the center, C.

In determining the position of this eccentric, we proceed upon the
assumption that the best results will be effected by such an arrangement
that when cutting off at the earliest point required, the cut-off valve
shall, at the instant of closing the port, be moving over it at its
highest speed. And this requires that the center of the eccentric shall
at the instant in question lie in the vertical line through C.

[Illustration: Figs. 3-12 IMPROVED STEAM ENGINE.--BY PROF MACCORD.]

Next, the least distance to be followed being assigned, the angle
through which the crank will turn while the piston is traveling that
distance is readily found; then, drawing an indefinite line C T, making
with the vertical line, G O, an angle, G C T. equal to the one thus
determined, any point upon that line may be assumed as the position of
the required center of the cut-off eccentric, at the beginning of the
stroke.

But again, in order that the cut-off may operate in the same manner when
backing as when going ahead, this eccentric must be symmetrically
situated with respect to both C and G; and since L O M bisects and is
perpendicular to G C, it follows that if the cut-off eccentric be fixed
on the shaft, its center must be located at H, the intersection of C T
with L M. This would require the edge of the cut-off valve at the given
instant to be at Q, perpendicularly over H; and the travel over the main
valve would be equal to twice C H, the virtual lever arm of the
eccentric, the actual traverse in the valve chest being twice O H, the
real eccentricity.