about the larger wheel E, passes round the pulley H, and is then wound in the opposite direction about the smaller wheel Fon the

same axis as E. When the handle BC is turned, the rope is wound on one wheel and off the other.

35. What tension is there on the portions of the rope D and G when W= 100 kgm.?

36. If E has a radius three times as large as F, how much will W be raised when 12 feet more of rope are wound upon E?

37. If the crank-arm AB is one and one half times the radius of E and four times that of F, what mechanical advantage is gained by the use of this machine ?

Inclined Plane.-38. How much work is done in drawing a cart weighing 100 kgm. up an inclined plane so that the cart may be 1 m. higher than its starting-point?

39. It is found that a force of 2 kgm. is required to draw a box up a sloping board. If the box weighs 50 kgm., how much work is done by drawing it 3 m. up the incline?

40. O (Fig. 42) is an object resting on a frictionless inclined plane ABC. OW represents the weight of the block O. Resolve OW into two components, one parallel to AC and one perpendicular to AC.

41. If OW (Fig. 42) 5 kgm., and its component per

pendicular to AC is of that parallel to AC, find the amount of each component.

42. Resolve OW (Fig. 42) into a component parallel to BC and one perpendicular to AC.

W

FIG. 42.

43. What proportion must be true between the weight of the block O (Fig. 43), the force to prevent motion OF, and the dimensions of the inclined plane ABC?

44. If OF is the force necessary to prevent the block (Fig. 43) from sliding down the frictionless incline AC,

A

B

FIG. 43.

express the work done by OF in moving the block from C to A.

45. Resolve OF into a component OP perpendicular to AC (pressure component) and a component OH parallel to BC, and show how the work done by OH in moving the block from C to A may be computed. он AB

46. Prove by geometry =
OF BC

47. What force parallel to the base of an incline is required to hold a cart weighing 5 kgm. if the slope of the incline is 3 m. and the base 2 m. long?

48. A porter who can exert a push of 150 lbs. has to roll a cask weighing 400 lbs. up a board 12 ft. long. How high can the upper end of the board be that he may just do so?

49. A car weighing 600 lbs. is held at rest on a frictionless incline by a force of 90 lbs. parallel to the incline. What is the ratio of the height of the incline to its length? 50. What mechanical advantage is gained by using an incline whose height is its horizontal length ?

51. A plank rests with one end on the ground and the other 2 ft. higher. If the plank is 14 ft. long, what force is required to roll a barrel weighing 196 lbs. up the incline?

52. In the diagram, Fig. 42, if O weighs 360 lbs., AC= 13 ft., BC= 12 ft., BA = 5 ft., what force is required to keep O at rest if there is no friction—

(a) When the force is parallel to AC?

53. Resolve OF (Fig. 43) into components perpendicular to AC and parallel to BA, and state the proportion between these components and the dimensions of the inclined plane.

Screw.-54. The thread of a certain screw passes found the core 10 times in each centimeter of length. How far will 170 turns lift a weight placed on the head of the screw?

55. The pitch of a screw is inch (i.e., the distance between two consecutive turns measured parallel to the axis of the screw). A wheel whose circumference is 3 ft. turns the screw. What pressure will be exerted at the end of the screw by a force of 1 lb. tangent to the rim of the wheel?

56. A screw whose pitch is 1 mm. is turned by a wheel 10 cm. in radius. What force tangent to the rim of the

wheel must be used to overcome a force of 10 kgm. at the end of the screw?

57. Show that in Probs. 55 and 56 the product in each case of the moving power by the distance through which the power moves is equal to the resistance overcome multiplied by its distance.

58. Draw a diagram to show the action of a screw turned by a lever at right angles to its axis.

CHAPTER VIII.

HEAT.

XXXV. TEMPERATURE-THERMOMETERS.

1. The scale of a certain thermometer is 180 mm. long between the freezing- and boiling-points of water. If it is graduated to C. scale, what is the length of one degree? Where will the 0° mark be?

2. What will be the length of one degree if it is graduated to F. scale? How many mm. from the freezing-point of water will the zero mark be?

3. 15° C. equals how many degrees F.?

4. Which is the higher temperature, 10° C. or 10° F. ? 5. Which is the lower temperature, 2° below zero F. or 20° below zero C.?

6. Reduce 23° C. to Fahrenheit scale.

7. Reduce 100° F. to Centigrade scale.

For small variations of temperature above or below 100° C. a difference of pressure of 27 mm., as indicated by the barometer, causes a variation of 1° C. in the temperature at which water boils. Increase of pressure above 76 cm. raises the boiling-point; decrease of pressure lowers the boiling-point.

8. At what temperature will water boil at a place or time where the barometer reads 74.2 cm.?

9. What is the error of a thermometer which with the barometer at 76 cm. gives the boiling-point of water as 99.4° C.?

10. What is the error in a thermometer which with

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