The
Pendent Globe
Manual

YALE UNiVERSlTf
APR 22 192?
LIBRARY-

The Cujcion Co.
'. Chicago : -.

Tendent Globe Manual.

BY

F. E. MITCHELL

Head of the Department of Geography, State Normal SchooJ,
Oshkosh, Wisconsin.

Second Edition.

Price Fifty Cents.

THE CAXTON COMPANY, PUBLISHERS.
378 Wabash Ave., Chicago, 111.

Copyright, 1904, by
THE PENDENT GLOBE COMPANY.

PREFACE.
A good globe, if properly used, is as much more valuable piece of
apparatus than is generally supposed. The authors have endeavored to
present in simple language some of the uses to which the globe should
be put, avoiding the use of technical terms as far as possible, except
in the appendix which is intended for those who can and are willing
to work out the harder problems.
Without intending to discourage the use of flat maps, the en
deavor is made to show that the globe should be used in a great many
cases where formerly flat maps have been used, and that it is only
by means of the globe that the flat map can be used intelligently.
Special attention is called to the fact that a number of problems
of an industrial or commercial nature are treated, whereas most man
uals confine themselves wholly to mathematical problems and, indeed,
a great many teachers have never used the globe for anything but
mathematical geography.
Whether the use of the Pendent Globe is profitable, depends
mainly upon the energy and knowledge of the teacher. Before at
tempting to use the globe the teacher should be familiar with at least
the larger part of the contents of this book. Some of it will be appar
ent at once but some will require study.
Become acquainted with the globe. Raise it, lower it, revolve the
ball, revolve the axis, turn it on the swivel, notice the time dial, the
equator, the ecliptic, etc.
When you have mastered the globe and the suggestions, the
teaching of geography with the Pendent Globe will be a pleasure and
result in great benefit to the pupils.
The author wishes to make special acknowledgements to Mr. L.
P. Denoyer for the very valuable assistance he has rendered in the
preparation of this edition of the manual. Mr. Denoyer 's long ex
perience in the handling of the globe has enabled him to make many
practical suggestions of great value. Indeed, the entire appendix and
paragraphs 28, 29 and 30 belong wholly to him, and constitute a very
valuable addition to the manual.
F. B. MITCHELL, State Normal School.
Oshkosh, Wis., January 20, 1904.

DEFINITIONS.
These definitions will be much better understood if you will il
lustrate each of the points by drawings or otherwise.
1. A circle is a plane figure, bounded by a curved line called the
circumference, every part of which is equally distant from a point
within called the center.
2. A diameter is a straight line passing thru the center and
terminating in the circumference.
3. The radius is a straight line passing from the center to the
circumference. 4. A degree (°) is 1-360 of the circumference of a circle. A de
gree may be of any length depending upon the size of the circle.
5. An arc is a part of a circumference. It is generally measured
in degrees. An arc of 60° is called a sextant; 90° a quardant; 180°
a semi-circle. 6. A chord is a straight line connecting the extremities of an
arc. 7. An angle is the degree of divergence between two lines, or
between two surfaces, or between a line and a surface. Angles are
generally measured in degrees. An angle is measured by the arc in
cluded between the lines forming the angle, the vertex of the angle
being the center of the circle of which the arc is a part.
8. A central angle is one whose vertex is at the center of a cir
cle and whose sides are radii. It is measured by the intercepted arc.
9. An inscribed angle is one whose vertex is in the circumfer
ence of a circle and whose sides are chords. It is measured by one
half the intercepted arc.
10. A sphere is a solid bounded by a curved surface every point
of which is equally distant from a point within called the center.
11. A great circle is a circle that separates a sphere into two
equal parts.
12. A small circle is a circle that separates a sphere into two
unequal parts.
NOTE— In the following definitions the earth is treated as if it
were a true sphere.
13. The axis of the earth is the diameter upon which it rotates.
Its ends are called poles. It is the diameter which points to the North

Star. 14. The equator is that great circle of the earth which is per
pendicular to the axis.
15. A meridian circle is any great circle that passes thru the
poles. That half of a meridian circle that lies between the poles is
called a meridian. The first or prime meridian is the meridian from
which longitude is reckoned. Any meridian may be used as a prime
meridian. The meridian of Greenwich is the one commonly made
use of. 16. Longitude is the angular distance between two meridians.
17. Lattitude is the angular distance from the equator. Lati
tude is distance north or south of the equator measured on a meridian.
18. A parallel of latitude, or simply a parallel, is a small circle
of the earth parallel to the equator.
19. The horizon is the plane tangent to the earth at the point of
the observer. 20. East is the direction in which the earth rotates. The oppo
site direction is west.
21. North is the direction along the earth's surface, perpendicu
lar to east and west, toward the North Star. The opposite direction
is south. 22. The direction of a place from any other given place is de
termined by their relative latitudes and longitudes.
23. The bearing of a place from any other given place is the di
rection in which a great circle that passes thru both points crosses
the horizon of the observer.
NOTE.— Bearing and direction must not be confused. For ex
ample, the bearing of Manila from San Francisco is west by north,
while the direction of Manila from San Francisco is west by south.
24. The ecliptic is the path the earth follows in its revolution
around the sun. The plane of the ecliptic is the plane in which this
path lies. It is often called the plane of the earth's orbit. This plane
bi-sects the equator at an angle of 23y2°. The line on the globe cut
ting the equator oi the globe at 23%° will be referred to as the eclip
tic. 25. The zenith is the point in the heavens directly overhead.
Every place on the earth is between its zenith and the center of the
earth.

26. Standard time, mean or local time, sidereal time, and sun
or sun-dial time is explained in Appendix I.
27. The analemma is a figure on the globe which tells the de
clination of the sun for every day of the year. It also shows the
amount of time that the sun is fast or slow as compared with the
mean solar time. This is explained in Appendix II.
28. The international date line is an arbitrary line on the earth
at which the day is supposed to begin and end. This is explained
fully in Appendix III.
29. The zodiac is explained in Appendix IV.
30. The isothermal lines will be referred to in Appendix V.
31. The ocean currents will be referred to in Appendix VI.
32. The time dial is a small sheet of brass on the globe at the
North Pole and will be referred to subsequently.
33. The brass meridian is the brass ring around the globe.

PROBLEMS FOR SOLUTION
WITH THE PENDENT GLOBE
1. To find the latitude of any given place : Elevate the North
Pole to 90°. Kotate the globe until the given place comes under the
brass meridian. The degree on the brass meridian over the place is
its latitude. Find the latitude of your place.
2. To find all those places on the earth having the same latitude :
Rotate the globe on its axis and all those places that come under the
same degree on the brass meridian as the given place, have the same
latitude. What places on the earth have the same latitude as New
York? Milwaukee? New Orleans? Cape Town? Cape Horn?
3. To find the longitude of any given place, and all those places
having the same longitude: Bring the given place, say New York,
under the brass meridian. The number of degrees on the equator,
counting from the prime meridian to the brass meridian, is the long
itude of the place. If the place is east of the prime meridian the long
itude is east longitude ; if west, west longitude. All places under the
brass meridian from pole to pole have the same longitude. What is
the longitude of Milwaukee ? Chicago? St. Louis? London? Pekin?
Manila? 4. To find the latitude and longitude of any given place : Ele
vate the north pole to 90°. Bring the given place under the brass mer
idian. The degree above it is its latitude, the degree on the equator
cut by the brass meridian is its longitude. What is the latitude and
longitude of San Francisco? Boston? Paris? Rome?
5. The latitude and longitude of a place being given, to find the
place: Elevate the north pole to 90°. Find the given longitude and
bring it to the brass meridian. Under the given latitude the required
place will be found. What region of the earth is latitude 22° north,
158° west?
6. To find the difference in latitude between two places : Find
the latitude of each place. If they are both north, or both south of
the equator the difference in latitude is the difference between the
numbers. If one is north and the other south the difference will be
their sum. What is the difference in latitude between Paris and Lon-

8
don? Between Paris and Rio Janeiro? Between Hammerfest and
New York?
7. To find the difference in longitude between two places : Find
the longitude of both places. If both be east or both be west their
difference in longitude will be the difference between the numbers.
If one be east and the other west, the difference in longitude will be
their sum, if it does not exceed 180°. If their sum exceeds 180°, take
it from 360°, and the remainder will be the difference in longitude.
What is the difference in longitude between New York and San Fran
cisco ? Between Sidney and Seattle ?
8. Show that latitude is the angular distance between two lines
which meet at the center of the earth, and that longitude is the angu
lar distance between two planes that meet at the axis of the earth ; or
that the center of the earth is the vertex of the angle of latitude
while the axis of the earth is the vertex of the angle of longitude.
9. The relation of time to longitude : Elevate the pole to 90°.
Have some particular pupil in the room represent the sun. Rotate
the globe so that he can see the United States. He can not now see
any part of India. Therefore when they are having day in the United
States they must be having night in India and China, for the pupil
representing the sun cannot see those countries. Paste a little piece
of paper, or draw a cross with a crayon, on the globe at your particu
lar place. Rotate the globe until your meridian is toward the pupil
representing the sun, that is, it is noon (approximately) at your place.
Have the brass meridian at right angles with your meridian. It is 6
o'clock in the morning in the region lying under the brass meridian
to the west, and 6 o 'clock in the evening in the region lying under the
brass meridian to the east.
10. The hour of the day being given to find the time at any other
place : Turn the time dial that is attached to the globe at the north
pole so that the number on the time dial which corresponds to the
given time is on the meridian of the place. The time at any other
place will be indicated by the number on the time dial over the meri
dian of that place. As the earth rotates from west to east the time
will be later to the east and earlier to the west. In crossing the heavy
red line on the globe called the international date line from east to
west add a day, in crossing it from west to east substract a day. Say,
for example, it is 10 A. M. Friday in Wisconsin. The time dial will
show that it is 11 A. M. in New York, 4 P. M. in England, 12 o'clock
midnight in the Philippine Islands, 1 A. M. Saturday in Japan, 4 A.

9
M. Saturday in extreme western Russia, while in the Aleution Islands
it is still Friday 4 A. M. and 8 A. M. in San Francisco.
NOTE.— Standard time, mean or local time, and sidereal time,
are explained in Appendix I. The international date line is explained
ni Appendix III. These should be studied in connection with this
subject. 11. The hemispheres : Whenever you look at the globe you will
see a hemisphere, consequently there are just as many hemispheres
as there are points on the globe— an infinite number. Geographers
have selected six hemispheres as of special importance, namely, north
ern and southern ; land and water ; eastern and western. The center,
or point of view, of the northern hemisphere is the north pole ; of the
southern hemisphere the south pole ; of the land hemisphere London ;
of the water hemisphere, New Zealand ; of the eastern hemisphere, 0°
latitude, 70° east longitude; of the western hemisphere, 0° latitude,
110° west longitude.
12. Northern and southern hemispheres: Turn the globe in
such a way that the class will be looking at the north pole and have
the ball so turned that the meridian of Hudson Bay and Wisconsin
will come under the brass meridian. The questions to be asked should
be somewhat as follows: What line divides the earth into these two
hemispheres? It crosses what regions of the earth? How much of
the equator falls on the water? Imagine yourself standing on the
north pole ; now look south. Is this a definite direction ? Give rea
sons for your answer. (Every point in the horizon is south.) Now
look into the region of Hudson Bay and Wisconsin. Is this a definite
direction? When you are looking into Wisconsin what region is on
your left? On your right? Back of you? How many degrees be
tween front and left, etc? How many degrees between Wisconsin
and western Europe? How much difference in time? What time is
it now in London ? What region is on your right ? Question same as
above. What region back of you ? Question same as above. Compare
and contrast the arrangement of land and water in these two hemi-
speres. 13. Eastern and western hemispheres : The meridian circle that
separates these hemispheres is made up of the meridians of 20° W.
and 160° E. Give the relative positions of each of these meridians
in respect to bodies of land and water. Draw a great circle that is
made up of these two meridians and draw and number every 15th
meridian in the eastern hemisphere; same for western hemisphere;

IO
also draw each 10th parallel. Give latitude and longitude of centers
of each of these hemispheres. What regions of the earth are found
in these centers ? Between what parallels does each of the continents
lie? Draw the parallels in your maps of the hemispheres. Same
with the meridians which bound the continental masses. Describe the
positions of the land masses in the different hemispheres, thus : North
America lies in the middle of the north half of the western hemis
phere. Australia lies in the southeast quarter of the eastern hemis
phere, etc. How many continents in each hemisphere? Point out the
differences that you notice in the arrangement of the land and water
in these hemispheres. Estimate the relative amount of land and wa
ter in each hemisphere. All the above points should be illustrated by
the use of the globe and also by drawings to make them clear and
definite. 14. Land and water hemispheres: Elevate the north pole to
38%°. Rotate the globe so that London comes under the 0 of the
brass meridian and rotate the meridian on the swivel and lower the
globe so that London will be on a level with the eyes of the class.
Now the class is looking at the land hemisphere. By rotating the
brass meridian on the swivel thru 180° the class will be looking at the
water hemisphere.
The distance around the earth is a little over 24,000 miles. One
fourth this distance is 6,000 miles. Therefore the distance from Lon
don to any point in the land hemisphere is within 6,000 miles.
Could the largest city in the world ever by in New Zealand or
near Cape Horn? Why? Give the position of the circle that sepa
rates the earth into these two hemispheres. Give an estimate of the
fractional part of the land in each hemisphere. What land on the
earth is more than 6,000 miles from London? What land on the earth
is within 6,000 miles of New Zealand? From the experiments can
you determine the influence this arrangement of land and water will
have on climate? How do you account for the fact that all the land
on the earth that is more than 6,000 miles from London is within
6,000 miles of New Zealand ?
15. To prove that the altitude of the north star equals the lati
tude of the place : Elevate the north pole to 90°. If you were stand
ing at the north pole the north star would appear directly overhead
and your latitude would be 90°. Now lower the pole to 0° If you
were standing at the equator you would see the north star on vour
horizon, and you would be at 0° latitude. It is 90° from your horizon
to your zenith, and it is 90° from the equator to the pole, therefore

II

for every degree you travel from the equator to the pole, the north
star will appear to rise one degree. Hence the altitude of the north
star equals the latitude of the observer. Observe the north star and
estimate its altitude. Prove also by means of drawings that the alti
tude of the north star equals the latitude of the place.
16. Every great circle passing thru a point on the earth must
pass thru the point opposite. See if you can prove this by means of
a string and the globe.
17. Every point on the earth is on some great circle that passes
thru your schoolroom. Demonstrate this by means of the globe and
a string. The direction in which these great circles cross your state
is the bearing of those places from you. Show that great circles run
from your schoolroom to London, Cape Town, the center of each of
the continents, and to Manila.
18. Review definitions TV to X. Prove that the distance meas
ured on a great circle between any point on the earth and the point
opposite you is 180°, less the distance from your place to that point.
Measure on a great circle how many degrees from a place opposite
you is a place 90° from you? 70° ? 60° ? 35° ? 22° ? Draw a great
circle thru your place and show that your answers are correct. Il
lustrate by means of the globe. Draw a great circle passing thru your
place. In this circle draw the line of the body. See illustration :

Vour pl<v*£

W frem jtur place

Now locate a place 80° from you and draw a chord connecting
this place with your location. Now notice that you have an inscribed
angle whose intercepted arc is 180°-80°. What is the size of the
angle? Locate places 60°, 90°, 120° and 45° from your place and pro
ceed as above. At what kind of an angle with the line of the body
would you have to point in order to point to a place 45° from you?
60° ? 75° ? 120° ? 180° ? Prove this by means of drawings and the
globe. Point to these places.

12
19. To prove that the arc of a great circle is the shortest dis
tance between two points on a sphere : Select a place 50° N. latitude
on the western coast of North America, and a place 50° N. latitude
on the eastern coast of Asia. Now these places are evidently east and
west of each other, and on the parallel 50° N. latitude, which is a
small circle passing thru both of them. Now the proposition is that
the arc of a great circle connecting these two places is a shorter dis
tance than is the arc of the 50th parallel which connects them. Take
a string and place one end at one of the places indicated above and
draw it tight, bringing the other end to the other place. The string
thus placed is lying on the arc of a great circle. Now lay it along the
parallel and see which is the shorter. If the measurements are care
fully made the distance represented by the string, which is the great
circle distance, will be found several degrees shorter than the paral
lel. This can also be proved by spherical geometry.
20. To find the shortest distance between two places: Lay a
string on the globe and draw the ends until the string is tight. The
string will then be lying on the arc of a great circle. Find how much
of the string is required to connect in this manner the two given
places. Find the length of this distance on a great circle by laying
the string on the equator, bringing one end to the prime meridian.
Note the longitude of the other end. The longitude will be the num
ber of degrees of a great circle that the string is along. Since a de
gree of a great circle is about 70 miles (69 1-6), multiply the number
of degrees of a great circle between the two places by 70, the product
will be the distance between the two places in miles. How far is it
from New York to London? From New York to San Francisco?
From San Francisco to Manila? From London to Japan, following
the water or Suez canal route? How far from Seattle to Japan?
From London to Buenos Aires ? All routes of travel should be worked
out from the globe in this way. Which is nearer Manila, San Fran
cisco or Seattle ? Which is nearer Seattle, Ireland or the west coast
of Africa ?
21. The direction in which a great circle, that passes thru your
place and some other point, crosses your horizon must be determined
by means of the globe. In what direction does a great circle cross
your horizon that passes thru your place and London? Cape Town?
Central Africa? Gulf of Guinea? Cape Horn? This gives bearing
but not direction.
22. To point thru the earth to any place : Elevate the pole to
the degree equal to the latitude of your place -and rotate the globe

13
so that your place is at the swivel. Have the north pole toward the
north. Now the globe is in proper position for your particular place.
The axis of the globe is now pointing to the north star and the axis
of the earth always points to the north star. Therefore in this posi
tion the axis of the globe and the axis of the earth are parallel. You
can see at a glance in what direction you should point thru the earth
to point to any of the following places. Point to Cape Town, Manila,
Cape of Good Hope, Honolulu, Pekin, Australia, the north pole, the
south pole. Make drawings to show that you are right. How many
degrees from the line of your body is your arm when you are pointing
to these places ? See definition IX and Problem XVIII.
23. To place the globe in the sunshine so that it may represent
the natural position of the earth with respect to the sun: Put the
globe in position for your place as explained in Problem XXH.
Should the globe not be in position so that the sun shines upon it,
unhook it from the hanger and carry it into the sunshine without
changing its position with reference to the altitude of the pole or the
north and south plane of the brass meridian. As the sun shines on the
globe, light and dark hemispheres, succession of day and night, etc.,
may be illustrated.
24. To find the antipodes of any place : Bring the given place
directly under the swivel as explained in Problem XVIII. Raise the
globe as high as it will go. Stand under the globe. The place direct
ly above you will be the antipodes. Find your antipodes. Find the
antipodes of London. How many miles is it thru the earth from a
given place to the antipodes of that place ? How many miles on the
surface of the earth ? Can a place on the earth be further away than
its antipodes? 25. To find the length of a degree of longitude in any given
parallel of latitude : The meridians drawn on the globe are 15° apart.
By the use of a string find the distance the meridians are apart on
the parallel selected. Reduce this distance to degrees of a great cir
cle by applying the string to the equator which is marked off in de
grees. Multiply the number found by 4.6, which is the same as multi
plying by 70, thus giving the number of miles for the 15° of longitude
for the parallel selected, and dividing by 15, the number of degrees in
order to find the number of miles in one degree. The product will
be the length of a degree in miles on the parallel measured. This is
not absolutely correct but near enough for practical purposes.
26. To find how rapidly the inhabitants of any region are car
ried from west to east by the rotation of the earth : Find how many

miles there ore in a degree of longitude in the latitude of the given
place. Since every place on the earth is carried thru 15° of longitude
in one hour of time, multiply the length of a degree by 15. The pro
duct will be the rate of miles per hour at which all places in that lat
itude, north or south of the equator, are being carried east by the
itude, north or south of the equator, are being carried to the east by
the rotation of the earth.
27. To show the use of correction lines in the United States Land
Survey : North and south lines are not parallel, but converge in the
northern hemisphere toward the north pole. Observe this by looking
at two adjacent meridians on the globe. Were there no correction
lines, townships which are supposed to be six miles square would be
come narrower toward the north. To obviate this, correction lines
or new base lines are run every tenth town. Base lines are east and
west lines from which the towns are numbered north and south.
NOTE.— In the three following paragraphs subjects that have
generally been shown from flat maps are taken up with the globe. It
seems to the author that many of the inaccurate ideas, and some whol
ly wrong ideas, in regard to comparative area, direction and distance,
which are so prevalent in the minds not only of people in general but
even of the majority of teachers, could be corrected by using the
globe instead of flat maps. The reason, doubtless, why flat maps have
been used in the discussion of these problems, is that they have been
convenient in the text books on geography and in the wall maps;
whereas, globes in the past have been inconvenient, the fact which
led to the invention of the Pendent Globe.
28. Comparative Area: By a glance at the Mercator Map of
the World, which is given on opposite page, and which will be found
in almost every text on geography, as well as in almost every set of
wall maps, it will be seen that Greenland appears larger than South
America, whereas, it is less than one-tenth as large. Alaska appears
one-half as large as the United States, whereas it is less than one-
fifth the area. British America appears over twice as large as the
United States, whereas, they are about the same in area. Illustra
tions of this exaggeration on the part of the Mercator Map could be
multiplied indefinitely ; but the Mercator Map is not the only map that
is misleading on the subject of comparative area. No flat map
has yet been devised which gives comparative area correctly, except
it be of a very limited area such as a county or state. In the accom
panying map of the hemispheres Greenland will seem much too large
as compared with portions of South America, Alaska as compared

i5

i7
with Mexico, etc. The reason for these apparent inaccuracies will
become clear in the study of the next paragraph.
29. The distance A B on the accompanying Mercator map rep
resents nearly 25,000 miles. C D, an equal distance on the map, rep
resents only about 4,000 miles. E F represents 692 miles ; while G H
a distance on the map more than four times as great, represents the
same number of miles. These distortions account not only for the ap
parent error in comparative distances, but also for the apparent error
in comparative areas.
In the accompanying map of the hemispheres the distance repre
sented by the curved line P E is a little over 6,000 miles ; while P F,
a little over half that distance, represents the same number of miles.
This shows, not only why comparative distances cannot be shown cor
rectly from a hemisphere map or any map based upon that projec
tion, but also why comparative areas cannot be shown correctly from
a hemisphere map or any map based upon such a projection.
30. Comparative direction: On the Mercator map it appears
that one would start southwest in order to take the shortest route
from San Francisco to Manila. The same is true on the hemisphere
map. By means of a string show on the globe that the nearest route
from San Francisco to Manila starts in a northwesterly direction
passing almost in sight of the Aleution Islands and touching the east
coast of Japan. Most of the large ocean steamers on the Pacific now
take that route ; in fact, all do so except those that wish to call at the
Hawaiian or other Islands for coal or commercial purposes.
Look at the hemisphere map. What bodies of land appear south
of Greenland? Now put Grenland under the brass meridian of the
globe and notice that North America is not south of Greenland, but
lies almost entirely to the west, while South America is really south
of Greenland. In fact, the west coast of Africa is even south of the
eastern part of Greenland. In the accompanying map of Europe
you will notice that the Ural Mountains appear to tend to the north
west, while on the map of Asia they appear to tend to the northeast.
In which direction do they really tend ? The outline maps given here
are copied from the best geographies uow in use in our schools.
PROBLEMS INVOLVING THE USE OF THE ANALEMMA.
31. The analemma shows the distance that the vertical ray of
the sun is from the equator for every day in the year. Each month
is indicated by a distinct color and each day by a separate dot. On
what days of the year is the vertical sun falling on the equator? 10°

19
north of the equator? 10° south of the equator? On what parallel
is the sun vertical today ? When is the sun vertical over the tropics ?
32. To find the place where the sun is vertical at any given
time: Review Problems IX and X. From the analemma determine
the parallel over which the vertical ray of the sun falls for the given
day. Bring the number on the time dial, which corresponds to the
given time, to the meridian of the observer. The meridian which
falls under the number 12 on the time dial is the meridian upon
which the vertical ray of the sun is falling. Hence the vertical sun
will be over that part of its parallel crossed by this meridian. Place
the globe in the sunshine as explained in Problem 23. Place a pen
cil perpendicular to the point found above and you will notice' that
'the pencil does not cast a shadow. Where is the sun's vertical ray
falling at 10 o 'clock standard time on May 13th ? Where at the pres
ent moment ?
33. To find the direction from the observer in which the sun
will rise for any given day: The sun always rises and sets on your
horizon at points 90°from your zenith. Therefore the vertical sun
is 90° of a circle from the observer at sunrise and at sunset. Take
a string and tie two knots in it just 90° of a great circle apart. This
may be ascertained by measurement along the equator. From the
analemma find the parallel over which the sun is vertical for the
given day. Now place one of the knots of the string over your posi
tion and the other knot on the parallel over which the sun is vertical.
Move the knot eastward on the parallel over which the vertical ray
is falling until the string is tight. Now notice the direction toward
the east in which the string crosses your state'. This is the direction
of the rising sun for the given day.
34. To find the direction in which the sun will set for any given
day: Same as the preceding, except instead of moving the knot
eastward along the parallel over which the sun is vertical, move it
westward. The direction toward the west in which the string crosses
your state will be the direction in which the setting sun will
be seen. 35. To find all those places on the earth which receive the ver
tical ray of the sun on any given day: Elevate the north pole to
90°. From the analemma find the parallel over which the sun is
vertical for that day. Rotate the globe on its axis and all places
coming under the number on the brass meridian which corresponds
to the parallel will receive the vertical ray of the sun on that day.
36. To find the time of sunrise for any given day at any given

20
place: From the analemma find the parallel on which the vertical
ray of the sun falls for the given day. Now find a place in that
parallel 90° from the observer by the use of a string the same as in
problem XXXIII. Find the longitude of this place and turn the time
dial so that the number 12 will be over the meridian representing
this longitude. The time indicated on the time dial over the meri
dian of the given place will be the time of sunrise.
As the meridians are very close together near the north pole,
more accurate results can be obtained by noting the following:
At six o 'clock the sun will be 90° east of the meridian of the observer ;
at 5 o'clock it will be 105° east; at 4 o'clock 120° east, etc. Find
the place over which the sun is vertical when it appears to rise at
the given place as indicated above. Estimate the time between these
meridians and reduce to minutes, remembering that each degree is
equal to 4 minutes of time. By doing careful work by this method
and correcting for the equation of time, as explained in Problem I of
Appendix II, and reducing to standard time as explained in Problem
I of Appendix I, you can get the time of sunrise correct to within
two or three minutes.
37. To find the time of sunset for any given day at any given
place : Use a method very similar to the above which will become
readily apparent.
38. To find the parallels on the earth beyond which no rays of
the sun are falling for any day of the year: The tangent ray is
always 90° from the vertical ray. From the analemma find the lati
tude which is receiving the vertical ray of the sun. Subtract this
number from 90° and the remainder will be the latitude in the hem
isphere opposite the one receiving the vertical ray, beyond which
the rays of the sun do not fall. What parts of the earth now have
continuous darkness? On what days do no parts of the earth have
continuous darkness?
39. To find the length of the longest day at any place in the
north frigid zone: Count the number of degrees the place is from
the north pole. The vertical sun will be the same number of degrees
north of the equator when the place begins to have continuous day.
From the analemma count the number of days required for the sun
to pass from its present position to the tropic of cancer and return.
The time thus found will be the length of continuous day at the given
place. What is the longest period of continuous day a place will
have 10° from the north pole ? From the analemma it be found that
of April, and that it will travel to the northern tropic and return
to the parallel of 10° north latitude by August 27th. From April

21
16th to August 27th is 4 months and 11 days. Therefore the longest
period of continuous day a place will have 10° from the north pole,
will be 4 months and 11 days.
40. To explain the change of seasons: The change of seasons
is due to two distinct, tho related causes. The one is the variation
in the length of day and night. The other the changing obliquity
of the sun's rays. Most of the heat of the earth is received from the
sun. As a general thing it is warmer during the day, than during
the night. When the days are longer than the nights we have sum
mer. When the days are shorter than the nights we have winter.
In summer not all the heat received from the sun during the day
is lost by radiation during the night, while in winter when the nights
are longer than the days more of the heat is lost during the night.
This is the main cause for the change of seasons. The reason for
this variation in the length of the day and night will be explained
in the next problem.

)un\s

Sutvuner and winter

ra y S m
The other very important cause is the change in the obliquity
of the sun's rays. This is due to the fact that the vertical ray of
the sun moves over 47° of latitude, from 23%° north to 23%° south.
When the vertical ray is nearest us we have summer. When far
thest away we have winter. In the summer time the vertical ray
is more nearly perpendicular than during the winter.
It can be easily seen from the accompanying figure that a ray
from the sun in the summer time has less surface to heat than a

22
ray from the sun in winter. Having a smaller area to beat it is more
efficient in the summer time.
To show why the vertical ray moves over 47° of latitude : Ele
vate the pole to 66%°. Rotate the globe until the ecliptic becomes
parallel to the floor; turn the globe on the swivel until the brass
meridian lies in a north and south plane with the north pole to the
north. Draw the globe to one side, say two or three feet, and place
a pupil on the spot over which the globe naturally hangs. Move the
globe up or down until the center of it comes to a level with the
pupil's eye. Revolve the globe around the pupil requiring him to
turn so as to face the globe in all parts of its circuit. If, in revolv
ing the globe around the pupil the parallelism of the axis is main
tained, the pupil's line of vision will follow the ecliptic. In this exer
cise the pupil will represent the sun, the globe the earth, and his line
of vision the vertical ray of the sun. He now has a clear idea of
why the vertical ray moves over 47°, inclination of the axis 23%°,
constant parallelism of axis, and the revolution of the earth around
the sun. It is not the warmest time of day at noon nor the coldest time
midnight. The warmest time is a few hours past noon, and the cold
est time a few hours past midnight, due to the fact that it takes the
sun sometime to heat up the earth after the cold night and some of
this heat is retained until past midnight. For a similar cause the
hottest time of the year is not during the longest day or when the
sun's ray is nearest to us, but the hottest time is about the first of
August and the coldest timeabout the first of February, more than
a month after the longest and shortest day respectively.
41. To explain the variation in the length of day and night:
The immediate thing that determines the length of day and night is
the way in which the circle of illumination cuts the parallels. If
it cuts them equally day and night will be of equal length; if un
equally, of unequal length. To illustrate this place the pupil and
globe in position and proceed as in 40. When his line of vision falls
north of the equator he sees more than half of each parallel in the
northern hemisphere and less than half of each parallel in the south
ern hemisphere. Consequently the days are longer than the nights
in the northern hemisphere and shorter in the southern. When his
line of vision, which corresponds to the vertical ray, falls south of
the equator the conditions are just the reverse. If his line of vision
falls on the equator he sees just one-half of each hemisphere and
days and nights are of equal length the world over.

APPENDIX L

The time as reckoned by the sundial is called solar time, or sun
dial time. As the sun does not always reach the meridian at the
same time thruout the year it is much more convenient to use the
average of the sun's time and this is called the mean solar time. It
is also known as local time. No clock could be made to keep time
with the sun. The reason for this irregularity of the sun's crossing
the meridian will be explained in Appendix IH. But even the mean
solar time is not very convenient for commercial purposes, altho
until within recent years it was generally used, so we have now in
general use what is known as standard time. This time agrees as
to the minutes and seconds all over the world. It only differs in
the hours. For example, when it is five minutes after twelve in
New York it is just five minutes after 11 in Chicago, and five minutes
after 10 in Denver, and five minutes after 9 in San Francisco, and so
on. This makes a very convenient arrangement, especially for
railroads and traveling men.
Standard time is the time that is used very generally thruout the
country, but at certain cities such as Detroit, two kinds of time are
still used. The mills, factories and most of the city use local or
mean solar time, while the Post Office, the hotels and the railroads
use standard time.
There is still another kind of time that is used by astronomers.
It is known as sidereal time, that is, time that is reckoned from the
fixed stars. It can be easily shown that sidereal time is slower than
either solar time or mean time, growing slower by 3 min. and 56
sec. each day. This is due to the fact that the earth makes one more
rotation on its axis than there are number of days in the year. In
order to show this, place a pupil in the place where the globe hangs
Revolve the globe around the pupil and at the same time rotate the
globe on its axis so that North America can be seen by the pupil all
the while. North America will be having day all the while, but as
you are revolving the globe around in this way the globe will also
be making a rotation. Now suppose someone in the back of the
room represents some fixed star. To that star North America has
passed thru a day and a night. Now what happens in reality is
that the earth in its revolution around the sun rotates on its axis
36614 times, whereas there are only 365^ days in a year.

24
Problem 1. To find the difference between standard time, and
local time or mean solar time, at any place : Find the number of de
grees of longitude the place is from one of the meridian lines indi
cated on the globe. Multiply this number by 4. This gives the differ
ence in minutes between the two kinds of time. If you have standard
time given add this number of minutes in order to get local time pro
viding your place is east of the meridian, and substract it if it is
west of the meridian. Reverse the operation in case you have local
time given and wish to find standard time.
NOTE.— This may not be true for certain places about halfway
between the meridian lines, but in general it is correct.
APPENDIX II.
The equation of the time or the difference between mean solar
time and sundial time : As suggested in Appendix I sundial time is
not uniform and can not be used satisfactorily in business or for
scientific purposes. On this account mean time has been adopted
which is reckoned from a "ficticious" or mean sun moving uniformly
in the equator at the same average rate as that of the real sun in the
ecliptic. It is mean noon when this "ficticious" sun crosses the mer
idian. This difference in time depends upon two causes :
First cause: The variable motion of the sun in the ecliptic due
to the eccentricity of the earth's orbit, or putting this a little more
simply, because the earth in its orbit around the sun describes an
ellipse instead of a circle. See drawing:

This drawing is greatly exaggerated for the purpose of illustra
tion. The actual path of the earth around the sun is almost a circle.
Kepler, a noted astronomer, in the year 1609 discovered three very
important astronomical laws, two of which are : 1st. The orbit of
each planet is an ellipse with the sun at one of its foci. 2nd. The
radius vector of each planet describes equal areas in equal periods
of time. The radius vector in the illustration is the line which con-

25
nects the earth and the sun at any moment. S represents the sun
and the ellipse represents the orbit of the earth. The areas aSb, cSd,
and eSb are equal. From the second law of Kepler, which depends
upon the law of gravitation, it will be seen that the earth moves more
rapidly at certain times than it does at others, moving from a to b
in the same period of time as it does from e to f. About December
31st the earth is nearest the sun and therefore its orbital motion is the
most rapid at this time of the year. This makes the sun's apparent
eastward motion among the stars greatest in December, and hence
at this time the apparent solar days exceed the sidereal days by more
than the average amount, thus making the sun-dial days longer than
the mean. The average solar day is 3 min. and 56 sec. longer than
the sidereal. The sundial will therefore lose time at this season and
will continue to do so for about three months until it comes to its
mean value. It will then gain until about June 21st when, if the clock
and the sun were starter together December 31st, they will once more
be together. Thus twice a year so far as this cause is concerned the
clock and the sun will be together, namely, at December 31st and
June 21st, while half way between they would differ by about 8
minutes. The equation of time (so far as due to this cause only) be
ing plus 8 minutes in the spring and minus 8 minutes in the autumn.
Second cause: The inclination of the ecliptic to the equator.
Even if the earth's orbital motion was uniform there would still be
an equation of time. If the true and "fictitious" suns started to
gether at the equinox they would be together at the solstices and the
other equinox, because it is just 180° from equinox to equinox and
the solstices are exactly half way between them, but at intermediate
points between the equinoxes and the solstices they would not be
together. This can be shown from the globe. Call the point 0 longi
tude and 0 latitude the vernal equinox at which point we will start
our true and "fictitious" suns. Notice that the meridian 90° E.
longitude cuts the ecliptic as well as the equator at right angles, but
the meridian 45° E. longitude does not cut the ecliptic at right angles.
All the meridians cut the equator at right angles and north and
south is determined by the meridians. Now the distance from the
vernal equinox to 90° E. longitude, 23%° N. latitude is 90° measured
along the ecliptic. Count 45° beginning at the vernal equinox along
the ecliptic and you will notice that 45° will take you not quite to
43° E. longitude. It will be remembered that the apparent motion
of the sun in the heavens is from east to west. Now suppose you were
standing in the little town of Kars latitude 41° N, longitude 43° E.,

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27
and were looking into the sky you would observe the real sun reach
ing your meridian about ten minutes earlier than the mean sun.
We can represent graphically each of these cases. In each of
the accompanying drawings the horizontal line is a scale of dates
one year long, the letters denoting the beginning of each month. The
vertical distances of the curve from this line indicates the amount
of the equation of time for that date. It will be easily seen that by
taking the algebraic sums of the points constituting the first two
curves it will form the 3rd or true equation.
Draw on a piece of tracing paper this curved line and fold the
paper about the vertical line and hold it to the light. You will ob
serve a figure like that on the globe.
Problem 1. To find the amount of the equation of time for any
day : Find the dot representing the day and bring the brass meridian
to that dot. Observe on the scale the number crossed by the meridian
and also whether this is to the right or left of the 120th meridian. On
what days is the equation of time 0, that is, on what days does the
real sun cross the meridian at noon? When will the sun cross the
meridian on Nov. 2nd ? Feb. 11 ? Today ?
APPENDIX HI.
The international' date line is a line arbitrarily chosen, at which
the day is said to begin and end. This is explained somewhat in
Problems LX and X. This line has been changed from time to time
and is correctly shown on the Johnston 12 inch globe covers used
with the Pendent Globe, but appears incorrectly on all other globes
on the market at the date of the publication of this
book (1904.) A number of years ago it was arranged so
that the Philippine Islands were just east of this line. It
was then changed so that it crossed the equator at the 150 meridian
of W. longitude. Now it crosses the equator at the 180th meridian.
The effort is made to bring it as near in coincidence with the 180th
meridian as possible, but it varies from this slightly for two impor
tant reasons : First : The people of eastern Russia want to have the
same date as the rest of Russia and the Aleution Islands should have
the same date as Alaska. Second : Vessels wish to change days at con
venient points, just as railroads change their time, not exactly half
way between meridians, but rather at convenient point. The
Samoan Islands are a convenient point at which to change. This
accounts somewhat for the bend in the line as it is now.

28
APPENDIX IV.
The Zodiac: By carefully observing the ecliptic on the globe
you will notice 12 peculiar signs. These are the Signs of the Zodiac.
The first, or the sign of Aries, will be found where the ecliptic crosses
the meridian of Greenwich. Every 30° another sign will appear. The
accompanying table shows the signs with their names and also the
dates for which they stand.
i. ARIES (Ram) T From March 21 to April 20.
2. TAURUS (Bull) » From April 20 to May 21.
3. GEMINI (Twins) H From May 21 to June 21.
4. CANCER (Crab) 25 From June 21 to July 23.
5. LEO (Lion) SI From July 23 to August 24.
6. VIRGO (Virgin) ttr. From August 24 to September 23.
7. LIBRA (Balance) =2= From Sept. 23 to Oct. 23.
8. SCORPIO (Scorpion) HI From Oct. 23 to Nov. 22.
9. SAGITTARIUS (Archer) f From Nov. 22 to Dec. 22.
10. CAPRICORNUS (Goat) V? From Dec. 22 to Jan. 20.
11. AQUARIUS (Water-bearer) zz From Jan. 20 to Feb. 18.
12. PISCES (Fishes) X From Feb. to March 20.
These Signs of the Zodiac represent certain constellations, or
groups of stars, in the heavens, extending not more than 8° on either
side of the ecliptic. As the sun follows in the path of the ecliptic it
is always in one of these signs. APPENDIX V.
Isothermal Lines: It will be observed that there are two series
of lines on the globe, the one red and the other blue. The red lines
indicate the average temperature of the regions thru which they
pass during the month of July. The blue lines indicate the same for
January. Find the coldest region on earth during January. Find
the hottest region during July. Are these regions on land or water?
Compare the January temperature on the western coast of North
America with that on the eastern coast. Do the same with Eurasia.
Now compare the July temperatures in the same places. How do
you account for these differences?

=9
APPENDIX VI.
Ocean Currents : The white lines on the globe indicate the main
ocean currents. The arrows indicate the direction. The cause of
ocean currents is still somewhat unsettled. The main causes, doubt
less, are the daily rotation of the earth and prevailing winds. As ex
plained in Problem 26 the surface of the earth at the equator is trav
eling from west to east at the rate of about 1,000 miles an hour. The
water naturally will tend to lag behind but is prevented from uni
formly doing this by continents and other causes and hence currents
are deflected to the north and south. At 60° north latitude the veloc
ity of the earth's surface is only one half as great as it is at the
equator, therefore, the water of a current starting from the equator
northward, is constantly coming to places where the bottom under it
has less and less eastward velocity. By the law of inertia the water
tends to retain the same velocity eastward with which it started and
thus it moves to the east of north, shooting ahead, as it were, of the
bottom over which it is flowing, as a rider does whose horse slackens
his pace. The contrary happens to a stream flowing from north to
south. In this case the eastward motion of the water is too slow for
the parts of the bottom to which it successively comes; the bottom
slips in a manner from under it and it flows to the west of south. An
other very important cause of ocean currents is the prevailing wiuds.
For a fuller treatment of this subject see any text book on physical
geography.

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