pense with the most of the teeth, retaining only those near the
extremities of the major axes, which are necessary in order to assist
and control the motion of the link at and near the dead-points. The arc
of the pitch-curves through which the teeth must extend will vary with
their eccentricity; but in many cases it would not be greater than that
which in the approximation may be struck about one centre; so that, in
fact, it would not be necessary to go through the process of rectifying
and subdividing the quarter of the ellipse at all, as in this case it
can make no possible difference whether the spacing adopted for the
teeth to be cut would "come out even" or not, if carried around the
curve. By this expedient, then, we may save not only the trouble of
drawing, but a great deal of labor in making, the teeth round the whole
ellipse. We might even omit the intermediate portions of the pitch
ellipses themselves; but as they move in rolling contact their retention
can do no harm, and in one part of the movement will be beneficial, as
they will do part of the work; for if, when turning, as shown by the
arrows, we consider the wheel whose axis is D as the driver, it will be
noted that its radius of contact, C P, is on the increase; and so long
as this is the case the other wheel will be compelled to move by contact
of the pitch lines, although the link be omitted. And even if teeth be
cut all round the wheels, this link is a comparatively inexpensive and a
useful addition to the combination, especially if the eccentricity be
considerable. Of course the wheels shown in Figure 255 might also have
been made alike, by placing a tooth at one end of the major axis and a
space at the other, as above suggested. In regard to the variation in
the velocity ratio, it will be seen, by reference to Figure 256, that if
D be the axis of the driver, the follower will in the position there
shown move faster, the ratio of the angular velocities being P x D/P x
B; if the driver turn uniformly, the velocity of the follower will
diminish, until at the end of half a revolution, the velocity ratio will
be P x B/P x D; in the other half of the revolution these changes will
occur in a reverse order. But P D = L B; if then the centres B D are
given in position, we know L P, the major axis; and in order to produce
any assumed maximum or minimum velocity ratio, we have only to divide L
P into segments whose ratio is equal to that assumed value, which wil