38. The length of an inclined plane is 300 feet, the height 75 feet; what time is required for a body to descend the plane?

39. A stone is thrown vertically downward from a height of 200 meters with a velocity of 15 meters per second; how long will it be in falling?

CENTRE OF GRAVITY.

40. If two bodies, weighing, respectively, 12 and 16 pounds, are connected by a bar, where is the common centre of gravity?

What is the length of a pendulum at Paris to vibrate half-seconds? To vibrate halfhours?

42. If the length of a pendulum is 4 meters, what is its time of vibration at Paris? 43. How will the times of vibrations of two pendulums compare whose lengths are, respectively, 6 inches and 5 inches?

44. In what time at Greenwich will a pendulum a kilometer long make a vibration? 45. A pendulum two meters long makes 350 vibrations during a certain time; how many vibrations will it make in the same time if the pendulum contracts a centimeter? 46. A pendulum vibrates twice in 3 of a second; how long is it?

47. One pendulum vibrates five times as fast as a second; what are the proportional lengths?

48. If the pendulum of a clock beating seconds at New York should expand rooo of its length, how many seconds would it lose each day?

ENERGY.

49. How many kilogram-meters are represented in raising 500 kilograms 10 meters high?

50. Which has the greater energy: a body weighing 100 pounds and having a velocity of 6 feet per second, or one weighing 6 pounds with a velocity of 100 feet? Represent the energy by numbers.

51. What is the work expressed in foot pounds that is required to raise 500 pounds 10 feet high?

52. A locomotive weighing 20 tons, moving at the rate of 30 miles an hour, has how much energy?

53. What is the horse-power of an engine that will raise 100,000 pounds 500 feet in 2 minutes?

54. What is the horse-power of an engine that can raise 50,000 pounds 10 feet in 5 seconds?

THE LEVER.

55. From a lever of the first class 3 feet in length, a weight of 500 pounds is suspended 23 inches from the fulcrum; what weight at the other end will keep the lever in equilibrium?

56. In a lever of the second class 12 feet long, where must the fulcrum be placed in reference to the weight so that a power of half a pound may balance a weight of 10 pounds?

57. In lever of the first class, the distance of the power from the fulcrum is 12 feet an from the weight to the fulcrum 4 inches; how much weight will a power of 1 gram balance?

58. In a lever of the first class, what weight will a power of 100 pounds balance, with a lever 16 feet long and weight 4 feet from the fulcrum? What would be the result with a lever of the second class?

59. Two men are carrying a weight of 300 pounds on a pole 8 feet long; where must the load be placed so that one will lift one third of the weight?

THE WHEEL AND AXLE.

60. The diameter of a wheel is 4 feet and the axle 5 inches; what power is required to sustain a weight of 500 pounds?

61. The barrel of a capstan has a radius of 5 inches, the radius of a circle described by the hand-spikes is 5 feet; what power is necessary to raise an anchor weighing 1,200 pour.ds?

THE PULLEY.

62. In a system of pulleys the power is 100 pounds; how many movable pulleys are required to sustain a weight of 600 pounds?

63. What power is necessary to sustain a weight of 500 kilograms with 5 movable pulleys?

THE INCLINED PLANE.

64. On an inclined plane whose base is 15 feet and height 5 feet, what power acting parallel with the base will balance a weight of 3 tons?

65. With a plank 10 feet long, to what height can a man capable of lifting 150 pounds roll a barrel containing material weighing 500 pounds?

THE SCREW.

66. If the threads of a screw are one half an inch apart, what weight will a power of 100 pounds raise, acting at a distance of 5 feet from the axis of the screw?

67. What is the distance between the threads of a screw when a power of 50 pounds will raise 2 tons acting on a handle 4 feet long?

HYDROSTATICS.

68. What is the pressure on the bottom of a cistern 50 feet long, 15 feet high, and 25 feet wide? What is the pressure on each side?

69. Suppose in the hydrostatic press the area of the smaller cylinder is 3 square inches and the larger 1,000 square inches; suppose, also, the pump-handle to be 4 feet long and the piston to be 3 inches from the fulcrum; what pressure will be exerted on the larger cylinder if a power of 500 pounds be applied to the end of the pump-handle ?

70. The whole pressure on the bottom of a pail of water, the radius of which is 25 centimeters, is 50 kilograms; what is the depth of the water in the pail?

71. What height must a column of mercury have to balance a column of water 20 feet high?

72. A body weighs 30 grams in air and 20 in water; what is its specific gravity? 73. What is the weight of a cubic foot of gold? Of platinum? Of iron? Of zinc ? 74. The specific gravity of cork being .24, how much must be used to float a man, his specific gravity being 1.12?

75. What is the weight of a bar of gold 30 centimeters long, 4 wide, and 12 thick? 76. A cylinder of oak is 30 centimeters in diameter and 3 meters long; the specific gravity of the woed is 1.17; what is the volume and weight of the cylinder?

77. How much bulk must a hollow vessel of iron occupy, weighing 2 tons, that it may float with half its bulk immersed in water?

air.

78. A body whose specific gravity is 3.53 weighs 5 pounds in water; find its weight in

79. An empty vessel weighs a pound, filled with water it weighs 11⁄2 pounds, filled with another liquid it weighs 1 pounds; what is the specific gravity of the liquid?

SOUND.

80. A cannon-flash is seen, and in 10 seconds the report is heard; how far away is the caunon?

81. Three seconds elapse between a flash of lightning and a corresponding peal of thunder; what is the distance of the place of origin?

82. How many miles will sound travel in an hour? How long will it take it to go around the earth?

83. A tuning-fork gives sound-waves 1 meter in length; how many vibrations per second does it make?

84. A shot is fired before a cliff, and the echo is heard in 7 seconds; what is the distance of the cliff?

85. The density of oxygen is about sixteen times that of hydrogen; show that the velocity of sound in hydrogen ought to be about four times that in oxygen.

REVIEW QUESTIONS.

PROPERTIES OF MATTER.

1. What is physics? What are physical agents? Name them. 2. Define a body; a material point; a molecule; an atom. 3. How are molecules kept in place? 4. What is the mass of a body? Density? Give examples of dense and rare bodies. 5. How are bodies divided? Define solids, liquids, and aeriform bodies. How is the term fluid applied? 6. What are the general properties of bodies? 7. Define extension. 8. What are English measures? 9. Explain the metric system. 10. What are the metric measures of length? of surface and volume? 11. What are the metric measures of capacity? 12. Define weight. 13. Give the metric table of weight. 14. Define impenetrability. Examples. 15. Define inertia. Examples. 16. Define porosity. Define sensible and physical pores. 17. Define divisibility. Examples. 18. Define compressibility. Experiments. Explain compressibility of gases, liquids, and metals. 19. Define expansibility. Expansion of gases, liquids, and solids. Give experiment. 20. Define elasticity. Examples. How can elasticity be brought into play? What bodies are most elastic? How is it shown that ivory is elastic? Explain the experiment. Explain some of the applications of elasticity.

21. Define molecular forces Name them. 22. Define cohesion and adhesion. Examples. Explain solution. Examples. 23 Explain capillarity. Experiments. 24. Give some applications of capillarity. 25. Define absorption. Examples Carbon, spongy platinum, animals and vegetables, paper. Application. Wood Application. 26. Define osmose, endosmose, and exosmose. Explain experiment Examples. 27. Define dialysis. To what substances can dialysis be applied? 28. Define tenacity. How measured? What bodies are most tenacious? Give table What is the form of greatest strength? Application to grasses, quills, bones, etc. How do we increase the tenacity of metals? 29. Define hardness. Give scale of hardness of minerals. How do we test the relative hardness of bodies? Examples. What are brittle bodies? What is the effect of alloying bodies? Explain the process of polishing. How is the diamond polished? 30. Define ductility. Examples of plastic bodies. Examples of ductile metals. 31. Define malleability. Effect of temperature. How is gold formed into sheets? Lists of metals malleable under the hammer and rolling-mill.

MECHANICAL PRINCIPLES.

32. Define mechanics. 33. Explain rest and motion. Explain relative and absolute rest and motion. Illustrate by examples. 34. Define uniform motion. Example. Define velocity. Example. 35. Define varied motion. When accelerated and when retarded? Examples. Define uniformly accelerated and retarded motion. Examples.

36. On what are the principles of mechanics based? 37. Give Newton's First Law of Motion. Illustrate. 38. Give Newton's Second Law. What three elements determine a force? Define each. How represented? 39. Define simple and compound motion. Define resultant. Illustrate. Define compounds. 40. Explain the parallelogram of forces. Define composition and resolution of forces. Illustrate by figure. 41. Explain the flight of a bird. 42. Explain the sailing of a boat. 43. Explain the resultant of parallel forces. When the forces act in the same and opposite directions. 44. Explain the composition of more than two forces. 45. Define momentum. Illustrate. Rule for finding momentum. Examples. 46. Explain collision of bodies. Illustrate. The effect is proportional to what? Illustrate. 47. Define striking force. Proportional to what? Illustrate the difference between momentum and striking force. 48. Define action and reaction. What is Newton's Third Law? 49. Illustrate reaction in non-elastic bodies. 50. Illustrate reaction in elastic bodies. Give some familiar examples. 51. Explain reflected motion. Define lines and angles of incidence and reflection. Give the law of reflected motion. Illustrate by figure. 52. Explain the centrifugal and centripetal forces. Illustrate by examples and figure. How does the body move when the centripetal force is destroyed? Explain the experiment with ivory balls. 53. Give some effects of the centrifugal force. Effect on the earth. Explain the experiment. Explain the tendency of bodies to revolve about their shortest axis. 54. Define the gyroscope. Explain figure.

55. Define the force of gravity; weight; universal gravitation. Explain the law of universal gravitation. Give the law of Newton. Explain further by figure. Why do not two bodies come together resting on a table? 56. Explain the effect of gravitation on the planets. 57. What is the law of the force of gravity? Why is gravity different at different places on the earth's surface? 58. Define a vertical line. Illustrate by figure. Define a horizontal line. Illustrate What instruments are based upon these lines? 59. What is the difference between weight and gravity? How is each determined? 60. Define the centre of gravity. Explain. What is the line of direction? Where is the centre of gravity in solids of regular figure and uniform density? Examples. In sheets of uniform thickness and density? How is the centre of gravity found in surfaces of irregular outline? How found in any solid? When not within the body, how is it found? 61. When is a body in equilibrium? When a body rests on a point, where must the centre of gravity be? When it rests on two points? Example. When on three points? Example. 62. What are the three cases of equilibrium? What is stable equilibrium? Illustrate. Examples. What is unstable equilibrium? Illustrate What is neutral equilibrium? Illustrate. Examples of the three kinds of equilibrium with the cone. 63. What bodies are the most stable? Explain the stability of the towers of Pisa and Bologna. How do men and animals maintain a stable position? Illustrate. 64. Give the three laws of falling bodies. How is the first law verified? Explain the reason of the second law. Third law. What is the rule for finding the velocity acquired by a falling body at the end of any given time? Example. What is the rule for finding the space pissed over during any given second of the descent? Example. What is the rule for finding the whole distance traversed by a falling body in a given time? Example. 65. Explain Galileo's method for verifying the laws of falling bodies. 66. What is the effect on a body thrown perpendicularly upward? How do we find the number of seconds it will continue to rise? Example. How do we find the whole distance it will rise? Example. 67. Define a projectile. Illustrate by figure when a ball is thrown horizontally. Illustrate the path of a ball by figure, fired obliquely, at different angles. 68. When will a ball fired horizontally reach the ground? When, if fired obliquely upward? 69. Define the pendulum. What causes the pendulum to vibrate? Explain the action in detail. What is oscillatory motion? What is an oscillation or vibration? What is its amplitude? What effect has the air on vibration? 70. What is a simple pendulum? Is it real or ideal? What is a compound pendulum? Explain its construction. 71. Give the four laws of the vibrations of the pendulum. How are these laws deduced? How is the first law verified? Second law? Limitation. Define isochronism. When are vibrations isochronical? Who discovered the pendulum, and when? 72. Explain the centres of suspension and oscillation. 73. What is the principal use