6. Define a Right Pyramid. Slant Height, Truncated Pyramid. D. 13. B. VII.

7. What is the altitude of a frustrum? Slant Height? D. 14. B. VII.

8. Define the diagonal of a polyedron. Similar polyedrons.

D. 16. B. VII.

9. What is a regular polyedron? Homologous parts of a polyedron? D. 18. B. VII.

10. Demonstrate Prop. IV. B. VII:

"The convex surface of a right pyramid is equal to the perimeter of its base multiplied by half its slant height."

11. Two triangular pyramids, having equivalent bases and equal altitudes, are equivalent, or equal in value. P. XV. B. VII.

12. Two similar pyramids are to each other as the cubes of their homologous edges. P. XX. B. VII. Give the general Scholiums to this Theo

rem.

BOOK VIII.

1. Define a Cylinder, Cone, Sphere, and Spherical Sector. D. 1. B. VIII.

2. Define a Great Circle. Small Circle. Zone. Spherical Segment. D. 14. B. VIII.

3. What are the Three round bodies treated of in the Elements of Geometry? D. 17. B. VIII.

4. The solidity of a Cone is equal to its base multiplied by a third of its altitude. P. 5. B. VIII.

5. Every section of a sphere, made by a plane, is a circle. P. VII. B. VIII.

6. The solidity of a sphere is equal to its surface multiplied by a third of its radius. P. XIV. B. VIII.

7. Demonstrate the above Propositions; also P. XVIII, and give General Scholiums. B. VIII.

BOOK IX.

1. Define a Spherical Triangle, Lune, Ungula, and the Pole of a Circle. D. B. IX.

2. "Two Symmetrical spherical triangles are equivalent." P. 16. B. IX.

3. "The sum of all the angles in any spherical triangle is less than six right angles, and greater than two." P. XIV. B. IX.

4. "The surface of a spherical triangle is equal to the excess of the sum of its three angles above two right angles multiplied by the tri-rectangular triangle. P. XVIII. B. IX.

Many other questions and Propositions might have been given, but the above will be suf ficient to indicate what may be expected in regard to this branch.

CHAPTER XV.

NATURAL PHILOSOPHY.

REMARK.-The increased attention given to Philosophy in our schools at the present day renders it essential that Teachers should be well acquainted with this practical science. The references in the following questions on Natural Philosophy are to "Peck's Ganot."

to

NOTE. The Author hesitated in making the selection of a Text-Book, which to refer. But the superior merits of "Peck's Ganot" induced him to take that excellent work, trusting that as soon as it should become known, it would be in general use.

Art. stands for Article. Ex. for Example. Exp. for Experiment. P. for Page. Fig. for Figure.

INTRODUCTION.

1. What is Science? What is a Law? Define the Universe. P. 9.

2. Define Mind. Matter. In what two states may matter exist? P. 9.

3. What are the two divisions of science? P. 9. 4. What is Natural Philosophy? P. 9.

5. Into what may Natural Philosophy be divided? 6. How may organized matter be divided? P. 10.

P. 10.

7. What are the corresponding divisions of General Physics? P. 10.

8. What is Physics Proper? Chemistry? P. 10.

9. What are the Pure Sciences? P. 10.

10. What are the Mixed Sciences? P. 10.

PRELIMINARY PRINCIPLES AND MECHANICS OF SOLIDS.

1. What are Physical Agents? Name them. Art. 1.

2. Define a Body. An Atom.

3. What are Molecular Forces?

Repellent Forces? Art. 2.

A Molecule. Art. 2.

What is Attractive Forces?

4. What is the Map of a body? Density? How are bodies divided? Art. 3.

5. Define solids and fluids. How are fluids divided? Art. 4. 6. Define liquids, and gases or vapors. Art. 4.

7. What are the general properties of bodies? Art. 5.

8. Define Magnitude, Form, and Impenetrability. Art. 6, 7. 9. Define Inertia. Give examples of the principle of Inertia. Art. 8.

10. What is Porosity? Explain the porosity of gold by the Florentine. Exp. Art. 9.

11. Define a Filter. Divisibility. Compressibility. Dilatability. Art. 10-12.

12. What is Elasticity? Give examples of the most and least elastic bodies. Art. 13.

MECHANICAL PRINCIPLES.

1. Define Mechanics. When is a body at rest? In motion? Art. 14, 15.

2. Give examples of Rectilinear and Curvilinear Motion. Art. 16.

3. Give examples of Uniform Motion. Varied Motion. Define Velocity. Art. 17.

4. Define Accelerated and Retarded Motion. Art. 18.

5. Define and give examples of Forces, Powers and Resistances. Art. 19.

6. What three elements determine a force? Art. 20.

7. What is a Resultant of several forces? Illustrate. Art. 21.

8. Explain the parallelogram of forces. Art. 22.

9. Explain the flight of an Eagle. The sailing of a boat. Art. 23, 24.

10. What is the Resultant of parallel forces acting in the same direction? Art. 25.

11. Acting in different directions? Ex. Art. 25.

12. When are forces in equilibrium? Illustrate. Art. 26. 13. Define Centrifugal force. Centripetal force.

Art. 27.

14. How does a body move when the centripetal force is destroyed? Art. 27.

15. State some of the effects of the centrifugal force. Art. 28. 16. What is a machine? A Motor? What is the advantage of machines?

Art. 29.

17. Define a Lever. Tell how many classes. Example of each. Art. 30.

18. What are the lever arms? What is the relation between the power and resistance? Art. 31.

19. What is the relation between the power and velocity? Art. 31.

31.

20. Is there any gain of power in using a lever? Ex. Art.

21. Explain the scissors, and nut-cracker. Art. 32.

22. Name any other simple machines. Art. 33.

23. What machines are formed by combinations of simple machines? Art. 33.

24. What are the seven mechanical powers? Name them. Art. 33

PRINCIPLES OF GRAVITATION.

1. What is the force of Gravity? What is Universal Gravitation? Art. 34.

2. Explain the law of Universal Gravity. Art. 34.

3. State Newton's law. Art. 34.

4. State the effect of gravitation on the planets. Art. 35.

5. What are the orbits of planets? What is the force of Gravity? Art. 36.

6. What is the shape of the Earth? Define a vertical line. Art. 37.

37.

7. Where do vertical lines meet? Illustrate by example. Art.

8. When are vertical lines parallel? When not? Give example. Art. 37.

9. What are antipodes? Define a horizontal Line. Level. Art. 37.

10. What instruments are constructed on the principle of verticals and horizontals? Art. 37.

41.

11. Define weight. Center of Gravity. Art. 40.

12. When is a body in equilibrium? Give an example. Art.

13. What are the three cases of equilibrium? Give example.

Art. 42.

42.

14. Define Stable, Unstable and Neutral equilibrium. Art.

15. What bodies are most stable? Illustrate by example. Art. 43.

16. How do men and animals maintain a stable position? Art. 43.

17. Where is the center of gravity in man?

18. Explain the principle of rope dancing. Art. 43.

19. Define a balance. Beam. Fulcrum. The scale. Art. 44.

20. On what principle are bodies weighed? Art. 44.

21. What are the requisitions for a good balance? Art. 45. 22. State the methods of testing a Balance. Art. 46.

23. What is the first law of falling bodies? The second? Art. 48.

49.

24. The third? Illustrate each by an example. Art. 48. 25. What is an Inclined Plane? Explain its principle. Art.

26. How would you prove the third law of falling bodies? Art. 50.

27. What use is made of the inclined plane? Art. 51.

28. What is a screw? A wedge? Art. 51.

29. What is a Pendulum? Why does it vibrate? Art. 52: 30. Explain the construction of the simple and compound pendulum. Art. 53.

31. Explain the laws that govern the vibration of the pendulum. Art. 54.

32. Mention some of the Applications of the Pendulum. Art. 55.

33. Why do clocks lose time in summer, and gain in winter? Art. 55.