ON PRESSURE AND EQUILIBRIUM. 55 



magnitude of the forces must be determined from the general law of the 

 composition of three pressures. (Plate V. Fig. 65.) 



If a prop or bar, leaning against a smooth vertical surface or wall, be 

 employed to support or to raise a weight, by means of a force which draAvs 

 its base along a smooth horizontal surface, the horizontal force must be to 

 the weight as the distance of the bottom of the prop from the wall to its 

 perpendicular height. And from similar principles, the conditions of the 

 equilibrium of arches, domes, and roofs may be determined. (Plate V. 

 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 hori- 

 zontally to the base of the wedge, and the weight which is to be raised as 

 acting vertically on its inclined surface : 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, pro- 

 vided 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 equi- 

 librium. (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 

 together, 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 divides 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 circumference, without any diminution of its power. Sometimes the 

 spires of a screw are made to act on the teeth of a wheel, when a very slow 

 motion of the wheel, 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 ;t which is somewhat similar, 

 in its operation, 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 little more or less than the internal screw which perfo- 

 rates it would rise or sink by the action of its own threads, and a weight 

 attached to this internal screw ascends, in each revolution, only through a 

 space equal to the difference of the height of the two coils. Here the ma- 



** Leupold. Theat. Machin. t. 6, 7. Com. Bon. iii. 131, 304. Kastner on the 

 Screw. Commentationes Soc. Gott. 4to, 1795, xiii. M. i. 47, 1797, xiv. M. 3. 

 Ibid, de Theoria Cochlese. Diss. VI. 38. Nicholson's Jour. i. 158. 



f Essay on a New Method of applying the Screw, Ph. Tr. 1781, Ixxi. 58. 



