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Ralph S. (Ralph Stockman) Tarr.

A laboratory manual for physical and commercial geography online

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_ Mark the equator on the apple. Make a drawing of a sphere,

shading it so that it appears round. On it mark the equator and the poles.



CI



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II. — PROOFS THAT THE EARTH IS A SPHERE

Materials. For Each Student. — Desk globe. Pencil.

For General Class Use. — An egg. Saucer. Bottle. Pebbles. Book.
Purpose. To show, by simple proofs, that the earth has a spherical form.

By journeys What did people believe the shape of the earth to be when Columbus started on his first

around the

earth. voyage ?



What did he believe?

What expedition was the first to make the voyage completely around the earth and return to

its starting place?

Push your finger around the globe from east to west ; from north to south ; in other directions.
In each case, if you follow a straight course, do you come back to the point where you started ?

Would that be possible if the earth were flat ? This

proves that the earth is a curved body. But does it prove it to be a sphere ?

Could you do the same thing on a body shaped like an egg? It is a longer

distance around an egg in some directions than in others. Is this true of a sphere ?

Is it true of the globe ?

By means Examine your desk globe to see that every part of its surface is curved. Place it in the

of eclipses sunlight so that its shadow will fall on the floor. What is the outline of the shadow ?
of the

moon - Turn the globe in various positions. Does the

shadow change in form ? Try the same experiment with several objects,

such as a bottle, a pebble, a saucer, an egg. What is the result?



Does any other object than a sphere always cast a circular shadow?

3



Sometimes the earth's shadow is cast on the moon, when the earth comes between the sun and

moon. This is called an eclipse. Have you ever seen an eclipse of the moon ?

Describe it.



The shadow of the earth is always round in such an eclipse. What does that prove?

By gradual Place an object on the flat surface of your desk. When your eye is above the level of the
disappear-
ance of d es k top, can you see this object from all points of view ? Is the same true

objects in

tance °^ an 0D J ec ^ placed on the curved surface of a globe? Stick a pin in the

globe and turn the globe. As it turns away from you the pin slowly disappears from view.

Which end of the pin disappears first?

Where are the most level places on the earth ?

What part of a ship at sea is first seen

as it comes toward you? Make a drawing to

show this. (See Fig. 6, Text-book.) Then make a drawing to show what would be the case
if the earth were flat.



Objects disappear on the curved earth at a regular rate, no matter in which direction one
looks. This rate is 8 inches the first mile, 32 inches the second mile, and so on. The rate is



#



the square of the number of miles times 8 inches. How much will the disappearance be at

the third mile ? (3 x 3 = 9 x 8 = 72 inches.) How much at the fourth ?

, The fifth?



Would it be true that an object would disappear at a regular rate in all directions and in all

places on a cylinder ? On an egg? On any other than a

spherical body ? What then do you conclude in regard to the form of the

earth?

By position Heavenly bodies also change position at a regular rate when viewed from different points
of the on fjhg earth. At the equator the north star is on the northern horizon, no matter at what
part of the equator one stands. At the north pole it is overhead. Where would it be half-
way between pole and equator? Could this

be true if the earth were egg shaped? Or pear shaped?

f

Or cylinder shaped ?



Other
spheres
in the
heavens.



Name other spherical bodies in the heavens.



What would be the appearance of the earth if it could be



seen from the moon ?

Make a drawing to scale (below) to show the comparative size of the earth and moon. (Text-book, p. 1.) Of
the earth and sun. (Text-book, p. 3.)



What is an eclipse of the sun ?



How does this prove that the moon is a sphere ?



o



cc



III. — WORLD MAPS

Materials. For Each Student. — Pencil (sharp). Ruler. Small desk globe. Several sheets of blank paper.

For General Class Use. — Maps of different scale. Pair of shears. Several baseballs. Sheet
of wrapping paper.

Purpose. To teach the meaning of scale, and to show the difficulty of representing the curved earth's

surface on a flat map.

What is the greatest distance that you can see in any one direction in your locality ?

(Express in city blocks or miles.) ,

If you wished to represent five miles, or

five city blocks, on a piece of paper the width of this note book, what would you need to do ?



Meaning
of scale.



1



As applied to maps, what is the term used to express this scheme ?



Draw below a distance of 6 miles expressed by a scale of f inch = 1 mile.



How must the scale of a map vary with the size of the area represented ?



If a map of an area 5 miles square, and one of an area 1000 miles square were both of the
same size, which would show more detail ?

Could a road 25 feet wide be

accurately located by double lines on a map drawn to the scale 1 inch = 1 mile ? (Make the
calculation on a separate sheet of paper and copy the calculations and your conclusion below.)



Examine different maps, as directed by the teacher, and note in the space below the areas
they represent and what scales are used.



Name of Map


Scale Used


Area represented in Square Mii.es (to be deter-
mined by Use op the Scale)

































Explain the significance of the fraction (such as ^^) used on maps in connection with
the scale.



Globes. What form would give the most accurate representation, in miniature, of the whole world ?

What are some of the disadvantages of a

globe map; for instance, for use in books? *



Plane

surface

maps.



Try to fit a sheet of paper over one half or more of your desk globe. What is the result?

Examine a baseball. How many parts are

there to its cover? What proportion of the ball's surface does each part of

the cover fit over? Draw an outline of one of these parts.



Why was such a shape adopted for baseball covers ?



Cut a piece of paper of the same shape,

and large enough to use in covering one half of your desk globe. Apply it to your globe in
different positions. What parts of what continents can you cover in different positions?



What great objection to making world maps of this shape does this experiment disclose?



Examine Figs. 28, 444, and 515 in Text-book to see the shape of some of the maps used to
represent the earth on a flat surface. What is the result of your observations?



o



G



#



Materials.



IV. —MAP CONSTRUCTION

For Each Student. — Pencil. Ruler. Desk globe. Dividers.
For General Class Use. — Several wall maps.



Purpose. To gain an understanding of the essential features of a map, methods of map projection, and

their application.

Meaning of In ancient times the land of the world was thought to be longer in an east and west direc-

latitude tion than in the north and south direction. Figure 1 is a copy of an early map of the world,
and

longitude. as Revised by Ptolemy. In what years did he live ?




Fig. 1. — Ptolemy's Map of the World.
Latin was then the language of the Mediterranean region. What is the meaning of the Latin

word longus ? Of the Latin word lotus ?

Which lines on Ptolemy's map are used to mark off the long directions ?

Which lines to

mark off the width?

11



Why were the lines running north and south called lines of longitude ?



called lines of latitude ?



.. Why were those running east and west
Where did Ptolemy start num-



bering the lines of latitude?



Latitude
and

longitude
on the
globe.



The lines of longitude?

What latitude would one have north of a zero point?
What latitude south of a zero point?



What is the zero line of latitude on your globe?

Do you know of any similar natural line which could be used for a zero line of longitude ?

Through what city does the zero line of longitude on your globe

pass? Might not Paris or Washington be used?

• Why, then, does the zero line for reckoning longitude often vary with the

country where the map is made ?

Consult several maps and state which line is most commonly used.



Where is Greenwich?

Trace several lines of latitude around the globe ? Why are these circles called " parallels

of latitude"?

Trace in the same manner several lines of longitude. Are they parallel?



At what two points do they meet?

The longitude lines are called meridians of longitude.

If you have studied geometry, prove that two straight lines can intersect at only one
point.



12



After examining your globe again, will you agree that with the exception of the poles this
proof also applies to the intersection of the parallels of latitude and the meridians of longi-
tude? Bearing this in mind, can any one point

on the earth's surface (except the north and south poles) have more than one latitude and one

longitude? On your desk globe locate the city which has (nearly) 60°

North Latitude and 30° East Longitude from Greenwich.

What is the longitude of this city, starting from Washington as the prime meridian 0°?

Determine from your desk globe the latitude

and longitude (Greenwich meridian) of your home region.

My home, , is at

latitude and at longitude of Green-
wich. How can the exact location, north or south of the equator, of any point on the earth's

surface be stated?

Its distance east or west of any given meridian?



How many degrees are there in the circumference of a circle?

In a half circumference? : A quarter circumference? ,

How many degrees of north latitude can there be?

East or west longitude?

Assuming that the earth's circumference is- 25,000 miles, what is the length, in miles, of a

degree of longitude at the equator? At the

poles? At 60° N. or S. latitude? (Use dividers

for measuring on the globe.) How do the distances

between meridians vary on your globe?



Plane Map makers have devised many schemes to overcome the difficulties of mapping a curved

surface surface on a plane surface. These schemes are called projections. Some of these are the

mapping. Orthographic, Stereograph ic, Globular, Gnomonic, Homolographic, Conic, Polyconic, Van der

Grinten, and Mercator's Cylindrical projections. (See Fig. 2.) How do some of these differ



in the manner of representing meridians and parallels of latitude?



13




100 120 140 ISO 180 180 140 120 100 80 60 40 20 20 40 60

Mercator Projection




Van der Grlnten Projection

« a




Equatorial Stereographic Projection



Western Hemisphere
In Equatorial Globular Projection



Fib. 2. — Various Projections.
14



Why are maps and charts of greater importance to sailors than to any other class of
people?



Kemembering that sailors have instruments for determining latitude and longitude, consider
and state your reasons in answering the following : Which is of more importance to sailors
— to have distances between points shown truly on a map, or to have directions between







points shown as straight lines?



(The Mercator projection was invented by a German whose name was Kramer. In Ger-
man this word means " retail merchant." The Latin for merchant is mercator, and thus the
projection got its name.)

The Mercator projection was designed to show all parallels and meridians as straight
lines at proportional distances ; hence, directions as straight lines. Thus the sailor has sim-
ply to draw upon the map a straight line from the point where he is to the point to which he
wishes to sail, in a straight course. He can then steer his ship according to the bearings thus
obtained.



15



a



o



Materials.
Purpose.



Construct-
ing a
map on
Mercator's
Projection.



V.— THE MERCATOR MAP

For Each Student. — Dividers. Sharp pencil. Ruler. Desk globe.

The construction of a Mercator map; and to get an appreciation of the distortion involved in
such a map.

Figure 3 is a beginning of a Mercator Cylindrical Projection. The circle represents a
north and south section of the globe. The diameter of the circle shows 180° of the equator as
a straight line, and this line is continued into the map diagram that adjoins the circle. From
the center of the circle angles are laid off for every 15° north of the equator. The line A-L,
representing the western edge of the map, is perpendicular to the equator line. The length of
the line parallel to A-L (that is, Bx), and extending from the end (B) of the first radius north
of the equator, gives the distance that the 15° parallel of latitude of the map is to be drawn
north of the equator line. (The 15° parallel, as drawn, is marked C-D on the diagram.) In
the same way the length of the line parallel again to A-L, and extending from the end of the
radius of 30° to the 15° radius, gives the distance that the parallel of 30° north latitude is to
be drawn above that of 15° north latitude. (This, the 30° line, is marked E-F.) Follow this
procedure and complete the drawing of the parallels for both north and south latitude up to 75°.

Draw the meridians of longitude at equal distances from each other, and the same dis-
tance apart as the first parallel of latitude is from the equator. Draw the 0°, or prime
meridian, through the circle printed on the map.

On your globe, with dividers and a ruler, measure the distance (in inches) between 15° of

longitude on the line of the equator. Do the

same along the line of the 60° parallel of north [or south] latitude. ,

What is the ratio between these two distances? r.



On your map, as



drawn, measure the distance between the equator and 15° north latitude.

Again, on your map, measure the distance between 52° 30' north latitude and 67° 30' north

latitude (=15°). What is the ratio between these latter two distances?



From these observations complete the following sentence : On the Mercator projection map,
the distortion in latitude distances is in the same ratio as the



§



and directions are consequently represented as straight lines.



17



a



a



c



f






Plotting in The little circle printed on the map represents the location of Washington, D.C., and is

I the outline on the prime meridian as you have drawn your map. From your globe plot in the outlines of
pi North ^ e con tinents of North and South America.
America
and South
America.



Distortion Compare the outline of these continents on your globe and on the Mercator map you have

of the

Mercator constructed. Where and how does the Mercator projection distort areas?

Projection.



Why, then, is no scale of miles given (except at times along the equator) on a Mercator map ?



1 Examine the maps in Figure 2 of this Manual

and, by comparison with the globe, make observations as to their correctness in representing

direction and distance.



21



Curvature
of earth
on small
areas.



Calculate and draw a line showing the curvature of the earth's surface over a distance of
5 miles, mapped on a scale of 1 inch = 1 mile.

Note. — To find the amount of curvature of the earth's surface for any given distance, use the following
rule : Square the number of miles representing the distance. Two thirds of the resulting number represents in
feet the departure from a straight line.

Calculation : —

Draw line here.



How does this result apply to the amount of appreciable areal distortion shown in maps of
small areas ? ,

How does it compare to the amount of distortion on the world maps ?



22



• UPRIGHT POST



\

i \



12 M.
SEPT. 26 *



\



\



\



\



\10 O'CLOCK"
*SEPT. 26



Fig. 4. — Diagram of Apparatus for establishing the Meridian by the Sun's Position.



23



t



Material.



Purpose.



Determina-
tion of
direction
by sun's
position
and use of
watch.



Method.



VI. — DETERMINATION OF DIRECTION AND ESTABLISHMENT OF MERIDIAN

For Each Student. — Watch (when possible). Ruler. Pencil.

For General Class Use. — Rod. Cardboard.

To study simple methods for determining the cardinal directions and for establishing a
meridian by the sun's position.

Since the sun apparently revolves around the earth from east to west, it must at some
time in its daily course he halfway between these two directions, and therefore where you

live be due (Add proper word.) At what time between sunrise and

sunset would the sun be in this position ?



With a watch in hand we can make use of the sun's position to determine approximately
the cardinal directions, i.e. south, north, east, and west.

Stand facing the sun ; hold your watch so that the hour hand points directly to the sun ;
then a line from the center of the dial, and equally dividing the distance between the hour
hand and the twelve o'clock figure, will point approximately south.

(To the Teacher. — Advise the students of the amount that standard time is slower or faster than sun time
for your locality, and how to apply the correction.)

Try this experiment at different hours of the day. Do the results coincide ?



When is



Establish-
ing a
meridian
by sun's
position.



there the greatest deviation?

Is there a deviation from day to day ?

Facing south, what direction is at your back ? To your right ?

To your left?



Erect a thin rod of wood, or metal, six inches or more high, exactly perpendicular to the
middle point of the long edge of a stiff piece of white cardboard. Put this cardboard on a
smooth table top, carefully leveled, and place the table before a south-facing window with the
edge of the cardboard which carries the rod toward the outside. Note the length and direction
of the shadow which the rod casts on the cardboard by marking on the board, as accurately as
possible, the length and direction when the shadow is shortest. Do this for several days. Set
down the data on Figure 4. Get these data, if possible, on or near Sept. 23 or March 21.

What directions are determined by the line of the sun's shortest shadow ?



25



Suggested On a clear night locate the north star by means of the " Big Dipper," as shown in the diagram (Fig. 5).

home work How well does your determination of north by the sun's position agree with the north as determined by the

■fnr

students position of the north star ?



NORTH STAR .



**






/



* -*«•

Fig. 5. — Diagram to illustrate Method of locating North Star by Means of the "Big Djpper."



26



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Online LibraryRalph S. (Ralph Stockman) TarrA laboratory manual for physical and commercial geography → online text (page 2 of 16)