If the latter mode be employed, any amount of eccentricity is given to the chuck, and between every cut the index-wheel of the chuck and division-plate of lathe are moved any number of divisions, in the proportion of 1 to 2 in opposite directions.

In the figure there are 96 circles. To obtain these between every cut the chuck-wheel was moved th and the latheths of a revolution; this had the effect

of causing the lathe to move around twice in one direction, whilst the chuck-wheel was moved once in the other direction. This is usually termed 'double counting.'

To produce Fig. 204, the counting was the same, but the movements were both in the same direction.

Fig. 205 was produced by the same instruments, but the movements were such as to cause the lathe to make three revolutions, whilst the chuck-wheel made one in the opposite direction. To make that figure the chuck had an eccentricity of 4 turns of its screw, the rest was moved 14 turns towards the operator.

Fig. 206 was made with the same relative velocity, namely 3 to 1. The eccentricity and movement of rest were also the same, but the lathe and chuck-wheel were both moved around in the same direction.

Fig. 207 was made in the same manner, with a velocity ratio of 3 to 1. The movements were in opposite directions, and the eccentricity of the chuck and movement of the slide-rest were equal.

Fig. 208. This figure had a velocity ratio of 4 to 1. For the inside the movements were in opposite directions, the eccentricity was equal to 5 turns of the screw, and the movement of the rest 11 turns of its screw.

For the inside the movements were in the same direction, the chuck's eccentricity was 3 and the rest's movement 1th of a turn.

Fig. 209 was produced by a velocity ratio of 5 to 2 in opposite directions. The eccentricity was 4, and the move

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ment of the rest 2 turns of the screw.

FIG. 209.

Fig. 210 had a velocity ratio of 8 to 1. For the outside the direction of motion was the reverse of what it was for the inside pattern.

By altering the relative velocity of the lathe-wheel

and chuck-wheel, figures of almost any number of sides or loops can be obtained by these instruments; and by substituting the ellipse instrument for the eccentric instrument, the same figures are produced in ellipses instead of circles. The ellipse patterns are, as a rule, much more beautiful than the others, but they are no more difficult to produce. Indeed, there is no great difficulty in producing a pretty pattern with any instru

I

may here say a word on the ornamental uses of the vibrating saddle, or apparatus for irregular shape turning, shown at Fig. 137.

If we have a true surface attached to the lathespindle, and we cut a line on it with a tool held in the slide-rest, while the sliding clutch is in gear with the

worm-wheel on the surface-screw, an Archimedian

FIG. 211.

spiral will be described, the pitch of which will depend on the relative velocity of the lathe and surface. screw. The circular spirals in the inside of Fig. 211 are spirals of that sort, and are so described.

The outside spiral of the same figure was cut by the combined action of the last motion, and the vibration of the saddle caused by an eccentric circle

for a shaper-plate. The shaper-plate made four revolutions whilst the lathe-spindle made one. So also in Fig. 212, the outside is formed of two of the same

same shaper-plate and with the same velocity ratio, but with the tool's point at smaller distances from the

centre.

Fig. 213 was produced by the motion of the slide, but the shaper-plate was a crank-pin, having a throw equal to half the diameter of the figure.

Fig. 214 was produced also by a crank-pin, having a throw equal to the width of the figure, the velocity

ratio being expressed by a mixed number or a whole number and a fraction. The figure produced is formed of one continuous line.

By combining the movement of the saddle with the eccentric instrument or ellipse instrument, the figures produced are very beautiful.

Figs. 215, 216, 217 were produced by the vibrating saddle and eccentric instrument.