In Integers the figures or periods are pointed from the right hand to the left: in Decimals, from left hand to the right.

The operation may be continued to any length when there is a remainder, by annexing two ciphers to it.

Extraction of the Cube Root.

1. Point every third figure, beginning with the unit. Find the greatest cube in the first period, and put the root of it as a quotient.

Subtract this cube from the first period.

Bring down the figures of the next period to the remainder: call it the Resolvend.

Square the root, and multiply the square by 300, for a Divisor.

2. Find how often the divisor is contained in the resolvend. Place the figure in the quotient.

Multiply the divisor by the last figure put in the root, and place the product under the resolvend.

3. For the Increase,

Square the last figure in the root:

Multiply that square by the former figure (or figures):
Multiply their product by 30:

Also cube the last figure in the root:

Place both these products under the preceding sum.

Add these three sums together: call this sum the Subtra

hend.

4. Subtract the subtrahend from the resolvend:

To the remainder bring down the next period:
Proceed as before.

Thus,

122615327232(4968

64

Divisor .42 × 300 = 4800) 58615 = Resolvend.

Divisor 4962 × 300 = 73804800)·591391232 = Resolvend.

30

CHAPTER II.

GEOGRAPHY.

I. MATHEMATICAL GEOGRAPHY.

What does Geography teach us?

The Description of the Earth.

How does it teach us to look upon it?

In a Mathematical, Physical, and Political view?

What do you mean by a Mathematical view?

This relates to the form, motions, size, and place of the earth, &c.

What do

you mean by a Physical view?

Here I look upon the Earth's surface, as consisting of
Land and Water.

What do you mean by a Political view?

Here I look upon it as divided into Kingdoms, &c.
Which of the twelve planets from the sun is the Earth?
It is the third of them.

Mention the following particulars
Its distance from the Sun.

Its diameter.

Its circumference.

Its year.

Its day and night.

Its Satellite.

respecting it.

95 millions of miles. 7912 miles; say 8000. 24,899 miles.

365 days, 6 hours.

24 hours.

The Moon.

What is the shape of the earth?

It may be represented by an orange. It is a globe somewhat flattened at the N. and S. poles.

What is the difference between the equatorial and polar diameters?

26.478 miles.

Here is a Map (or Globe).

What are these points?

The north and south Poles.

How far distant are they from each other?

Half a circle: 180 degrees.

What is this line?

A Great circle.

What does every great circle do?

Its plane passes through the centre, and divides the globe

into two equal parts.

What do you call each of those parts?

A Hemisphere: half a sphere.

What are small circles?

Circles whose planes do not pass through the centre. Into what does each small circle divide a globe?

Into two unequal parts.

What is the length of a degree at the equator?

69 miles speaking loosely, nearly 70 British statute miles.

What is this circle called?

The Meridian.

For what reason?

When the sun comes to the meridian of any place, it is noon or mid-day at that place.

Into what does it divide the globe?

Into the eastern and western Hemispheres.

What is this circle called?

The Equator.

Into what does it divide the globe?

Into the northern and southern Hemispheres.

Why is it called the Equator?

Because when the sun is in its plane, the days and nights

are of equal length.

Where does it lie upon the globe?

At 90° degrees from each pole.

What is this line called?

The Tropic of Cancer: the northern tropic.

What is this line called?

The tropic of Capricorn.

What do you mean by "tropic."?

The point from which the sun seems to "turn" from the north to the south, and then from the south to the

north.

What are the points called from which he seems then to turn back?

The Solstitial points: Summer solstice; Winter solstice. At what distance is each tropic from the equator?

23 degrees, 28 minutes.

What is this line called?

The Ecliptic, or apparent path of the sun, being the great circle of the celestial sphere which the sun appears to describe in the course of a year.

What is it in reality?

The path which the earth would appear to describe if it were viewed from the sun's centre.

Whence has it its name?

Because "Eclipses" only take place when the moon is in it, or near to it.

What is the Obliquity of the ecliptic?

The angle which it makes with the equator.

What is the measure of it?

23 degrees, 28 minutes.

Where are its poles?