uch impulse is, as
previously stated, termed the "lifting angle." This "lifting angle" is
by horological writers again divided into real and apparent lifts. This
last division is only an imaginary one, as the real lift is the one to
be studied and expresses the arc through which the impulse face of the
tooth impels the balance during the act of escaping, and so, as we shall
subsequently show, should no more be counted than in the detached lever
escapement, where a precisely similar condition exists, but is never
considered or discussed.

We shall for the present take no note of this lifting angle, but confine
ourselves to the problem just named, of so arranging and designing our
escape-wheel teeth and cylinder that each half of the tooth space shall
give equal impulses to the balance with the minimum of drop. To do this
we will make a careful drawing of an escape-wheel tooth and cylinder on
an enlarged scale; our method of making such drawings will be on a new
and original system, which is very simple yet complete.

DRAWING THE CYLINDER ESCAPEMENT.

All horological--and for that matter all mechanical--drawings are based
on two systems of measurements: (1) Linear extent; (2) angular movement.
For the first measurement we adopt the inch and its decimals; for the
second we adopt degrees, minutes and seconds. For measuring the latter
the usual plan is to employ a protractor, which serves the double
purpose of enabling us to lay off and delineate any angle and also to
measure any angle obtained by the graphic method, and it is thus by this
graphic method we propose to solve very simply some of the most
abstruce problems in horological delineations. As an instance, we
propose to draw our cylinder escapement with no other instruments than a
steel straight-edge, showing one-hundredths of an inch, and a pair of
dividers; the degree measurement being obtained from arcs of sixty
degrees of radii, as will be explained further on.

In describing the method for drawing the cylinder escapement we shall
make a radical departure from the systems usually laid down in
text-books, and seek to simplify the formulas which have heretofore been
given for such delineations. In considering the cylinder escapement we
shall pursue an analytical course and strive to build up from the
underlying principles. In the drawings for this purpose we shall
commence with one having an escape wheel of 10" radius, and our first
effort will be the primary