Isaac Newton Matlick.

Handbook to the Matlick Tellurian; guide to mathematical and astronomical geography online

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ISAAC NEWTON MATL1CK, A. M.



HAND BOOK



TO THE



itatltrk 5te lUtriatt



GUIDE TO MATHEMATICAL
AND ASTRONOMICAL GEOGRAPHY



BY



ISAAC NEWTON MATLICK. A. M.




PUBLISHED BY

AMERICAN TELLURIAN MFG. Co
SEATTLE T A E u L L 5 G m A A N M WASH.

AGENCIES IN PRINCIPAL CITIES IN U. S.



AND IN FOREIGN COUNTRIES



Copyrighted by
The American Tellurian Co.
1915.

Press of

MECHANICS PUBLISHING COMPANY
Seattle, Wash., U. S. A.



Isaac Newton Matlick, A. M.



Isaac Newton Matlick, inventor of the tel-
lurian which bears his name, was born in
Pleasant Township, West Virginia, in the year
1846; and died in San Francisco, California,
February the third, 1913: His remains being
interred in Lone Fir Cemetery, Portland, Ore-
gon. It was in this city where Prof. Matlick
served many years as a principal 'of schools
that he brought to completion the invention of
his tellurian. iTo this great task he gave
thirty-one years of painstaking effort. The
achievement should give him rank among the
great mathematicians and mechanics of the
world.

Those who knew him testify to his great
strength of character, combined with kind-
liness of heart and fine humility. His inven-
tion, wonderful in its capacity to make plain
the great laws of the world and the solar
system, should make his name familiar to the
youth of many generations.



PSALM XIX.



The Heavens declare the glory of God

And the firmament showeth His handiwork.

Day unto day uttereth speech

And night unto night showeth knowledge.

There is no speech nor language;

Their voice is not heard ;

Their line is gone out through all the Earth

And their words to the end of the World.

In them hath He set a tabernacle for the Sun

Which is as a bridegroom coming out of his

chamber
And rejoiceth as a strong man to run His

course.
His going forth is from the end of the

Heavens,

And His circuit unto the ends of it,
And there is nothing hid from the heat

thereof.

Psalms XIX, vs. 1-6.



Table of Contents



Page

Isaac Newton Matlick, A. M 6

Introduction 11

Description of the Tellurian . 15

The Earth 19

Change of Seasons 34

The Moon 45

The Tides 67

Time 78

Precession of the Equinoxes ...... 81

The Solar System 85

Glossary of Technical Terms 88

How to Set up and Adjust the Tellurian. 96

How to Demonstrate to a Class What the Axis of

the Earth Means . . 97



List of Illustrations



Plate Page
Frontispiece 3

II. The Tellurian Insert

[II. The Moon 44

IV. Eclipse of the Sun 57

V. Precession of the Equinoxes ,...,..,. 3



Diagrams



Fig. Page

1. Illustrating Kepler's Second Law 26

2 48

3 48

4 49

5 49

6 48

7 55

8 55

9. ^..,,.,.. r ^. 56



Introduction



This Hand-book is designed as, a guWe to the
Teacher or Student m, using .Matlick's New
Tellurian. In the preparation of this work we
have endeavored to present the principal points
to be shown by the Tellurian, in a plain, simple
manner, so that the inexperienced Teacher, as
well as the Pupil, may readily comprehend
them. There are many 'other points that the
thoughtful Teacher will find valuable to present
which can be accurately explained with the
Tellurian.

The Tellurian represents accurately, in the
most simple mianner, the intricate and complex
movements of the Earth and Moon around the
Sun, showing their relative positions to each
other any day of the year, so that the following
points may be readily comprehended:

1. The causes of a change of season.

2. The causes of day and night, and of the

variations in length of day and night
in different latitudes.

3. The portion of the Earth illuminated

each day in the year.



12

4. The point on the Earth where the direct

rays of the Sun will shine each day of
the year.

5. The cause of the difference in length of

; days or nights,

6. The inclination of the Earth's equator

and axis to the plane of the ecliptic.

7. The direction of the Sun's rays to the

surface of the Earth at different
seasons of the year, and at any hour
in the day.

8. Causes of the present shape of the

Earth.

9. The nature and causes of trade winds.

10. The Sun's declinations.

11. Causes and phenomena of the Equi-

noxes.

12. Nutations of the Earth's polar axis.

13. The difference between solar and

siderial time.

14. The difference between siderial and

clock time.

15. Causes of the Sun being slow or fast.

16. How mean time is computed.

17. The extent and duration of twilight on

any part of the Earth.

18. The different phases of the Moon.

19. Causes of annular, partial and total

eclipses of the Sun.

20. Eclipses of the Moon.



13

21. Umbra and penumbra.

22. The Moon's nodes and their revolution.

23. Eevolution of the apsides.

24. Causes and phenomena of the tides-

spring and neap tides.

25. Effects of perigee and apogee upon

eclipses and tides.

26. The siderial and lunar month.

27. Comparative size of the Earth and

Moon.

28. Center of gravity of the Earth and

Moon.

29. Causes of the harvest Moon.

The following geographical and astronomical
terms can also be illustrated, viz. : Latitude,
longitude, meridians, palallels, axis, poles,
tropics, polar circles, zenith and nadir, vertical
circles, celestial meridian, prime vertical,
azimuth, etc.

In this Hand-book the phenomena of the
tides are explained on a different hypothesis
from that generally given in text-books ; a com-
prehension of the lunar motion of the Earth,
which is represented by the Tellurian, being
necessary to explain the subject.

Thus it will be readily seen that it is not only
a necessity, but an indispensable apparatus for
the Public School, and valuable for High
Schools and Colleges, where the more intricate
problems are to be studied, as it is impossible



14

for any Teacher, however apt in illustration, or
concise in language, to present clearly to the
mind of the pupil the above points without the
aid of proper apparatus. As such apparatus,
it is conceded by the leading educators that
the Matlick Tellurian has no equal.

Although heretofore, for the want of proper
apparatus, these subjects have been imper-
fectly understood, it is now certain that, in the
imimediate future, they will be properly ex-
plained in every school-room through the use
of this marvelously complete and accurate in-
strument.



Description of the Tellurian



The top of the stand (Plate 1) is elliptical to
represent the ellipticity of the Earth's orbit.
The periphery is made to represent the
zodiacal belt a belt 16 in width with the
ecliptic as its center.

Upon the center of the stand is a revolving
hub having a socket (No. 7) into which is
placed the Earth-arm, (No. 3) which is held in
place by a set-screw (No. 8). At the outer end
of the Earth-arm, driven by a bevel gear, is a
vertical shaft which by a simple mechanism
carries the globe made to represent the Earth,
and also the Moon-arm-cam (No. 10). Upon
the Moon-arm (No. 4) is placed the Moon
which is constructed upon the same scale as the
Earth. The Earth is supplied with a time
band (No. 13), a day-band (No. 16), and an
adjustable meridian (No. 17).

As the vertical shaft is rotated the Earth and
Moon revolve about their common center of
gravity, the Earth maintaining its proper in-
clination to the plane of the ecliptic, the North
Pole being always directed to the same objec-
tive point, thus showing very clearly the third



16

or lunar motion of the Earth. The Moon rises
and falls in its orbit and passes through all its
phases, showing the inclination of its orbit to
the ecliptic and the gyration of its nodes, which
are so arranged that not only the cause but the
date of recurring eclipses may be shown by the
Tellurian.

The day-band shows the exact portion of the
Earth illuminated by the Sun each day in the
year. With the day-band, time-band and ad-
justable meridian a child of ten can tell the
time of sunrise and of sunset for any place and
date. The degree of latitude on the Earth im-
mediately under the noon point of the time-
band will indicate the distance of the vertical
rays of the Sun north or south of the Equator
for each day in the year.

The mechanism may be thrown out of gear
by releasing the clutch (No. 12) by means of
the thumb-screw. When released the Earth
may be revolved on its orbit without rotating
on its axis ; or the Earth and Moon may be re-
volved about their common center of gravity
without moving the Earth along its orbit. The
axis rod (No. 14) is rotated by simple friction
so that the Earth may be rotated on its axis
without moving any other parts.

The top and periphery of the stand is cov-
ered with a colored chart. On the central disk
is the general plan of the Solar System, in-



17

eluding all the Planets, their satellites, and a
comet, with their corresponding sizes and dis-
tances, as near as practicable. The perihelion
point of each Planet is marked in its orbit with
the letter P. The Planets all move in the same
general direction around the Sun as that of the
Earth. On the main portion of the stand, and
extending to the edge, the chart shows the
months of the year, and their divisions into
days ; the different signs of the zodiac through
which the Sun will pass any month or day ; the
right ascension of the Sun in hours and de-
grees for any day; the number of minutes the
Sun is slow or fast for any day in the year;
the autumnal and vernal equinoxes; the sum-
mer and winter solstices; the aphelion and
perihelion; when the seasons begin, etc. The
chart on the rim shows the ecliptic or orbit of
the Earth through the great zodiacal bell,
showing the signs in which the Earth will ap-
pear, looking from the Sun, and its right ascen-
sion in hours and degrees for any day in the
year; the astronomical and almanac signs
representing each particular sign of the zodiac.
At the perihelion point the Earth is shown to
be several inches nearer the Sun than at the
aphelion.

The instrument is so perfect and durable in
its construction that nothing less than actual
violence can break of put it out of order, and,



18

with the accompanying instructions, any one
can operate it, and understand the subjects
designed to be illustrated.

The object of this highly instructive ap-
paratus is to illustrate and simplify, to the eye
of the learner, the whole theory of Celestial
Mechanics, including the rudiments of Astron-
omy and Mathematical and Astronomical Geo-
graphy.

No other instrument can claim but a small
part of what this instrument actually does, as
the Matlick New Tellurian is the only instru-
ment that correctly represents the true motions
of the Earth and Moon, showing their exact
relation to each other and to the Sun for each
day in the year. There are no fewer than one
hundred theorems and problems included with-
in the above subjects that this instrument is
capable of illustrating.



SUN BALL

No.- 2






SET SCREW
No. 8



Shipped Complete
Assembled




EARTH ARM SOCKET
No. 7



AXIS ROD

MOON ARM CONNECTION No. 14
No. 9



MOON ARM
No. 4

I MOON ARM
CAM j
\ No. 10

\

EARTH ARM CONNECTION
No 6




RELEASE NUT
No. 12



MOON ARM STANDARD
No. 11



The Earth



The form of the Earth is very nearly that of
a globe, slightly flattened at the poles. This
figure is known to mathematicians as oblate
spheroid. This flattening at the poles is very
slight, being about l-300th part of the diameter
of the Earth. The axial' diameter is about
twenty-six miles less than the equatorial. The
circumference of a great circle of the earth is
about 25,000 miles, and the diameter of that
circle is about 8,000 miles. The surface of the
Earth embraces an area of 200,000,000 square
miles, of which 50,000,000 is land and the re-
mainder water. For the convenience of de-
termining positions on the Earth, certain
imaginary lines, or circles, are supposed to be
drawn upon it.

The Axis of the Earth is the diameter about
which it revolves, and the extremities of the
axis are donominated the poles; the one above
the equator the North Pole, and the one below,
the South Pole.

The Equator is a great circle, at equal dis-
tances from the poles, and dividing the Earth
into two parts, called the Northern and South-
ern Hemispheres.

The Parallels of Latitude are small circles
parallel to the Equator, and are drawn for



20

every ten degrees, and are numbered, from the
Equator to the poles, 90., North ! of the Equa-
tor is called North Latitude, and south of the
Equator is called South Latitude. The width
of a degree of latitude is 69 1-6 miles.

Meridians are great circles passing from the
North Pole to the South Pole, and crossing the
Equator at right angles. Upon the globe used
on the Tellurian to represent the Earth, the
meridians are marked every 15, which cor-
responds to one hour of time. That is, it will
require one hour for the vertical rays of the
Sun to pass over 15 of longitude. These cir-
cles are numbered to the east 180 and to the
west 180, from the meridian of Greenwich,
which passes near London. East of this estab-
listed meridian is called East Longitude, and
west, West Longitude. The width of a degree
of longitude on the Equator is 69 1-6 miles, but
terminates at the poles, where the width is 0.

The Tropics. It will be observed, in the
motion of the Tellurian, that the vertical rays
of the Sun fall upon the Earth 23y 2 north and
23y 2 south of the Equator, when the Earth is
in different points of its 'orbit, marking,
respectively, the Tropic of Cancer and the
Tropic of Capricorn. The day circle of the
Earth, at the point where the vertical rays are
farthest north, will show that the rays of the
Sun shine 23i/ 2 beyond the North Pole, and



21

fall 23y 2 short of reaching the South Pole, or
when the vertical rays are farthest south the
reverse of this order will be the result. These
positions of the Sun's rays to the Earth mark
the Arctic Circle, 23y 2 from the North Pole,
and the Antarctic Circle, 23 1 /2 from the South
Pole.

Zones. We thus see why the Earth is
naturally divided into five zones. The region
north and south of the Equator, and between
the Tropics of Cancer and Capricorn, over
which pass the vertical rays of the Sun, is
called the Torrid Zone, and is 47 in width.
The region between the Tropic of Cancer and
the Arctic Circle is called the North Temperate
Zone, 43 in width. The region between the
Tropic of Capricorn and the Antarctic Circle,
the South Temperate Zone, 43 in width. The
regions beyond the polar circles are called the
North and South Frigid Zones.

Daily Motion. If we observe the positions
of the Sun, Moon and Stars for a few succes-
sive nights, we shall see their relative positions
gradually change. In our observations for any
day or night, all the heavenly bodies appear to
move to the west. The motions are, of course,
only apparent, as there is absolute proof of
the motions of the Earth in an opposite direc-
tion to the apparent motion of the heavenly
bodies. All the apparent motion of the heaven-



22

ly bodies that seemingly pass to the westward,
is the result of the daily revolution of the
Earth on its axis to the east. As a result 01
the diurnal motion of the Earth, we see the
Sun rise in the east and set in the west each
day, producing day and night. When the Sun
passes below the horizon its light is no longer
visible, and one-half the Earth is wrapped in
darkness. As the pin in the center of the solar
semi-circle band indicates noon ( on any merid-
ian brought to it, so the meridian on the oppo-
site side of the Earth must indicate mid-night ;
consequently to an observer on the midnight
meridian, the Earth is directly between him and
the Sun. Strictly speaking, the Earth revolves
on its axis in about 23 hours and 56 minutes,
but, as the Earth is continually changing its
longitude, the day is 24 hours long. It will,
therefore, make 366 revolutions in a year of
365 days.

Difference in the Length of Day and Night.

Since the Sun shines on but one-half of the
Earth at a time, it is evident that at the
Equator the days and nights must always be of
equal length. If the axis of the Earth were
perpendicular to the plane of the ecliptic, so
that the Sun always shone from pole to pole,
the days and nights would forever be of the
same length on all parts of the Earth. But to
an observer, on any parallel north or south of



23

the Equator, the length of the days and nights
will vary in different parts of the year, and the
nearer he approaches the poles the greater will
be the difference, until he reaches the poles,
where the days and nights are alternately six
months in length. Sometimes the days are
longest, and again the nights. These differ-
ences are regular and uniform, and their re-
currence is the same for each year.

Annual Motion. The various changes in the
length of day and night must be looked for
from another cause than the rotation of the
Earth on its axis. In observing the fixed Stars,
it will be noticed that they do not appear on
the same meridian at the same time each night,
but about four minutes earlier, so that they
appear to have a general motion to the west, in
addition to their apparent diurnal motion.
Any particular Star seen to rise in the east at
a certain hour in the night will be seen to
gradually course its way across the heavens so
that in six months from that night, at a cor-
responding hour, it will fall below the western
horizon. It will, of course, rise and set each
day or night, but will come to the meridian
earlier each night. From this and other causes
it has been fully demonstrated that the Earth
has an annual course around the Sun from the
west to east. By this motion the Sun appears
to be carried around the ecliptic through the



24

fixed Stars. Now, as the Sun appears high in
the heavens in one part of the ecliptic, and
again falls toward the horizon, it is evident
that the Earth's axis is not perpendicular to
the plane of the ecliptic, but inclines from this
perpendicular. It is found that the Sun's high-
est and lowest meridian altitude differ 47.
Now, one-half of this, or 23%, must represent
the inclination of the Earth's axis, and the
Earth's Equator must necessarily make an
angle with the plane of the ecliptic of 23%.

The Poles. The North Pole of the Earth
is denominated the elevated pole, because it is
always about 66% above the plane of the
ecliptic, or about 23% from a perpendicular to
the plane of the ecliptic; and the South Pole is
denominated the depressed pole, because it is
about 66% below the plane of the ecliptic, and
23% from a perpendicular to the plane. These
motions and the direction of the Earth's axis
are so perfectly represented in the Tellurian
that the student cannot fail to comprehend the
entire subject.

The Day Circle on the globe, as used on the
Tellurian, when properly adjusted, shows
exactly the portion of the Earth illuminated
each day, and the variation in the lengths of
day. So the learner's attention is directed
wholly to it at the present. At the Vernal
Equinox the Sun's rays shine from pole to



25

pole, but, as the Earth moves along in its orbit,
the North Pole is gradually turned into the
sunlight, and the South Pole into the darkness,
until the Earth arrives at the summer solstice
June 21 when the North Frigid Zone is
\vliolly in the sunlight, and the South in dark-
ness. It will be seen that for six months tne
days in the Northern Hemisphere hctve grad-
ually increased in length, and in the Southern
Hemisphere have diminished. They are now
longest north of the Equator and shortest
south. Now, as the Earth is moved around to
the autumnal equinox, the days naturally di-
minish in length in the Northern Hemisphere,
and increase in the Southern Hemisphere, until
they are again equal. If the motion is con-
tinued to the winter solstice December 21
the days in the Northern Hemisphere will be
shortest, arid in the Southern Hemisphere long-
est. The North Frigid Zone is wholly in dark-
ness, and the South Frigid Zone in the sun-
light. For any day between these dates the
day circle will show the corresponding lengths
of day and night on any portion of the Earth.
The length of a parallel on the Earth shown
by the day circle to be illuminated, as com-
pared by that portion on the opposite side, will
indicate their relative lengths. The meridians
marked on the Earth, followed to the hori-
zontal band with the 24 hours of day and night



26

on the dark and illuminated sides, will serve as
a means of measurement.

When the Sun Rises, and When It is Mid-
night at the Poles. When the Sun passes the
vernal equinox, it rises to the Arctic, 'or elevat-
ed, Pole, and sets to the Antarctic Pole. When
the Sun arrives at the summer solstice it is
noon at the North Pole, and midnight at the
South Pole. When the Sun passes the
autumnal equinox, it sets to the North Pole,
and rises to the South Pole. When the Sun
arrives at the Winter solstice, it is midnight at
the North Pole, and noon at the South Pole;
and when the Sun comes again to the vernal
equinox, it closes the day at the South Pole,
and lights up the morning at the North Pole.




Illustrating Kepler* s Second Law.
Fig. 1.

The illuminating band, or day circle, on the
Earth, will show how the sunlight approaches
or recedes from the pole.

The Nights at the Poles Not Equal. By con-
sulting an almanac for any year one discovers
that the time required for the Sun to make its
apparent journey from the autumnal equinox



27

to the vernal equinox is V7Sy 2 days, while from
the vernal equinox to the autumnal requires
186V 2 days. This results from what is known
as Kepler's second law of planetary motion.
(Fig. 1). The radius vector describes equal
areas in equal times. That is, in our winter,
the Earth being in perihelion, moves more rap-
idly in its orbit than when in aphelion. This
is clearly exhibited by the Telurian.

Night Within the Polar Circle. At the Arc-
tic Circle, 23 27y 2 ' from the Pole, the longest
day is 24 hours, and goes on increasing as you
approach the Pole. In latitude 67 18' it is 30
days; in latitude 69 30' it is 60 days, etc. The
same takes place between the Antarctic Circle
and the South Pole, with the exception that the
day in the same latitude south is a little
shorter, since the Sun is not S'o long south of
the Equator as north of it. At Spitzbergen the
day gradually increases in length from the first
glimpse of the Sun on February 21, to 12 hours
on March 21; then to 24 hours on April 21,
when the Sun remains continuous above the
horizon until August 21. The day then alter-
nates with night, decreasing from 24 hours to a
parting glimpse on October 21, when night con-
tinues for four months. In the southern part
of Nova Zembla we find continuous day and
night of about six weeks each, and then day
and night alternate for twenty weeks each.



28

Further north, the periods of alternate day and
night are shorter, decreasing to the Pole. At
Wanderbus, in Norway, the day lasts from the
21st of May to the 22d of July, without inter
ruption.

Day in the Temperate and Torrid Zones.

The greatest length of day in the Torrid Zone,
which must be on the tropics, is 13Vi> hours.
The greatest length of day in the Temperate
Zone, which must be on the polar circle, is 24
hours. At Portland, Oregon, the longest day
has 151/2 hours; at Boston, IS 1 /!; at Berlin and
London, IG 1 /^; at Stockholm and Upsaal, IB 1 /-!*;
at Hamburg, Dantzic and Stettin, 17, and the
shortest, 7. At St. Petersburg and Tobolsk the
longest day has 19, and the shortest 5 hours.
At Bornea, in Finland, the longest day has
21%, and the shortest 2y 2 hours. The night
must, in all cases, be 24 hours, minus the length
of the day, and vice versa. As the change of
the Sun's declination is less at the solstices
than at the equinoxes, so the change in the
relative length of day and night must also ho
variable in the same places. To illustrate this
point more fully, the learner's attention is
called to the position of the Earth to its orbit.
It will be noticed that at the equinoxes the
Earth moves in a direction very nearly indi-
cated by its axis; so that from March 21 to
April 21 the Sun moves northward about 10,



29

and from April 21 to May 21 about 9, and
from May 21 to June 21 about 4 ; so that the
Sun changes its declination very slowly at the
solstices, as the Earth then is moving very
nearly in a direction indicated by a parallel of


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