placed. Here again, to obtain the advantage, divide the circumference of the circle described by P, by the distance between the threads. 264. Screws, applied in this or some similar way, are extensively used when a great and continued pressure is required within a small space. Cotton is compressed into bales, juices are extracted from fruit, coins are stamped, and houses are raised from their foundations, with the aid of the screw. 265. HUNTER'S SCREW.-When intense pressure is required, the threads of the screw have to be so close together that they are necessarily thin and liable to break. To prevent this, an ingenious contrivance, called after its inventor Hunter's Screw, is used. Hunter's Screw consists of two screws, working one within the other, in such a way that as the larger descends the smaller ascends, though not quite so far. The difference between the respective distances of the threads in the two screws determines how far on the whole the screw advances. With Hunter's Screw, therefore, the power produces a pressure as many times greater than itself, as the E Fig. 124. A W HUNTER'S SCREW. difference between the respective distances of the threads in the two screws is contained in the circle described by the power. A is the larger screw, B W the smaller one. CD is the lever by which it is worked, and EF the stationary nut. The pressure is produced at W. If the threads of the larger screw are 1 inch apart, and those of the smaller 3/4 of an inch, the difference is 1/4 of an inch. Then, if the extremities of the lever describe a circle of 100 inches, the advantage will be equal to 100 divided by 1/4, or 400; that is, a power of 1 pound applied at either end of the lever will produce a pressure of 400 pounds at W. the advantage gained by this machine to be calculated? 264. For what purposes are screws used? 265. When great pressure is required, what difficulty attends the use of the screw? To remedy this, what ingenious contrivance is used? Describe Hunter's Screw. With this screw, how great a pressure does a given power produce? By making the threads of the two screws nearly the same distance apart, an immense power is obtained without diminishing the size and strength of the threads. The action of the screw is of course proportionally slow, time being always lost as power is gained. Fig. 125. 266. THE ENDLESS SCREW.-Instead of working in a nut, a screw is sometimes made to act on teeth cut in the circumference of a wheel. In this case, the only motion of the screw is round its axis. The winch being turned, the threads of the screw catch the teeth of the wheel and move it forward. As fast as one tooth passes out of reach, another is caught; and, the motion being thus continuous, the machine is called the Endless Screw. Its operation will be understood from Fig. 125, where it is combined THE ENDLESS SCREW. with a wheel and axle for the purpose of lifting a weight. l EXAMPLES FOR PRACTICE. 1. (See § 204.) A lever of the first kind is 20 inches in length: the long arm is 15 inches; the short arm, 5. How great a power will balance a weight of 112 pounds? With the same lever, how great a weight will a power of 50 pounds balance? 2: A farmer, in forcing a stump from the ground, uses a crow-bar 6 feet long, which he rests on a stone five feet from the end where his hand is applied. The resistance of the stump is equal to a weight of 500 pounds; how great a pressure must he exert, to move it? 3. A man weighing 180 pounds, and a boy of 60 pounds, are teetering on a board 12 feet long. That they may balance each other, how near must the man sit to the horse on which the board rests? 4. A man whose strength enables him to use a pressure of 120 pounds, wishes to move a rock weighing 600 pounds with a lever of the first kind. What must be the comparative length of the arms of the lever? If with his unaided strength he could move 120 pounds thirty feet in one minute, how long will it take him to move the rock with the lever the same distance? Illustrate this with Fig. 124. How may an immense power be gained with Hunter's Screw? 266. Describe the Endless Screw and its mode of operation. With what is it combined for lifting weights? 5. (See § 207.) The short arm of a steelyard is 2 inches long; at its end a 10 pound weight is suspended. How great a weight must be attached to the other end to balance it, the length of the steelyard being one foot ? 6. (See § 213.) There is a compound lever formed of two simple ones, the first arms of which are 10 inches each, and the short arms 2 inches each. How great a weight at the extremity of the last short arm will be supported by a power of 1 pound at the other end? 7. (See § 215.) A lever of the second kind is 20 inches long; the weight is 5 inches from the fulcrum. How great a power must be applied, to balance a weight of 112 pounds? 8. With the same lever as in the last sum, how great a weight will a power of 50 pounds balance? 9. A is rowing with an oar 9 feet long, and has his row-lock 2 feet from his hand; B rows with an eight-foot oar, and his row-lock is 1 foot from his hand. If they strike the water with an equal length of oar, which exerts the greater power on the boat? 10. (See § 217.) A man and a boy, at opposite ends of a bar 5 feet long, are carrying a 150-pound weight suspended between them. The boy can carry but 30 pounds; how far from his end must the weight hang, to give him that portion of it, and the man the rest? 11. Three men are bearing a weight suspended from a bar in the manner shown in Fig. 100. The single man at one end is twice as strong as each of the two at the other end. How must the weight be placed (the bar being 4 feet long), that each may bear a part proportioned to his strength? 12. (See § 219.) A lever of the third kind is 20 inches long; the power is 5 inches from the fulcrum. How great must it be, to balance a weight of 112 pounds? The biceps 13. A pair of pincers is 6 inches long. How great a force must be applied, 2 inches from the top, to overcome a resistance of 3 ounces? 14. The distance of a man's hand from his elbow is 16 inches. muscle is inserted in his fore-arm 2 inches from the elbow. great power must the muscle act to sustain a weight of 56 pounds in the extended hand? 15. (See § 225.) The circumference of a wheel is 8 feet; that of its axle, 16 inches. The weight, including friction, is 60 pounds; how great a power will be required to raise it? 16. The pilot-wheel of a boat is 3 feet in diameter; the axle is 4 inches. The resistance of the rudder is 180 pounds, to which one-tenth of itself must be added for friction, &c. How great a power must be applied to the wheel, to move the rudder? 17. An axle one foot in circumference, fitted with a winch that describes a circle of 6 feet, is used for drawing water from a well. How great a power will it take to move 60 pounds of water, allowing one-tenth for friction? 18. Four men are drawing in an anchor that weighs 1,000 pounds, with a capstan. The barrel of the capstan has a radius of 6 inches. The circle described by the handspikes has a radius of 5 feet. How great a pressure must each of the four men exert, to move the anchor? 19. (See § 232.) With a fixed pulley, how great a power will it take to hoist a weight of 50 pounds, 20 per cent., or one-fifth, being added for friction? 20. (See § 238.) With a movable pulley, how great a power will it take to hoist a weight of 50 pounds, twenty per cent. being allowed for friction? 21. (See § 239.) With a fixed and a movable pulley, how great a power will it take to hoist a weight of 50 pounds, 40 per cent., or two-fifths, being allowed for friction? 22. (See § 241.) With two fixed and two movable pulleys, how great a power will it take to hoist a weight of 50 pounds, 60 per cent., or three-fifths, being allowed for friction? 23. (See § 242.) How great a power will it take to hoist a weight of 100 pounds with one of White's Pulleys having five grooves in each block, 35 per cent., or seven-twentieths, being allowed for friction? 24. (See § 243.) With a system of six movable pulleys, having each its own rope, and arranged as shown in Fig. 115, how great a weight (including friction) will a power of 20 pounds raise? 25. With a similar system of five movable pulleys, how great a power will it take to balance a weight of 64 pounds, to which the friction of the pulleys adds 50 per cent., or one-half of itself?—Ans. 3 pounds. [64+32=96 25 = 32 96323 Answer.] 26. (See § 247.) How great a power will be required to balance a weight of 40 pounds (friction included), on an inclined plane, whose length is 8 times its height? 27. (See § 253.) A weight of 1,500 pounds is to be raised with a wedge 60 inches long and 12 inches high at its head. How great must the power be? 28. A builder desires to raise a weight of 900 pounds with two similar wedges, as shown in Fig. 122. Each wedge is 3 feet long and 9 inches through at the head. How great a power must be applied to each ? 29. A weight of 1,020 pounds is to be lifted 1/2 feet. The greatest power that can be applied is 255 pounds. Give the dimensions of the wedge. 30. (See § 257.) Of two wedges 4 inches thick at the head and respectively 6 and 8 inches long, which can be driven into a log the more easily? Which will break the sooner, both being made of the same material? 31. (See § 262.) How great a pressure (including friction) will be exerted by a power of 15 pounds applied to a screw whose head is 1 inch in circumference, and whose threads are one-eighth of an inch apart? 32. A book-binder has a press, with a screw whose threads are one-third of an inch apart, and a nut worked by a lever which describes a circle of 8 feet. How great a pressure will a power of 5 pounds applied at the end of the lever produce, the loss by friction being equivalent to 240 pounds? 33. (See § 265.) How great a pressure is produced by a power of 1 pound with one of Hunter's Screws, worked by a lever which describes a circle of 75 inches; the threads of the larger screw being half an inch apart and those of the smaller one-third of an inch, 331/3 per cent., or one-third, of the pressure being deducted for friction? CHAPTER IX. MECHANICS (CONTINUED). WHEELWORK.-CLOCK AND WATCHWORK. 267. ALL machines, however complicated, are combinations of the six simple mechanical powers described in the last chapter. The chief objects in combining them are to gain a sufficient degree of power, and to give such a direction to the motion as will make the machinery do the work required. Wheelwork. 268. The wheel enters more largely into machinery than any other of the Mechanical Powers. 269. Several wheels combined in one machine are called a Train. 270. In a train of two wheels, the one that imparts the motion is called the Driver; the one that receives it, the Follower. 271. MODES OF CONNECTION.-There are three ways in which motion may be transmitted from one wheel to another:-1. By the friction of their circumferences. 2. By a band. 3. By teeth on their outer rim. 272. Friction of the Circumferences.-One wheel may move another by rubbing on its circumference, or outer rim. The wheels are so placed that their rims touch, and one of them is set in motion. The circumference of each 267. Of what are all machines combinations? What are the chief objects in combining them? 268. Which of the mechanical powers enters most largely into machinery? 269. What is meant by a Train of wheels? 270. In a train of two wheels, which is the Driver? Which, the Follower? 271. In how many ways may motion be transmitted from one wheel to another? Mention them. 272. How may one wheel be made to move another by rubbing on its circumference? What is the ad |