, up to the present
time, no remedy has been devised to overcome it. All the other
escapements, including the chronometer, duplex and cylinder, are quite
as wasteful of power, if not more so. It is usual to construct
ratchet-tooth pallets so as to utilize but ten degrees of escape-wheel
action; but we shall show that half a degree more can be utilized by
adopting the eight and one-half degree fork action and employing a
double-roller safety action to prevent over-banking.

[Illustration: Fig. 10]

From the point _e_, which represents the center of the pallet staff, we
draw through _b_ the line _e f_. At one degree below _e f_ we draw the
line _e g_, and seven and one-half degrees below the line _e g_ we draw
the line _e h_. For delineating the lines _e g_, etc., correctly, we
employ a degree-arc; that is, on the large drawing we are making we
first draw the line _e b f_, Fig. 10, and then, with our dividers set at
five inches, sweep the short arc _i_, and on this lay off first one
degree from the intersection of _f e_ with the arc _i_, and through this
point draw the line _e g_.

From the intersection of the line _f e_ with the arc _i_ we lay off
eight and one-half degrees, and through this point draw the line _e h_.
Bear in mind that we are drawing the pallet at _B_ to represent one with
eight and one-half degrees fork-and-pallet action, and with equidistant
lockings. If we reason on the matter under consideration, we will see
the tooth _A_ and the pallet _B_, against which it acts, part or
separate when the tooth arrives at the point _c_; that is, after the
escape wheel has moved through ten and one-half degrees of angular
motion, the tooth drops from the impulse face of the pallet and falls
through one and one-half degrees of arc, when the tooth _A''_, Fig. 10,
is arrested by the exit pallet.

To locate the position of the inner angle of the pallet _B_, sweep the
short arc _l_ by setting the dividers so one point or leg rests at the
center _e_ and the other at the point _c_. Somewhere on this arc _l_ is
to be located the inner angle of our pallet. In delineating this angle,
Moritz Grossman, in his "Prize Essay on the Detached Lever Escapement,"
makes an error, in Plate III of large English edition, of more than his
entire lock, or about two degrees. We make no apologies for calling
attention to this mistake on the part of an authority holding so high a
position on such matters as Mr. Grossman, because a mistake i