=129. The Screw.=--The screw is a cylinder around whose circumference winds a spiral groove. (See Fig. 103.) The raised part between the two adjacent grooves is the =thread= of the screw. The screw turns in a block called a =nut=, within which is a spiral groove and thread exactly corresponding to those of the screw. The distance between two consecutive threads measured parallel to the axis is called the =pitch= of the screw. (See Fig. 104.) If the thread winds around the cylinder ten times in the space of 1 in., the screw is said to have ten threads to the inch, the pitch being {1/10} in. The screw usually is turned by a lever or wheel with the effort applied at the end of the lever, or at the circumference of the wheel. While the effort moves once about the circumference of the wheel the weight is pushed forward a distance equal to the distance between two threads (the pitch of the screw). The work done by the effort therefore equals _F × 2πr_, _r_ being the radius of the wheel, and the work done on the weight equals _W × s_, _s_ being the pitch of the screw. By the law of machines _F × 2πr = W × s_ or _W / F = (2πr) / s_. Therefore the mechanical advantage of the screw equals _(2πr) / s_. Since the distance the weight moves is small compared to that the power travels, there is a great gain in force. The screw is usually employed where _great force_ is to be exerted through small distances as in the vise (Fig. 105) the jack screw (Fig. 106), screw clamps, to accurately measure small distances as in the micrometer (Fig. 107) and spherometer, and to lessen the motion in speed-reducing devices. The worm gear (Fig. 108) is a modification of the screw that is sometimes used where a considerable amount of speed reduction is required. [Illustration: FIG. 103.--The screw is a spiral inclined plane.] [Illustration: FIG. 104.--The pitch is _S_.] [Illustration: FIG. 105.--A vise.] [Illustration: FIG. 106.--A jack screw.] [Illustration: FIG. 107.--A micrometer screw.] [Illustration: FIG. 108.--This large worm-wheel is a part of the hoisting mechanism employed for the lock gates of the Sault Ste. Marie Canal.] Important Topics 1. Efficiency of machines. 2. The inclined plane, wedge and screw. Applications. Exercises 1. A plank 12 ft. long is used to roll a barrel weighing 200 lbs. into a wagon 3 ft. high. Find the force required parallel to the incline. 2. How long a plank will be needed to roll an iron safe weighing 1-1/2 tons into a wagon 3 ft. high using a pull of 600 lbs. parallel to the incline. 3. An effort of 50 lbs. acting parallel to the plane prevents a 200-lb. barrel from rolling down an inclined plane. What is the ratio of the length to the height of the plane? 4. A man can push with a force of 150 lbs. and wishes to raise a box weighing 1200 lbs. into a cart 3 ft. high. How long a plank must he use?