II. All conical surfaces: that is, surfaces in which the straight generating lines all pass through one point. The transverse sections of such a surface may be circular, as in the pitch-cone of a circular bevel wheel (Article 105, page 86); or they may be noncircular curves, as in the acting surfaces of the teeth of such a wheel (Article 144, page 143).

III. Hyperboloidal or skew-bevel surfaces: in which the straight generating lines, not intersecting in one point, traverse a series of similar transverse sections of the surface. Such transverse sections may be circular, as in the pitch-surface of a circular skew-bevel wheel (Article 106, page 87); or non-circular, as in the acting surfaces of skew-bevel teeth (Article 145, page 146).

The PLANING MACHINE cuts straight surfaces of all kinds; and is used especially for the cutting of plane surfaces to a certain degree of approximation; that is to say, the longitudinal straightness of the surface is perfect; but the transverse straightness is approximate. In a planing machine of ordinary construction, there is a fixed horizontal bed, very strongly and stiffly supported: its essential parts being a pair of most accurately made straight, parallel, horizontal guides, of a V-shape in cross-section. In those guides there slides a pair of straight, parallel, horizontal, triangular bars, forming the supports of a stiff and strong horizontal table, having in it several slots or oblong openings, for the purpose of enabling the work to be secured to it. From the two sides of the bed rise a pair of standards, carrying a straight horizontal saddle that bridges across the table. The saddle, by means of straight horizontal guides, supports the tool-holder, which has a transverse traversing motion. The sliding surfaces of the saddle and toolholder are usually of a dove-tail shape in cross-section.

The cutting action is effected by a longitudinal motion of the table carrying the work: the gearing which communicates that motion ought to be extremely smooth and accurate in its action; such as the rack and helical pinion described at page 289; and the pitch-point of the rack and pinion ought to be as directly as possible below the cutting tool. As to the speed, see Article 482, page

567.

During the return stroke, the tool is lifted clear of the work, and the motion of the rack and pinion is reversed by means of selfacting reversing gear; such, for example, as that mentioned in Article 264, page 299; and the train of wheelwork which produces the return stroke is so proportioned as to give an increased speed of motion to the table, usually about double that of the cutting stroke.

The transverse traversing motion of the tool-holder is intermittent, being made during the return stroke of the table. The combination which directly produces it is usually a transverse horizontal screw driving a nut that is fixed to the tool-holder.

The screw is driven by a suitable train of wheelwork, the first wheel of which is driven by a click, usually of the reversible kind (Article 194, page 207). The extent of traverse after each cutting stroke can be regulated by the help of adjustments of length of stroke (Article 273, page 312), or of change-wheels (Article 271, page 311).

In some large planing machines for very heavy work, the cutting stroke is effected by a longitudinal motion of a strong frame carrying the saddle and the tool-holder; the table with the work being at rest.

For cutting straight surfaces of more or less complex cross-section, and especially for cutting straight grooves and straight rectangular holes, such as key-ways and slots, the SLOTTING-MACHINE is used. In this machine the tool-holder or cutter-bar usually slides vertically in a guiding groove in the slide-head, which is carried by a strong overhanging frame. Below the slide-head is a table to which the work is secured, capable of being turned about a vertical axis, and traversed horizontaliy in two rectangular directions, so as to bring the work into any required position relatively to the cutting-tool.

A SHAPING MACHINE differs from a slotting machine mainly in having a slide-head that is capable of being turned into different positions, so as to cause the tool to make strokes in different directions when required. It is used for cutting ruled surfaces of various kinds. Circular cutters (page 568), driven by suitable shifting trains (Article 228, page 235), are sometimes used in shaping machines.

487. Scraping Plane Surfaces.—When the highest practicable degree of accuracy is required in a plane surface, its form may in the first place be given approximately by the planing machine, but it must be finished by the hand-scraper. Scrapers for iron are usually made of very hard steel, with edges of 60°.

When an existing standard plane surface (or planometer, as it is sometimes called) is available, it is smeared with a very thin coating of a mixture of red chalk and oil. The new plane, in its approximate condition, is laid face to face on the standard plane, and gently rubbed on it. The prominent places on the new plane pick up the colouring matter, and are marked by it; and thus the workman is guided to the parts that require scraping down. The process is repeated again and again until the new plane fits the standard plane with the required degree of precision.

In the absence of a standard plane, three approximately plane castiron plates are made, stiffened at the back by ribs. One pair of those are taken in the first place; and one of them being smeared with a suitable mixture, they are repeatedly rubbed together, so as to mark the prominent places, and both are scraped, until

they fit each other with a certain degree of accuracy. At this stage of the process, they may be both plane; or both spherical, and of the same radius, one being convex and the other concave. Then the two plates first taken are compared in succession with the third plate, and the operations of rubbing and scraping repeated, with the plates combined by pairs in every possible way, until all three plates accurately fit each other in every combination and position; when they must necessarily be truly plane. This is the process by which standard planes are made; and when a set of three have been made, it is usual to reserve one of them very carefully for testing from time to time the accuracy of the other two, which are employed as standards of planeness and straightness for ordinary use.

488. Making Surfaces of Revolution — Turning, Drilling, and Boring.—A turning-lathe usually contains the following principal parts. The bed, truly plane and horizontal. The head-stocks, or supports for the axis of rotation of the work; one fixed, and the other capable of being shifted longitudinally on the bed to a greater or less distance from the fixed headstock, so as to suit the size of the work. The saddle, which slides longitudinally ou the bed, carrying the rest, which carries the tool-holder. The rest has longitudinal and transverse traversing motions, usually produced by means of screws and nuts, acting on slides with dovetail-shaped straight bearing surfaces; the position of the tool-holder is adjustable vertically and horizontally.

The longitudinal traversing motion of the saddle is sometimes produced by a pinion driving a rack, like the motion of the table in a planing machine, and sometimes by a strong and very accurately made screw, extending the whole length of the bed; the latter method is used in screw-cutting lathes. Many lathes are provided both with a guide-screw and with a rack-and-pinion motion for traversing, either of which can be used at pleasure. The guide-screw is commonly reserved for screw-cutting, and the rack and pinion used for ordinary purposes.

The moveable headstock carries the screw-spindle, which does not rotate, but can be slid back and forward by means of a screw, in order to adjust the position of its point, which forms one of the supports of the work. The fixed or fast headstock carries the lathe-spindle, which is a rotating horizontal shaft, driven at a proper speed by means of a suitable belt and pulleys; the speed is capable of adjustment by means of speed-cones, usually of the stepped kind described in Article 171, page 185.

The journals of the lathe-spindle are in most cases made slightly conical, and are tightened in their bearings, when required, by means of screws acting endwise.

The ends of both spindles project inwards from the headstocks: they are capable of being fitted with various contrivances for

supporting and holding the work. The screw-spindle usually, and the lathe-spindle sometimes, is fitted with a conical point of steel called a centre, the angle at the point ranging from 60° for wood, to 80° or 90° for metal; such points support the work and keep it truly centred on the axis of rotation. The lathe-spindle can also be fitted with chucks of different sorts; being discs provided with holes, pins, and other means of holding the work, and causing it to rotate along with the lathe-spindle; or with a mandril or cylindrical continuation of the spindle, on which wheels and pulleys, and other pieces of work having eyes in their centres, can be keyed for the purpose of being turned.

A chuck in the form of a large circular disc is called a face-plate. Some lathes have face-plates on both spindles; and then the two spindles are driven at the same speed, by means of two pinions on one shaft, gearing with teeth on the rims of the face-plates.

The greatest radius of the work which can be turned in a given lathe is limited by the height of the axis of rotation above the bed; and the lathe is described as a "twelve-inch lathe," a "twenty-fourinch lathe," &c., according to that height.

The tool-holder is adjusted so that the point or cutting part of the tool is exactly in a horizontal plane traversing the axis of rotation. The direction of rotation is such that the surface of the work moves downwards at the point of the tool, which accordingly cuts upwards.

The screws and nuts, or the pinions and racks, by which the traversing motions of the tool-holder are produced, are driven from the lathe-spindle through trains containing change-wheels (Article 271, page 311); and by means of these the velocity-ratio and directional-relation of the cutting motion and of the traversing motion can be adjusted so as to produce the required resultant or aggregate relative motion. As to the rate of traverse per revolution, see Article 485, page 569.

When the word traversing is used without qualification, it generally means that the tool traverses in a direction parallel to the axis of the lathe, so as to turn a cylindrical surface. When the tool is made to move in the direction of a radius perpendicular to the axis, it turns a plane surface; and the process is called surfacing. This is very often the means used of making a plane approximately, previous to correcting it by scraping. By combining those two motions, so as to make the tool traverse in a straight line cutting the axis obliquely, a conical surface is turned. When the point of the tool is made to traverse in a circle, one diameter of which coincides with the axis, a spherical surface is turned. A hyperboloidal surface might be turned by making the point of the tool traverse along one of its straight generating lines (see Article 84, page 70; Article 106, page 87).

All the preceding operations are examples of circular turning,

in which the point of the tool describes, relatively to the work, a circle about the axis, if the traversing motion be neglected, or a helix or spiral of a pitch equal to the traverse per revolution, if this component of the motion be taken into account. In eccentric turning, the point is made to describe, relatively to the work, paths of various other kinds, such as eccentric circles, ellipses, epicycloids, and arbitrary curves of various sorts. Such aggregate paths are produced, sometimes by epicyclic trains carried by the chuck which holds the work, as in the eccentric chuck, elliptic chuck, and geometric chuck; sometimes by the action of cams or shaperplates on the tool-holder. The actions of such combinations have been treated of in Part I., Chapter V., Section IV., pages 261 to 267; and in the Addenda, pages 290, 291.

Drilling and Boring may be looked upon as modifications of turning, applied to the making of concave surfaces of revolution, and especially of hollow cylinders. The word boring is often applied to both processes; but when drilling and boring are distinguished from each other, drilling means the making of a cylindrical hole by a tool which advances endways, cutting shavings from the flat or conical bottom of the hole (see fig. 287); and boring, the enlarging and correcting of a hollow cylindrical surface already made; such as that of a cast-iron steam-engine cylinder. In drilling, the tool or drill usually rotates about a vertical axis; and it is very often driven by a shifting train, carried by a jib or train-arm. (As to shifting trains, see Article 228, pages 235 to 238.) This is in order that the position of the drill may be shifted to various parts of the work. The train-arm or jib projects horizontally from a strong hollow standard, containing the vertical shaft that drives the shifting train. The work is supported by a table, which is often made so as to be capable of being turned about a vertical axis, and shifted horizontally on slides in two rectangular directions, in order to bring different points in the work below the drill.

The feed-motion is given sometimes by gradually lowering the drill, sometimes by gradually raising the table.

In a multiple drilling machine (used for making rows of holes in iron plates) a set of drills are driven from one shaft by means of skew-bevel pinions or other suitable mechanism. The feed motion is given by raising the table. The forms of drilling tools are very various.

In a boring machine, the inner surface of a hollow cylinder is pared by means of one or more tools carried by a cutter-bar or cutter-head; being a cylinder a little smaller than the hollow cylinder to be bored. When the work is a very large cylinder, it is usually fixed; and the rotation and traversing motion are both given to the cutter head.

489. Screw-Cutting. The operation of cutting screws is per