72 LECTURE VII. 



dicular height. And from similar principles, the conditions of the equilibrium 

 of arches, domes, and roofs may be determined. (Plate IV. Fig. 66, 67.) 



The action of a screw depends on the same principles as that of an inclined 

 plane; for by rolling a thin and flexible wedge, for instance, a triangular 

 piece of card, round a cylinder, we form a screw. We may consider the force 

 tending to turn the screw round its axis, as applied horizontally to the base of 

 the wedge, and the weight which is to be raised as acting vertically on its in- 

 clined surfice: the circumference of the cylinder will represent the horizontal 

 length of the wedge, and the distance between the threads, measured in the 

 direction of the axis, will be its height, provided that the threads be single; 

 consequently, the forces required for the equilibrium are to each other, as the 

 height of one spire to the circumference of the screw. But besides these 

 forces, it is necessary that some obstacle be present, which may prevent the 

 body, on which the screw acts, from following it in its motion round its axis, 

 otherwise there can be no equilibrium. (Plate V. Fig. 68.) 



The cylinder, which is the foundation of a screw, may be either convex or 

 concave, making a cylindrical or a tubular screw, and these, when fitted to- 

 gether, are sometimes called a screw and a nut. The nut acts on the screw 

 with the same mechanical power as a single point would do, since it only di- 

 vides the pressure among the different parts of the spire. In general the 

 screw is applied in combination with a lever, in order to procure an advantage 

 in overcoming the friction, which is always considerable in the simple screw 

 and nut, and which would resist a force applied immediately at the circum- 

 ference, without any diminution of its power. Sometimes the spires of a 

 ?crew are made to act on the teeth of a wheel, when a very slow motion of 

 the wbeel, or a very rapid motion of the screw, is required for the purposes of 

 the machine. (Plate V. Fig. 69, 70. ) 



The power of screws may be increased, in a great proportion, by means of an 

 arrangement invented by Mr. Hunter; which is somewhat similar, in its opera- 

 tion, to the double axis already described. A cylindrical screw is bored, and 

 made at the same time a tubular screw, with a little difference in the distances 

 of the threads, so that when it is turned within a fixed nut, it rises or sinks a 



