As delineated in Fig. 92, the impulse planes of the tooth and pallet are in contact; but we have it in our power to delineate the pallet at any point we choose between the arcs _p s_. To describe and illustrate the above remark, we say the lines _B e_ and _B f_ embrace five degrees of angular motion of the pallet. Now, the impulse plane of the pallet occupies four of these five degrees. We do not draw a radial line from _B_ inside of the line _B e_ to show where the outer angle of the impulse plane commences, but the reader will see that the impulse plane is drawn one degree on the arc _p_ below the line _B e_. We continue the line _h h_ to represent the impulse face of the tooth, and measure the angle _B n h_ and find it to be twenty-seven degrees. Now suppose we wish to delineate the entrance pallet as if not in contact with the escape-wheel tooth--for illustration, say, we wish the inner angle of the pallet to be at the point _v_ on the arc _s_. We draw the radial line _B l_ through _v_; and if we draw another line so it passes through the point _v_ at an angle of twenty-seven degrees to _B l_, and continue said line so it crosses the arc _p_, we delineate the impulse face of our pallet.
We measure the angle _i n B_, Fig. 92, and find it to be seventy-four degrees; we draw the line _v t_ to the same angle with _v B_, and we define the inner face of our pallet in the new position. We draw a line parallel with _v t_ from the intersection of the line _v y_ with the arc _p_, and we define our locking face. If now we revolve the lines we have just drawn on the center _B_ until the line _l B_ coincides with the line _f B_, we will find the line _y y_ to coincide with _h h_, and the line _v v'_ with _n i_.
HIGHER MATHEMATICS APPLIED TO THE LEVER ESCAPEMENT.
We have now instructed the reader how to delineate either tooth or pallet in any conceivable position in which they can be related to each other. Probably nothing has afforded more efficient aid to practical mechanics than has been afforded by the graphic solution of abstruce mathematical problems; and if we add to this the means of correction by mathematical calculations which do not involve the highest mathematical acquirements, we have approached pretty close to the actual requirements of the practical watchmaker.