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Full text of "An angular tour of the world, or, The curiosities of latitude and longitude; a book for teachers"

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 



PUBLISHED BY 

THOMAS CHARLES CO 
CHICAGO 



COPYRIGHTED 1894 

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 

Angle of Night Shadow 28 

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 

Night Shadow 19-30 

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 

Zones How Made t 18 

ILLUSTRATIONS. 

1. The Earth 6ti 

2. Rotation of the Northern Heavens 35 

3. Twilight Projection 37 

4. The Hour Angle 47 

5. Longitudinal Quadrants 54 

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 

LATITUDE BREADTH. 

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 
place on the parallel, provided he had adjusted his 
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 : 




ZONES HOW MADE. 

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 
is the one removed 12 hours from your own your 
Antipodes, the point on that meridian in opposite lat- 
itude to your own. 

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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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 
south, it must be deducted instead of added. For 
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 
corresponding angle of the night shadow is made 
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 
of shadow. 

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, 

The eastern sky's adorning; 
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. 

York about 17 hours old, and at San Francisco about 
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 
your meridian. This will give your opposite meridian 
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- 
eter, a finely made and nicely adjusted watch, with a 
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. 
90 = i Quadrant. 
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 



in z 



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^ 
?~o 

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o o o N oo 

ro LO M ro 



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M M CO 10 



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78 CURIOSITIES OF LATITUDE AND LONGITUDE. 






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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" 


I 


1 7-^6 


< < 


I C 


12-40 " 


"& 




14.- 2 


44 


j. j... 








. A<^. <. 




21... 


T C\ 1 A ' ' 


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. 

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