l
give the foci of the ellipse, whence the minor axis may be found and the
curve described. For instance, in Figure 255 the velocity ratio being
nine to one at the maximum, the major axis is divided into two parts, of
which one is nine times as long as the other; in Figure 256 the ratio is
as one to three, so that the major axis being divided into four parts,
the distance A C between the foci is equal to two of them, and the
distance of either focus from the nearest extremity of the major axis is
equal to one, and from the more remote extremity is equal to three of
these parts.

CHAPTER XII.

_PLOTTING MECHANICAL MOTIONS._

[Illustration: Fig. 257.]

Let it be required to find how much motion an eccentric will give to its
rod, the distance from the centre of its bore to the centre of the
circumference, which is called the throw, being the distance from A to B
in Figure 257. Now as the eccentric is moved around by the shaft, it is
evident that the axis of its motion will be the axis A of the shaft.
Then from A as a centre, and with radius from A to C, we draw the dotted
circle D, and from E to F will be the amount of motion of the rod in the
direction of the arrow.

This becomes obvious if we suppose a lead pencil to be placed against
the eccentric at E, and suppose the eccentric to make half a revolution,
whereupon the pencil will be pushed out to F. If now we measure the
distance from E to F, we shall find it is just twice that from A to B.
We may find the amount of motion, however, in another way, as by
striking the dotted half circle G, showing the path of motion of B, the
diameter of this path of motion being the amount of lateral motion given
to the rod.

[Illustration: Fig. 258.]

In Figure 258 is a two arm lever fast upon the same axis or shaft, and
it is required to find how much a given amount of motion of the long arm
will move the short one. Suppose the distance the long arm moves is to
A. Then draw the line B from A to the axis of the shaft, and the line C
the centre line of the long arm. From the axis of the shaft as a centre,
draw the circle D, passing through the eye or centre E of the short arm.
Take the radius from F to G, and from E as a centre mark it on D as at
H, and H is where E will be when the long arm moves to A. We have here
simply decreased the motion in the same proportion as one arm is shorter
than the other. The principle involved is to take the motion of both
arms at an e