44. Screws are right or left-handed, according to the direction in which the nut moves; when the screw is turned round in the direction of the hands of a watch, the nut moves in the direction ba, figs. 92, 94, 96, from left to right, the screw is therefore right-handed; and lefthanded if vice versa.

A left-handed square-threaded screw, 21" diameter, pitch, is shown in figs. 97, 98, drawn to a scale of 1. Fig. 98 shows a common approximation to the true form of the thread. If the screw be turned round in the direction indicated by the arrows, the nut will move in the direction ab, from right to left.

Screws are considered to be right-handed single thread, unless otherwise stated. Left-handed screws are only used in special cases.

45. For square-threaded screws there is no strict standard for the number of threads per inch of length according to the diameter of the screw, as there is for the V-threaded screw. In some establishments the rule is, for the same diameter of screw, to allow the number of threads per inch to be one-half that of the V-threaded screw. This rule agrees very nearly with the following table :—

CHAPTER VII.

46. In this chapter we shall consider some of the kinds of wheels used as connecting pieces between shafts for the direct transmission of motion.

Spur Wheels are used for the purpose of transmitting motion from one shaft to another when the shafts are parallel. If the wheels are circular the motion is regular; and it is irregular in the case of elliptic and lobed wheels. We shall only consider the former kind, and confine ourselves to the simplest form of spur wheels, those having teeth projecting from the rim and parallel to the axis of the wheel. By giving proper diameters to the wheels we may obtain any required number of revolutions, within certain limits, for each shaft respectively.

47. In figs. 99, 100, Plate IX., A and B are the centres of two shafts, which are required to be connected by spur wheels, so that B shall make two revolutions to one of A. Required the diameters of the wheels. From A draw any line Ab, making an angle of about 30° with AB, and upon it set off Ac, cb, so that Ac = 2cb. Join Bb, and from c draw cC, parallel to Bb, cutting AB in C, then AC, BC are the required semi-diameters or radii. We could have found C by dividing AB by trial, as the division is a simple one; but the plan adopted can be applied whatever be the ratio of the diameters of the wheels, and is therefore a general solution. The wheel A we shall term the driver and B the follower.

The act of giving motion to a piece is termed driving it, and that of receiving motion from a piece is termed following it.*

In this example we have considered the wheels to be toothless, and to be rolling together without sliding, so that for each inch or fraction of an inch of the circumference of the wheel A passing the point C, an equal length * Principles of Mechanism, by Prof. Willis.

of the circumference of the wheel B passes the same point. The two shafts rotate in opposite directions; thus, if A turns in the direction of the hands of a watch, B will turn in the opposite direction. Wheels used to transmit motion are usually provided with teeth to ensure regularity of motion and the transmission of greater force than could be obtained conveniently with toothless wheels. The circles CDE, CFH, then become the pitch circles of the wheels, which are situated near the middle of the length of the teeth. See Ch. IX. on the Teeth of Wheels.

48. The diameters of wheels are generally referred to their pitch circles; thus we speak of the diameter of the pitch circle of a wheel of, say, 30 teeth, 1" pitch. Figs. 101, 102 represent a pair of wheels in outline (not showing the form of the teeth), A has 24, and B 18 teeth, " pitch. The pitch is the distance, measured along the pitch circle, from the centre of one tooth to the centre of the next tooth. In fig. 101 the dotted circle marked t represents the top, and that marked b the bottom of the teeth. A is a plate wheel, the boss is marked a; c is the plate, and d the rim of the wheel. The wheel B is solid, having projecting pieces, e, on each side, termed facings. The figures are drawn to a scale of To draw the wheels it is necessary to know the distance AB and the diameter of one of the wheels, from which we can readily obtain the diameter of the other, or the diameters of both wheels. We will take the problem as follows:

49. Given the number of teeth and the pitch of a pair of spur wheels, and the kind of wheels (solid, plate, or with arms), to make a drawing of them in outline. Having drawn the common centre line AB, fix upon A or B for one centre; now find the diameter of each pitch circle, which may be done as follows:-The diameter of a circle bears a constant ratio to its circumference, the ratio is 1: 31416, or 1: 3 nearly, that is to say, the circumference is 31416 times the diameter; therefore, knowing the number of teeth and the pitch, we can easily find the