of the parts shown in Fig. 130.  The first position of which we should take cognizance is, the tooth D is moved back to the left so as to rest on the outside of our cylinder.  The cylinder is also supposed to stand so that the lips correspond to the line f.  On pressing the tooth D forward the incline of the tooth would attack the entrance lip of the cylinder at just about the center of the curved impulse face, imparting to the cylinder twenty degrees of angular motion, but the point of the tooth at d would exactly encounter the inner angle of the exit lip, and of course the cylinder would afford no rest for the tooth; hence, we see the importance of not cutting away too much of the half shell of the cylinder.

But before we further consider the action of the tooth D in its action as it passes the exit lip of the cylinder we must finish with the action of the tooth on the entrance lip.  A very little thought and study of Fig. 130 will convince us that the incline of the tooth as it enters the cylinder will commence at t, Fig. 130, but at the close of the action the tooth parts from the lip on the inner angle.  Now it is evident that it would require greater force to propel the cylinder by its inner angle than by the outer one.  To compensate for this we round the edge of the entrance lip so that the action of the tooth instead of commencing on the outer angle commences on the center of the edge of the entrance lip and also ends its action on the center of the entrance lip.  To give angular extent enough to the shell of the cylinder to allow for rounding and also to afford a secure rest for the tooth inside the cylinder, we add six degrees to the angular extent of the entrance lip of the cylinder shell, as indicated on the arc o’, Fig. 131, three of these degrees being absorbed for rounding and three to insure a dead rest for the tooth when it enters the cylinder.

WHY THE ANGULAR EXTENT IS INCREASED.

Without rounding the exit lip the action of the tooth on its exit would be entirely on the inner angle of the shell.  To obviate this it is the usual practice to increase the angular extent of the cylinder ten degrees, as shown on the arc o’ between the lines f and p, Fig. 131.  Why we should allow ten degrees on the exit lip and but six degrees on the entrance lip will be understood by observing Fig. 130, where the radial lines s and r show the extent of angular motion of the cylinder, which would be lost if the tooth commenced to act on the inner angle and ended on the outer angle of the exit lip.  This arc is a little over six degrees, and if we add a trifle over three degrees for rounding we would account for the ten degrees between the lines f and p, Fig. 131.  It will now be seen that the angular extent is 196 degrees.  If we draw the line w we can see in what proportion the measurement should be made