Manual to accompany the lunatellus globe, containing a complete course of problems and illustrations of the fundamental principles of geography and astronomy, for the use of teachers, schools and families

Preface

This Manual is a guide to the proper use of the Lunatellus Globe, which faithfully illustrates the principles of Geography and Planetary motion. The pupil's greatest difficulty in obtaining a correct knowledge of Mathematical Geography and Astronomy, often arises from previous false conceptions of their principles acquired sometimes with the use of imperfect Apparatus. This fact intruding itself so frequently in the Class-room, suggested the necessity of the Lunatellus Globe; which on account of its convenience, accuracy and durability, is rapidly filling a vacuum in Families and Schools. It contains three bodies, one of them being a twelve inch Terrestrial Globe, which by their relations and motions exhibit the natural relations and motions of the Sun, Earth and Moon. The body representing the Sun, is made to turn on its axis, while the Terrestrial Globe, having its axis properly inclined, has a similar motion, and at the same time revolves in its orbit around the Sun, showing his rising and setting, his Declination, or apparent motion North and South, the change of Seasons, the vicissitudes of Day and Night and their alternate increase and decrease in length. The body representing the Moon, is made to revolve around

PREFACE.

the Earth in an elliptical orbit, whose plane is at an angle of about five degrees with the plane of the Ecliptic; also around the Sun and on her own axis, exhibiting her days and nights, changes, phases and fulling and the interestingphenomena of Solar and Lunar Eclipses. The principles of Geography and Astronomy and t-he phenomena resulting therefrom, being involved in the form and movements of this Apparatus, the manual contains a consecutive series of Problems and Examples based upon these principles \vhcreby the pupil may have an accurate, and practical illustration of their meaning.

The Author while preparing this Manual, carefully consulted the best English, French and American Authorities on the use of Globes, with the view of having it simple, brief and at the same time sufficiently comprehensive for the purpose for which it is designed.

The Definitions and Explanations which relate to the subjects considered in this Manual are, for the sake of convenience placed after the Illustrations and Problems. And in connection with each of the Illustrations and Problems reference is given to such Definitions and Explanations as should be studied with care before entering upon its solution.

Part I. Illustrations

I. To illustrate the motions of the Sun, Earth and Moon.

II. To illustrate the Plane of the Ecliptic and its relation to the Plane of the Equator.

III. To illustrate the Inclination of the Earth's axis

and its Parallelism.

IV. To illustrate the cause of Day and Night.

V, To illustrate the equality of Day and Night on the 21st of March, or 21st of September.

VI. To illustrate the cause of long Days and short

Nights in the Northern Hemisphere.

VII. To illustrate the cause of long Days and short Nights in the Southern Hemisphere.

VIII. To illustrate the cause of six months Day at the North Pole and six months Night at the South Pole, and vice versa*

IX. To illustrate the cause of the inequality in the length of Days and Nights.

X. To illustrate the rising and setting of the Sun.

XI. To illustrate the cause of Winter in the Northern Hemisphere and Summer in the Southern Hemisphere.

XII. To illustrate the cause of Summer in the Northern Hemisphere and oi Winter in the Southern Hemisphere.

Part II. Problems

I, To find the Longitude of a given place.

II. To find all places which have the same Longitude as that of any given place.

III. To find the Latitude of a given place.

IV. To find all places which have the same Latitude

as that of any given place.

V, The Longitude and the Latitude of any place being given to find the place.

VI. Two places being given to find their difference of Latitude.

VII, Two places being given to find their difference of Longitude.

VIII. To find the distance between to places.

IX. To find places equally distant from a given place.

X. The Latitude of a place, its distance and general direction from a given place, bekig given, to find the place whose Latitude is given.

XI. The Longitude of a place, its distance and general direction from a given place, being given, to find the place whose Longitude is given.

XII. Any parallel of Latitude being given, to find how many miles make a degree of Longitude on it.

Part III. Illustrations

XIII. To illustrate the distribution of Solar light and

heat when the Earth is at either Equinox,

XIV. To illustrate the distribution of Solar light and

heat on the longest day in the Northern Hemisphere.

XV. To illustrate the distribution of Solar light and heat on the longest day in the Southern Hemisphere.

XVI. To illustrate the succession of the Seasons.

XVII. To illustrate the cause and width of the Zones.

XVIII. To illustrate Sun time and Clock time alternately fast and slow,

XIX. To illustrate the Sun rising North of the East point and seating XoYth of the West point during one-half of the year, and rising South of the East point and setting South of the West point during the other half of the year,

XX. To illustrate the cause of the Sun rising earlier on places East of us,

XXI. To illustrate the cause of the apparent motion

of the Sun, Moon and Stars, from East to West.

XXII. To illustrate the declination of the Sun, or his

apparent motion North and South.

XXIII. To illustrate the relation of the Sun's declination

to the Horizon every day in the year.

XXIV, To illustrate the relative position of the Earth

to the Sun every day in the year.

PART IY.

PROBLEMS.

XIII. To find at what rate per hour any given point

on the Earth's Surface moves by its axial rotation.

XIV. To find the difference of time between any two

places which are not under the same Meridian. XV. The hour being given at anyplace, to determine what hour it is at any other given place.

XVI. To find the Sun's place in the Ecliptic on anygiven day in the year,

XVII, To find the Sun's Longitude on any given day in the year.

XVIII, To find the Sun's Declination and Right Ascension for any given day in the year.

XIX, To find on what two days of the year, the Sun will be vertical at any given place within the Tropics.

XX, To find all places where the Sun is vertical on any given day.

XXI. To find that part of the Globe where the Snn ceases to rise and that part where he ceases to set on any given day.

XXII. To illustrate a Right Sphere.

XXIII. To illustrate an Oblique Sphere.

XXIV, To illustrate a Parallel Sphere.

PART Y.

ILLUSTRATIONS.

XXV. To illustrate the Sun and Earth as always in opposite Signs of the Zodiac.

XXVI. To illustrate the inequality of Sidereal and

Solar days.

XXVII. To illustrate the Spring and Neap tides.

XXVIII. To illustrate the effects on the tides of Solar and Lunar declination.

XXIX. To illustrate the cause of the trade winds.

XXX. To illustrate the influence of the Sun in producing the Monsoons.

XXXI. To illustrate the cause of land and sea breezes.

XXXII. To illustrate the Moon as always having the same side towards the Earth.

XXXIII. To illustrate the length of Lunar days and

nights.

XXXIV. To illustrate the Conjunction, Quadrature,

Opposition and Phases of the Moon,

XXXV. To illustrate the eccentricity of the Moon's orbit.

XXXVI. To illustrate the relation of the Moon's orbit to the Plane of the Ecliptic.

XXXVII. To illustrate the Sidereal and Sy nodical revolutions of the Moon.

XXXVIII. To illustrate Solar and Lunar Eclipses.

LUNATELLUS GLOBE.

Letters representing the principal parts of the Lunatellus Globe.

A, The Arm which carries the Earth and Moon. F, The Semi-circle, representing the plane of the Ecliptic. C, The Circle of Illumination. I, The Calendar Index. H, The Hour Index, B, The Base.

Q, The Quadrant. S, The Sun.

M, The Moon. E, The Earth.

D, The Cap which carries the Sun.

Directions for putting the parts together.

ist. Place the rear end of the Arm A in the Cap D and tighten the screws in the Cap. Then revolve the gear in the Arm A with the fingers, till the central axis of the Globe over which we place its tubular axis, inclines directly towards the center of the Cap D.

2nd. Place the Cap Don the central part of the Base B, with the Arm A directly over the word Solstice, June 21st, and fasten the Cap, Arm and Base together with the bolt which contains a thumb nut.

3rd. Place the tubular axis of the Globe on its central axis which is carried by the Arm A, so that the gear on the upper end of the standard, fixed in the outer end of the Arm A and the gear connected with the South Pole of the Globe, will come together; observing at the same time to have the outer ends of the yoke extending from the South Pole equally distant from the center of the Cap D.

LUNATELLUS GLOBE.

4th. Place the Hour Index on the North end of the tubular axis of the Globe, and attach with a screw to the central axis of the Globe, the small metal bearing, containing a square hole in one end and a knob with a groove in it loosely pivoted in the other end ; observing to incline the bearing in putting it on directly away from the center of the Sun when it is in place, and then put the inner edge of the Circle of Illumination in this groove, as it is being connected to the Instrument by the pivots of the yoke.

5th. Finally, place the Sun S with the Semi-circle F attached, at right angles with his Polar axis, on the center of the Cap D, and adjust the Moon Rod as the parts at the outer end of the Arm A suggest, and the Apparatus will be ready to operate.

The Lunatellus Globe is the only device in existence which faithfully illustrates the mutual relations and various movements of the Sun, Earth and Moon. It is composed wholly of Iron Brass and Steel, except the Terrestrial Globe which represents the Earth, and the Chart that covers the Base.

BASE AND CHART.

The Base of the Instrument is cast in one piece and has p!a ed upon it a Chart showing how the Sun, Earth and Moon perform their functions, as members of the £olar System, every day and hour in the Year.

T!ie Chart contains in their proper relations, the Signs of the Zodiac, the months and days of the Year, the various lengths of the Seasons, the periods when the Sun is fast and slow, the degrees of Celestial Longitude, the Perihelion, Aphelion, Solstitial and Equinoctial points, together with other Symbols relating to the various movements of the Apparatus.

SUN AND SEMI-CIRCLE.

The Sun is represented by a body composed of Brass and connected by one of its Poles to the gearing within. To the Equator of this body is attached a Semi -circle which, when properly adjusted represents the Plane of the Ecliptic.

LUNATELLUS GLOBE.

EARTH.

The Earth is represented by a Terrestrial Globe, twelve inches in diameter, and is pivoted by the South Pole to the gearing which gives it rotary motion.

MOON.

The Moon is represented by a Globe relative in size to that of the Terrestrial Globe, and is attached at one of its Poles to the outer end of a bent rod, the inner end of which is loosely pivoted to an upright placed on a disk which revolves, carrying the Moon around the Earth and and causing her to cross and recross the plane of the Ecliptic at an angle of about 5 degrees, as both Earth and Moon revolve around the Sun.

CIRCLE OF ILLUMINATION.

The Circle of Illumination is a flat Metallic Ring surrounding the Globe and loosely pivoted in the plane of the Equator, so that it is at liberty to change its position every moment as the Globe revolves around the Sun.

Note. — This is the only Invention which produces this result In a natural way.

CALENDAR INDEX.

The Calendar Index is located in the Arm A that carries the Earth and Moon around the Sun, and it can be set in a moment by revolving the Arm, so as to point to any day of any month, or any day of the Year.

LUNATELLUS GLOBE.

.QUADRANT OF ALTITUDE.

The Quadrant of Altitude is a flexible strip of Metal graduated into equal parts, each corresponding in length to a degree on the Terrestrial Globe and bent when in use so as to closely fit its surface.

GEARING.

This Apparatus is operated by Brass and Steel Gearwheels, some of which are inside of the case and some enclosed in the outer end of the Arm that carries the Earth and Moon around the Sun.

UTILITY AND ECONOMY.

The principles of Geography and the various positions, -motions and phenomena of the Sun, Earth and Moon are expressed by this Instrument with such precision and accuracy that more can be learned with its use in a few lessons, than can be learned m months without it, hence its necessity in every School and Family.

The Lunatellus Globe is manufactured by skillful Mechanics in the most sustantial manner , and an exact duplicate of any part of it may be obtained at any time, by applying to the Patentee.

EQUINOXES AND SOLSTICES.

That the Language of this Manual may be adapted with equal advantage to instruction in Schools and Families both North and South of the Equator; and that there may be no misapprehension, as is frequently the case in the use of terms, descriptive phrases are employed when necessary, which convey definite ideas. Instead of referring to the four Cardinal points of the Earth's orbit in the illustrations within, by their usual names Vernal Equinox, Autumnal Equinox, Summer Solstice and Winter Solstice, they are designated by the first points of the Signs where they are, and simply named Equinox and Solstice as the case may be. The Sun and Earth are at opposite Solstice^ at the same time and also at opposite Equinoxes at the same time, consequently they are just entering opposite Signs. On the 21st of March the Sun is at the first point of the Sign Aries which is named Vernal Equinox and from which Celestial Longitude and Rirht Ascension are reckoned. On the same date, 21st of March, the Earth (though at the first point of the Sign Libra) is sometimes said to be at the Vernal Equinox, as Spring in the Northern Hemisphere immediately follows. Language equally ambiguous is frequently employed in expressing the relation of the Sun and Earth to the Solstices at different Seasons of the year. Hence to avoid all uncertainty as to the points referred to in the following illustrations, they are definitely described by naming the first points of the Signs where they are.

Part I Illustration I

To Illustrate the Motions of the Sun, Earth and Moon.

See Definition 50.

It will be apparent if motion is imparted to the Arm

A in the order of the Signs of the Zodiac, that the Sun's

motion on his axis, the Earth's annual motion around the

Sun and her daily motion on her axis, and the motions of

the Moon around the Sun, around the Earth and also on

her axis are in the same general direction, Eastward.

Note. — The order of the Signs is as follows : Aries, Taurus, Gemmini, Cancer, (Sic.

ILLUSTRATION II.

To Illustrate the Plane of the Ecliptic and its relation to the Plane of the Equator.

As the Planes of the Equator and Ecliptic cross each other in the centre of the Earth at an angle of about 23^ degrees, by placing the Semi-circle F, which is attached to the Equator of the Sun in a horizontal position, it will show the natural relation of the Plane of the Ecliptic to the Plane of the Equator as the Earth revolves around the Sun.

ILLUSTRATIONS.

ILLUSTRATION III.

To Illustrate the Inclination of the Earth's Aoois and its Parallelism.

As the axis of the Earth is inclined about 23*^ degrees to the Plane of the Ecliptic, by revolving the Earth around the Sun it will be apparent that its natural inclination is constantly maintained and also its parallelism.

ILLUSTRATION IV.

To Illustrate the Cause of Day and Night.

See Definition 4.

The Earth being globular and opaque, the Sun enlightens constantly that half next himself, making day, while the other half which is opposite to him is in darkness, making night. By giving the Arm A motion, the Earth will turn on its axis and that half next to the Sun will be turned into the shade of the Earth which is night, while the other half which is in darkness, will be turned into the light of the Sun which is day.

Note. — That half of the Earth's surface on the opposite side of the Circle of Illumination C from the Sun is regarded as being in darkness.

The Circle of Illumination is the metal ring which surrounds the Globe and it represents the line around the Earth which divides day from night.

ILLUSTRATIONS.

ILLUSTRATION V.

To Illustrate the Equality of Day and Night on the 21st of March or 21st of September.

Move the Arm A till it is over the First point of the Sign Aries, marked Equinox on the Base of the Instrument, or over the First point of the Sign Libra, also marked Equinox, and it will be apparent from the position of the Circle of Illumination that each Pole is equally distant from the Sun and that the light of the Sun extents to each Pole) consequently half of the Equator and half of each of the Parallels are in the presence of the Sun and half of each is in darkness.

Now since the Earth turns with uniform motion on her axis each half \\\\\ revolve through the same space in the same period, hence day and night are equal.

ILLUSTRATION VI.

To Illustrate the Cause of Long Days and Sho t Nights in the Northern Hemisphere.

Bring the Arm A to the First point of the Sign Capricornus (marked Solstice), and the Circle of Illumination will be 23^ degrees distant from each Pole dividing the Northern Hemisphere, which is inclined towards the Sun into two unequal parts, with the larger part next the Sun: hence, as the Earth turns uniformly on her axis, the cause of Long days and Short nights in the Northern Hemisphere will be apparent.

ILLUSTRATION VII.

To Illustrate the Cause of Long Days and Short Nights in the Southern Hemisphere.

See Definition 77.

Bring the Arm A to the First point of the Sign Cancer (marked Solstice), and the Circle of Illumination will be 23*^ degrees distant from each Pole dividing the Southern Hemisphere which is inclined towards the Sun into two unequal parts with the larger part next the Sun; hence as the Earth turns uniformly on her axis, the cause of long days, and short nights in the Southern Hemisphere will be apparent.

ILLUSTRATION VIII.

To Illustrate the cause of Six Months Dai/ at the

North Pole and Six Months Night at the

South Pole, and vice versa.

Bring the Arm A to the First point of the Sign Libra (marked Equinox), and the Circle of Illumination C will be over the Poles. Move the Arm A in the order of the Signs, observing that the North Pole is irside towards the Sun, and the South Pole is outside of the Circle of Illumination away from the Sun, till the Arm A reaches the first point of the Sign Aries (marked Equinox) when the Cir

ILLUSTRATIONS.

cle of Illumination C will be again over the Poles. Continue the motion of the Arm A, observing that the North Pole passes outside and the South Pole passes inside the Circle of Illumination and remain so till the Arm A reaches the Equinox from which it started ; hence as the distance which the Earth has traveled around the Sun represents one year, each pole was in alternate light and darkness for half of this period.

ILLUSTRATION IX.

To Illustrate the Cause of the Inequality in the Length of Days and Nights.

Were the Earth's axis perpendicular to the plane of the Ecliptic the Planes of the Equator and the Ecliptic would coincide, and day and night would be always equal, as the light of the Sun would constantly extend to each Pole ; but the inclination and constant parallelism of the Earth's Axis, and her annual motion, as may be observed by giving the Globe a complete revolution around the Sun from either Equinox will show each Hemisphere to be unequally divided during each half year by the Circle of Illumination ; hence the inequality of the days and nights in each Hemisphere.

ILLUSTRALION X.

Ho Illustrate the Rising and Setting of the Sun.

Move the Arm A in the order of the Signs and the Globe will turn Eastward on its axis, thereby causing those portions of the Globe that are in the darkness or away from

ILLUSTRATIONS.

the Sun to pass under the Circle of Illumination into the presence or light of the Sun, and those portions of the Earth that are in the light of the Sun to pass under the Circle of Illumination away from the Sun into darkness.

ILLUSTRATION XI.

To Illustrate the Cause of Winter in the Northern

Hemisphere and Summer in the Southern

Hemisphere.

See diagram of Summer and Winter Rays on the Base B.

Bring the Arm A to the first point of the Sign Cancer (marked Solstice) and the North Pole will be inclined away from the Sun; hence his rays will be oblique and the days short in the Northern hemisphere, and in the Southern Hemisphere the Sun's rays will be more direct and the days long, making Winter in the former and Summer in the latter.

ILLUSTRATION XII.

To Illustrate Summer in the Northern Hemisphere and Winter in the Southern Hemisphere.

Bring the Arm A to the first point of the Sign Capricornus (marked Solstice) and the North Pole will be inclined towards the Sun; hence his rays will be more direct North of the Equator and the days long in the Northern Hemisphere, and in the Southern Hemisphere the Sun's rays will be oblique and the days short, making Summer in the former and Winter in the latter.

Part II. Problem I

To Find the Longitude of a given Place.

See Definitions 48, 26, and Notes.

Count the number of degrees on the Equator of the Globe, East if the given place is East, or West if the given place is West, between the Prime Meridian and the Meridian passing through the given place and it will be the required Longitude.

EXAMPLES.

1. What is the Longitude of Ottawa?

2, What is the Longitude of Tokio?

PROBLEM II.

To Find all Places which have the same Longitude as that of a given Place.

Find the Longitude of the given place by Problem I. and under the Meridian passing through the given place will all other places be found which have the same Longitude.

EXAMPLES.

1. What is the Longitude of Montevideo?

2. Find other places having the same Longitude.

3. What is the Longitude of Quebec?

4. Find other places having the same Longitude.

PROBLEMS AND EXAMPLES.

PROBLEM III.

To Find the Latitude of a given Flaoe*

See Definitions 18, 46.

Find the given place on the Globe and lay the Quadrant on the Globe with O on the Equator and its graduuated edge touching the place and at right angles wi h the Equator, and the number of degrees counted on the Quadrant from the Equator to the given place will be the Latitude required.

Note. — For the sake of brevity the word Quadrant is used instead of the phrase "Quadrant of Altitude. ,,

Note. — The Quadrant of Altitude is ^.flexible strip of metal graduated into equal parts, each corresponding in length to a degree on the Globe and bent when in use so as to lit its surface.

EXAMPLES.

i. What is the Latitude of St. Paul? 2. What is the Latitude of Santiago?

PROBLEM IV.

'•To Find all places ivhicJi have the same Latitude as that of a given Place*

See Definition 30.

Find the Latitude of the given place by Problem III. and imagine a Parallel drawn through the given place, and all other places on this Parallel will have the same Latitude as that of a given place.

i. What is the Latitude of Paramarabo?

PROBLEMS AND EXAMPLES.

2. Find other places having the same Latitude,

3. What is the Latitude of Bahia?

4. Find other places having the same Latitude.

PROBLEM V.

The Longitude and Latitude of any Place being

Find the given degree of Longitude as in the first part of Problem I. and place the Quadrant on the Globe at right angles to the Equator, with O at the given degree of Longitude, and the required place will be found under the degree on the Quadrant corresponding to the given Latitude.

EXAMPLES.

i. Find the Point on the Globe whose Longitude is 150 degrees East and Latitude 40 degrees South.

2. Find the Point on the Globe whose Longitude is 10 degrees West and Latitude 15 degrees North.

PROBLEM VI.

Two Places being given to find their difference of Latitude.

Find the Latitude of each place by Problem III. and if both places are on the same side of the Equator, subtract the less number of decrees of Latitude from the greater and the remainder will be the difference of Latitude; but if the Latitude of one of the places is North of

PROBLEMS AND EXAMPLES.

the Equator and that of the other South of the Equator,

add them together and their sum will be their difference of Latitude.

EXAMPLES.

i. What is the difference of Latitude between Pittsburgh and Charleston?

2. What is the difference of Latitude between Cape Town and Cairo?

PROBLEM VII.

Two Places being given to find their Difference of Longitude.

See Definition 21, Note 3d, and Definition 26, Note 1st.

Find the Longitude of each place by Problem I. and if both places are East or both places West of the Prime Meridian, subtract the less number of degrees from the greater for the difference of Longitude; but if one place is East and the other West of the Prime Meridian, add them together and their sum if it be less than 180 degrees will be the difference of Longitude.

If the sum exceeds 180 degrees subtract it from 360 degrees for the difference of Longitude.

EXAMPLES.

1. What is the difference of Longitude between Copeuhagen and Pekin?

2. What is the difference of Longitude between Madrid and Vienna?

PROBLEMS AND EXAMPLES.

PROBLEM VIII.

To find the Distance between two Place**

Place O of the Quadrant over one of the places on the

Globe and extend it to the other, and the number of

degrees between the two places will be the distance in

degrees which multiplied by 60 will give the distance in

Geographical miles, or multiplied by 69.1 will give the

distance in Statute miles.

xfoTE. — Sixty Geographical make a degree and 69.1 Statute miles make a degree.

EXAMPLES.

i. What is the distance in Geographical miles between New York and San Francisco?

2. What is the distance in Statute miles between Philadelphia and Mobile?

PROBLEM IX.

To Find Places Equally Distant from a given place,

„ lace O of the Quadrant on the given place as a centre of motion and move the Quadrant around this centre on the surface of the Globe, and all plaees over which the same degree of the Quadrant passes are equally distant from the given place.

EXAMPLES.

1. Find two places equally distant from Boston.

2, Find four places equally distant from Denver.

PROBLEMS AND EXAMPLES.

PROBLEM X.

The Latitude of a place, its distance and general

direction from a given place being given, to find

the place whose Latitude is given.

If the distance is given in miles, convert the miles into degrees; then place O of the Quadrant over the place and move the other end of it Eastward if the required place is Eastward, or Westward if the required place is Westward, till the degree marked on it representing the distance arrives at the Parallel of Latitude indicating the Latitude of the required place and this point will show the place required.

EXAMPLES.

i. Find the place whose Latitude is 40 degrees North and distant from Vera Cruz in a North-western direction 1,680 Geographical miles.

2. Find the place whose Latitude is 20 South and distant from Pernambuco in a South-western direction 2,145 Statute miles.

PROBLEM XI.

The Longitude of a place, its distance and general

direction from a given place being given, to find

the place whose Longitude is given*

Reduce the distance if given in miles to degrees; then place O of the Quadrant over the given place and move the other end of it Northward if the required place is

PTOBLEMS AND EXAMPLES.

Northward, or Southward if the required place is Southward till the degrees marked on it representing the distance arrives at the given Meridian which point is the place required.

EXAMPLES.

i. Find the place whose Longitude is 90 degrees West and distant from Louisville in a South-western direction 540 Geographical miles.

2. Find the place whose Longitude is 113 degrees East and distant from Teheran in a South-eastern direction 3,550 Statute miles.