point-tool on a surface attached to the face-plate will be determined by the position of the point of the tool, its distance from the lathe-centres, and whether above or below the centres.

1. It is, therefore, essential in most cases that the tool's point should be level with the centres.

2. With equal revolutions of copy and work, and when the tool's point describes a figure much smaller than the eccentric plate, the figure produced is cardoid, or shaped like a heart, and this shape will gradually become more decided, and finally become looped, as the figure becomes very small.

3. When the figure is of the same size as the copyplate, its shape will also be the same, namely, an eccentric circle, and this rule applies to other shaped copy-plates.

4. When the figure is made much larger than the copy-plate, its shape is still the same as the copy, but the eccentricity will not be increased, the motion of the tool's point being the same in every case.

The tool's point describing an eccentric circle on a surface, if this point be traversed by the leading screw in the usual manner, an eccentric cylinder is produced, and this cylinder may be turned the entire length of the distance between the lathe-centres, as in ordinary traverse turning.

For producing an ellipse, the copy-plate must be an ellipse having equal rotations with the lathespindle, or it may be an eccentric circle rotating twice whilst the work revolves once. In either case the shape of the ellipse produced will be determined also to a great extent by the position of the tool's

point. By altering its position, ellipses of almost any proportion may be made from one copy-plate.

Parallel eccentric circular, and parallel elliptic, and other shaped shafts, are thus produced by traversing the tool in the usual manner.

Taper eccentric circular, taper elliptic, and other shaped articles, are turned also just as for plain concentric circular turning, namely, by moving the headstock out of line, or speeding the surfacing slide

screw.

Spiral eccentric circular, spiral elliptic, and other shaped articles, are turned by giving the shaper-plate a slightly faster or slower speed than the work. In the case of the former, the line passing through the concentric and eccentric centres, and in the other case the long diameter continually alters its position at every revolution of the work. Thus, when turning a spiral elliptic shaft, if the difference between the speeds of the work and copy-plate be the one-hundredth of a rotation, then at every rotation of the work, the long diameter of the ellipse will be 10 of a revolution behind or in advance of the same diameter of the ellipse which was cut at the last rotation. At the end of twenty-five rotations of the work, the long diameter will have shifted just quarter round, at fifty rotations just half round, and at one hundred rotations the spiral will have made one complete turn. This work is very singular in appearance; when cutting, it looks like and really is a double-threaded screw or spiral, and is cut with a slow traverse of the tool. If the copy-plate rotate faster than the work, the spiral will. be left-hand; if slower, it will be right-hand.

The pitch of the spiral depends upon the relative speeds of work, copy-plate, and screw. The figure makes one complete turn in every one hundred or other number of rotations; the pitch of the spiral will consequently be the distance traversed by the tool whilst the work has rotated one hundred times. The article may be made of a tapering spiral-elliptic, or other shape, by shifting the head-stock, or speeding the surface slide.

When the leading screw is driven in the usual manner by the change-wheels, the spiral is formed of one continuous line, but it may be formed of a series of separate circles, by disconnecting the leading screw and back-shaft, and by moving the leading screw a certain portion of a rotation by hand after turning each circle.

A secondary spiral or screw may be cut upon these shapes in almost any position, and either with rotating drills, revolving cutters, or ordinary tools, as is most convenient.

Some of these shapes, both wood and metal, can be cut with the same tools that are used for ordinary cylindrical turning, but in most cases the work is better performed by revolving cutters in the wheelcutting apparatus, or other frame made to carry a cutter, but without the slides.

The shapes to be produced are almost unlimited, and I purpose giving more information on this point when treating of ornamental turning. The foregoing examples are given mostly to show how all the various motions may be combined, each being capable of independent alteration and arrangement.

The shaper-plate, &c., will not admit of very rapid using, and in most cases it is advisable to keep its speed as slow as possible. When the work is such that revolving cutting tools are used, the lathe is only required to move very slowly; in these cases, therefore, the lathe must not be driven by the belt in the ordinary way, but by the worm and wheel on the leading This manner of driving I find convenient for most work when the copy-plate runs at the same speed or faster than the lathe-spindle.

screw.

The irregular shape mechanism is very useful when applied to turning cams, the cutting tool being either the ordinary slide-rest tool or a revolving cutter, according to the shape and size of the cam. They are thus turned far better and cheaper than by the old process of chipping and filing to a template.

Another useful application is to the cutting of curved slots and grooves; this is done by a rotating drill in a frame, guided automatically by a properlyshaped copy-plate.

It will be understood that when articles are to be turned of irregular transverse section only, the work and copy-plate must make equal rotations; when the position of the shape is required to vary, there must be a slight difference between the number of rotations.

By giving the copy-plate a very slow motion compared with the work, instead of the article being turned of irregular transverse section, it is turned circular, but of irregular longitudinal section. For instance, by means of this mechanism, we can produce taper shafts and angular work. The shaper-plate for this work must be a portion of a true spiral, and the

rise of this spiral will determine the difference between the small and large diameters of the shaft, and the relative speeds of leading screw and copy-plate will determine the length of the base of the taper-shaft or angle. Thus if the spiral have a rise of a quarter of an inch, the large diameter of the shaft will be half an inch larger than the small diameter, and the base of the angle will be equal to the distance travelled by the tool whilst the shaper-plate has made its rotation.

curves.

With an eccentric circle, as the shaper-plate, and with it rotating slowly compared with the work, the work produced is of circular section, but is longitudinally formed of a series of alternating internal and external The difference in diameter of the small and large places is equal to double the eccentricity of the copy-plate, and the length of the curve is equal to the distance travelled by the tool during one rotation of the copy-plate. This irregular shape can be continued for any length, or can be varied by making it tapering in the same manner as for ordinary turning.

A screw or spiral of fine or coarse pitch can also be cut upon these shapes just as easily as upon a plain cylinder.

In these applications of the mechanism, the copyplate runs much slower than the work, so therefore the work, even if of wood, may be run at about its usual speed; and the ordinary slide-rest tools I find to act efficiently.

Eccentric circular plates of different degrees of eccentricity are very useful, but it is not necessary to have a separate plate for each purpose, as one plate