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How are the solid contents of a wedge found?
What is a prism? What are some of its forms?
How are its solid contents found?

What is a cylinder? Give an example.

How are its solid contents found?

What are pyramids? Have all the same form?

If the base of the pyramid be a square, what is it ca.led ?
If a triangle? If a circle?

What is meant by the vertex of a pyramid?

What is its height? What is the frustrum of a pyramid2
How are the cubic contents of a pyramid found?

How the cubic contents of the frustrum of a square pyramid? Of the frustrum of a cone?

How are the cubic contents of a globe found?
How the cubic contents of an irregular body?

What is meant by Gauging of Casks?

Can their dimensions be exactly found? Why?
What result, nevertheless, may be obtained?

What is the Rule for gauging a cask?

How may the contents of a cask be found in bushels?

How may the length of the cask be taken ?

What allowance must be made?

What for?

How is the length taken, when no callipers can be had?

How is the head diameter taken?

What deduction is made? On what account?

How many methods are there of ascertaining the Tonnage of Ves

sels? By whom practised?

What is the Carpenter's Rule?

What is the Government Rule?

XL.

MECHANICAL POWERS.

What are the Mechanical Powers?

How many are there?

Is the quantum of force exerted increased by their use?-
In what, then, consists the advantage of their use?

How is this done? How illustrated?

What do the terms Weight and Power, used in contradistinction, signify?

What is a Lever? How and by what supported?

What is the relative position of the power, weight, and fulcrum, in the more common kind of lever?

In the common lever, what is the proportion of the power to the weight?

In this and the succeeding proportions, what is the power estimated to be?

What increase of power is requisite to raise the weight?

On what does the comparative velocity of the weight and power depend?

What universal principle in mechanics is stated?

How are the Wheel and Axle represented in the figure?

On what principle do they act?

What answers to the fulcrum of the lever?

What to the long arm? What to the short arm?

What proportion is hence derived?

In the wheel and axle, what is the proportion of the power to the weight, as usually stated?

What is a Pulley? How does it receive its motion?

In a single fixed pulley, what is the proportion of the power to the weight? Explain its operation.

What is said of their velocity when in motion?

If the fixed pulley be combined with a movable one, what is the proportion of the power to the weight?

What the proportion of their velocity when in motion?

How does every additional movable pulley affect this proportion? In a system of pulleys, what is the proportion of the power to the weight?

What is an Inclined Plane? Give an example.

How is its convenient use exemplified?

On the inclined plane, what is the proportion of the power to the weight?

What may the Wedge be viewed to be?
Where is the power applied?

To what, in the inclined plane, does the head of the wedge answer?

In what respects does it differ from the inclined plane?

In the wedge, what is the proportion of the power acting against the head to the force produced at the side?

If the forces against both sides be required, what will the propor tion then be? State it.

What is said of the effect of friction, in the use of the wedge? What part of the power, then, is lost?

Is any allowance made for this, in the given proportion?

What, then, is the peculiar advantage of the wedge?
What is said of the power thus obtained?

What is the Screw?

What ascent is made in one round of the spiral thread?

What would this spiral, unfolded, form?

What is the proportion of its length to its height?

In the screw,

what is the proportion of the power to the weight? Where is the power applied?

How may the circumference of the circle described by one revo.ution of the power be found?

What is said of friction, in the use of the screw?

XLII.

CANCELLATION.

What does cancellation primarily signify?

In what sense is the term used in arithmetic?

How, then, may it be defined?

In what cases is it chiefly used?

How is an operation abridged by its use?

What is said respecting the magnitude of the quotient?

Which gives the greater quotient 400

200 or 4 ÷ 2?

Why!

What factor common to 400 and 200 may, then, be rejected?

What is said of the remaining factors?

In what Prop. is this principle stated? Repeat it.

What form of expressing division is generally used in cancella tion? Why? Illustrate this.

What is said of this form, on page 37, 1st paragraph?

Express the division of the product of 8, 7 and 9, by the product of 14, 6 and 4. Read the expression.

Into what may nearly all operations, which admit of cancellation, be resolved?

Recite the Rule for cancellation.

What is Observation 1st?

What is Observation 2d?

What is Observation 3d?

If any number (as 7) be measured by itself (7), what is the result? What, then, if the number be cancelled?

What is Observation 4th?

What are the prime factors of 36? Of 12 X 3? Of 4X9?
What is Observation 5th? What is to be done then?

When is one number prime to another ?

If a fraction occur in the divisor, what must be done? What, if it occur in the dividend?

How are mixed numbers prepared for cancellation?

Express in order for cancellation 3.2 X 7 ÷ 34 X 3.

THE IND.

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