32. Nuts.-On Plate VII. is shown the bearing surface of a screw; fig. 87 is an elevation of the screw; fig. 89 a sectional elevation of the bearing or nut, taken through the line SP in fig. 88; fig. 90 shows a section of the screw and nut in contact. The drawing of the screw and nut will be explained later on.

33. Couplings.-Shafting is usually made in lengths, whose length varies according to circumstances, for convenience in erecting and mounting, and to allow of disconnecting portions of it. These lengths are connected by couplings. We may divide couplings into two classes; first, those used for shafts, which require disconnecting only at long intervals; and, secondly, where they are being disconnected constantly.

The box butt, box half-lap, and face-plate are the chief kinds used in the first class. In the second class there is a great variety, including clutches with from two teeth

upwards, friction cones, &c. Plate V. shows two forms of the first class, viz., the butt and the half-lap box couplings.

Figs. 72, 73, 74, are views of the butt box coupling; fig. 74 is a plan; fig. 73 an elevation, showing in section the box and portion of the shaft ends, a and b; fig. 72 is an end-elevation. The two shafts are swelled out at the ends so as not to reduce the strength of the shaft by the key-ways, and also that the box may pass over any collars that may be on the shaft. The ends of the shafts and the box are firmly connected by the key d. It is usual to place couplings near to the bearings, as shown in the figures; the bearing is on the shaft a, and is marked e; c is the box.

34. The half-lap coupling is represented in figs. 75, 76, 77, which are respectively end-elevation, front-elevation, and plan. The front-elevation is in section, showing the half-lap of the shafts and the connecting key. This coupling was introduced by Mr. Fairbairn.* The following are the proportions given by him :

Figs. 75, 76, 77, represent the coupling adapted for a 3" shaft, drawn to a scale of

35. Helical or Screw Curve.-Figs. 78, 79, Plate VI., represent in front and end-elevation the helical curve, which is traced as follows:-If during the revolution of a cylinder a marker, which moves parallel to the axis of the cylinder and at a uniform rate, traces upon its surface a curve, the curve so traced is called the helical or screw The distance moved through by the marker during one revolution of the cylinder is termed the pitch, and the direction in which it moves determines whether the Now Sir William Fairbairn, Bart.

curve.

curve is right or left-hand. Assuming the cylinder to be turning in the direction of the hands of a watch, as indicated in fig. 78, and the marker to move from right to left (0-16, 0-8 in fig. 79), the curve is right-handed, and left-handed if vice versa. The curves shown in figs. 78, 79, are right-handed and of the same pitch, but differing in diameter; the pitch is the distance ab (0—16). In the example illustrated, the curves are supposed to be fine wires bent to the required form, or the cylinders upon which they are traced are supposed to be transparent, so that the back half of the curve may be seen; the front half of the curve is marked 0-8, the back half 8-16. If the curve were a left-handed one, the portion marked 8-16 would be the front, and that marked 0-8 the back half.

The length of the curve is equal to the hypothenuse of a right-angled triangle abc, fig. 81, having for its base the circumference of the cylinder, fig. 80, and for its height the pitch ab, fig. 82. And if the triangle be

wound round the cylinder, keeping the base at right angles to the axis, the hypothenuse will assume the curved form shown in figs. 82 and 79, where ab the pitch,

=