e
locate the real impulse radius and draw the arc _ri ri_ which describes
the path made by the face of the ruby pin. The ruby pin is to have
1/4deg. of shake in the slot; it will therefore have a width of
4 7/8deg.; this width is drawn in with the ruby pin imagined as standing
over the line of centers and is then transferred to the position which
the ruby pin is to occupy in the drawing.

The radius of the safety roller was given as 4/7 of the theoretical
impulse radius. They may be made of various proportions; thus 2/3 is often
used. Remember that the smaller we make it, the less the friction during
accidental contact with the guard pin, the greater must the passing
hollow be and the horn of fork and guard point must be longer, which
increases the weight of the fork.

Having drawn in the safety roller, and having specified that the freedom
between the dart and safety roller was to be 1 1/4deg., the dart being
in the center of the fork, consequently _k_ A is the center of it;
therefore we construct the angle _k_ A X of 1 1/4deg. At the point of
intersection of X A with the safety roller we draw the arc _g g_; this
locates the point of the dart which we will now draw in. We will next
draw _d_ A' from the balance center and touching the point of the dart;
we now construct _b_ A' at an angle of 5deg. to it. This is to allow the
necessary freedom for the dart when entering the crescent; from A' we
draw a line through the center of the ruby pin. We do not show it in the
drawing, as it would be indiscernible, coming very close to A' X. This
line will also pass through the center of the crescent. At the point of
intersection of A' _b_ with the safety roller we have one of the edges
of the crescent. By placing our compass at the center of the crescent on
the periphery of the roller and on the edge which we have just found, it
follows that our compass will span the radius of the crescent. We now
sweep the arc for the latter, thus also drawing in the remaining half of
the crescent on the other side of A' X and bringing the crescent of
sufficient depth that no possibility exists of the dart touching in or
on the edges of it. We will now draw in the impulse roller and make it
as light as possible consistent with strength. A hole is shown through
the impulse roller to counterbalance the reduced weight at the crescent.
When describing Fig. 24, we gave instructions for finding the dimensions
of crescent and position of guard pin for