bank. The ruby
pin _o_ touches it, but has not as yet acted on it; _s s_ illustrates a
single roller, while S2 illustrates the safety roller for a double
roller escapement. In order to find the dimensions of the crescent in
the single roller we must proceed as follows: WA is in the center of the
fork when it rests against the bank, and is, therefore, one of the sides
of the fork angle, and is drawn from the pallet center; V A W is an
angle of 1 1/4deg., which equals the freedom between the guard point and
the roller; _g g_ represents the path of the guard pin _u_ for the
single roller, and is drawn at the intersection of VA with the roller A'
A2 is a line drawn from the balance center through that of the ruby pin,
and therefore also passes through the center of the crescent. By
planting a compass on this line, where it cuts the periphery of the
roller, and locating the point of intersection of VA with the roller,
will give us one-half the crescent, the remaining half being transferred
to the opposite side of the line A' A2. We will notice that the guard
point has entered the crescent 1 1/4deg. before the fork begins to move.

The angle of opening for the crescent in the double roller escapement is
greater than in the single, because it is placed closer to the balance
center, and the guard point or dart further from the pallet center,
causing a greater intersection; also the velocity of the guard point has
increased, while that of the safety roller has decreased. Fig. 24, at
_ff_, shows the path of the dart _h_, which also has 1 1/4deg. freedom
between bank and roller. From the balance center we draw A' _d_ touching
the center or point of the dart; from this point we construct at 5deg.
angle _b_ A' _d_. This is to ensure sufficient freedom for the dart when
entering the crescent. We plant a compass on the point of intersection
of A' A2 with the safety roller, S2, and locating the point where A'_b_
intersects it, have found one-half the opening for the crescent, the
remaining half being constructed on the opposite side of the line A' A2.

_The Horn_ on the fork belongs to the safety action: more horn is
required with the double than with the single roller, on account of the
greater angle of opening for the crescent.

The horn should be of such a length that when the crescent has passed
the guard point, the end of the horn should point to at least the center
of the ruby pin.

The dotted circle, _s s_, Fig. 25, represen