-6I5

10

68.719

59.618

ii

68.723

59.621

12

68.728

59-625

J 3

68-733

59.629

14

68.738

59-634

15

68.744

59-639

STATUTE

NAUT.

LAT.

MILE.

MILE.

45

69.044

59-899

46

69.056

59.910

47

69.068

59.920

48

69. 080

59-931

49

69.092

59-941

50

69.104

59-951

5i

69.116

59.962

52

69.128

59-972

53

69. 140

59.982

54

69.151

59-992

55

69.162

60.002

56

69.173

6O.OI2

57

69.184

60.022

58

69. 195

60.032

59

69.206

60.041

60

69.217

60.050

CURIOSITIES OF LATITUDE AND LONGITUDE. 73

STATUTE

NAUT.

LAT.

MILE.

MILE.

16

68.750

59-645

17

68-757

59-65I

18

68.764

59-657

19

68.771

20

68.779

59.669

21

68.787

59.676

22

68.795

59-683

23

68.804

59.691

24

68.813

59.699

25

68.822

59-707

26

68.831

27

68.840

59-723

28

68.850

59-731

29

68.860

59-740

3

68.870

59-749

31

68.881

59-758

32

68. 892

59-767

33

68.903

59-776

34

68.914

59.786

35

68.925

59-796

36

68.936

59.806

37

68.947

59.816

38

68.959

59.826

39

68.971

59-836

40

68.983

59.846

4 1

68.995

59.856

42

69. 007

59.866

43

69.019

59-877

44

69.031

59.888

STATUTE

NAUT.

LAT

. MILE.

MILE.

6l

69.228

60.059

62

69.238

60.068

63

69.248

60.077

64

69.258

60.086

65

69.268

60. 094

66

69.277

60. 102

67

69.286

60. no

68

69.294

60.117

69

69.302

60.124

70

69.310

60.131

7 1

69.318

60.137

72

69.326

60. 143

73

69-333

60. 149

74

69-339

60.155

75

69-345

60. 161

76

69-35I

60.166

77

69-357

60.171

78

69.362

60.175

79

69.367

60.179

80

69.371

60.183

81

69-375

60.186

82

69.378

60.189

83

69.381

60.192

84

69.384

60.194

85

69.387

60.196

86

69.389

60. 198

87

69.390

60. 199

88

69.391

60. 200

89

69.392

60.201

74 CURIOSITIES OF LATITUDE AND LONGITUDE.

To convert nautical miles into statute miles,
multiply nautical miles by 1.15266.

To convert statute miles into nautical miles, divide
statute miles by 1.15266.

A nautical or sea mile is the length of a minute of
longitude at the equator at the level of the sea.

The circumference of the earth contains 131,459,-
328 feet *- 360 X 60 = length of a knot = 6086. +
feet.

The value of a degree of longitude at the equator
is 60 geographical or 69^ English miles. To ascer-
tain the distance between any two places on a globe
or map on a globular projection, take the distance
between the two places with a thread or the edge
of a piece of paper, apply this to the equator, and
get the exact number of degrees, then multiply by
60 or 69*^, as the case may be.

ANGULAR MEASUREMENT.
60" = i'.
60' = i.
30 = i Sign.
4 Quadrants, or 360 = i Circle.

To CONVERT LONGITUDE INTO TIME,
divide degrees, minutes and seconds by 15, or mul-

CURIOSITIES OF LATITUDE AND LONGITUDE. 75

tiply by 4 and the result will be in minutes and
fractions of a minute. For example:

86 - 24' - 30"

4
60) 349 m j and f|

5 49 38

To CONVERT TIME INTO LONGITUDE,
multiply by 15, or divide the time reduced to minutes
by 4. For example: 5 h - 49 38 s = 349 m and ff
* 4 -87 -24' -30".

76 CURIOSITIES OF LATITUDE AND LONGITUDE.

CURIOSITIES OF LATITUDE AND LONGITUDE. 77

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CURIOSITIES OF LATITUDE AND LONGITUDE. 79

80 CURIOSITIES OF LATITUDE AND LONGITUDE.

SUN'S DECLINATION.

Jan.

i 4

4 4

4 1

Feb.

March

April

44

I 4

May

a

June

23- 2 S

Tuly

i

22-7

N.

J

21- O "

j ui j .

...21-^4

21

a

21

OT^

2O- 3 1

1 1

30...

,...17-41 "

30.

* v O

44

I

17-08 "

Aue"

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1 7-^6

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12-40 "

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14.- 2

44

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21...

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i(

21

12- O

( (

28..

.... 8- o "

a

3 0..

9- o

4 t

I

7-7'3 "

Sept.

8-17

( i

2- 8 "

I c

/

I 4

21

o-i s N

a

J
21

O-4.2

|(

. . . . \J X ^ AH .

a

, . . . . w ^^
2-50

S.

I..,

.... 4-35 "

Oct.

I..

3- 4

44

T 5

,... 9-48 "

11

15.,

8-25

"

21...

,...11-52 "

"

21..

10-27

44

3 0...

....14-48 "

u

3 0.,

J 3-43

4 4

I...

-15- 5 "

Nov.

I.,

14-22

44

15...

...18-52 "

"

15.,

....18-27

44

21..

....20-10 "

"

21..

19-53

44

30...

...21-48 "

' 4

30.,

21-39

44

I...

...22- I "

Dec.

I..

21-47

4 4

15...

...23-19 "

44

15.,

23-16

44

21...

... 23-28 "

44

21..

23-27

44

3 0...

...22- 8 "

' 4

30.

23-13

44

QB Cowell-LAtitude and Longitude.

631

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