the arc ACB. Next decide on a desired lead, and, with that as a radius, draw an arc with A as a centre. Draw a line from C tangent to the lead circle around A, when the lap of the valve is found to be equal to

FIG. 33.-Combination of the Reauleaux and Zeuner Diagrams. the perpendicular distance from the line CS to the centre O of the diagram. The crank will then be in position OS when the valve commences to open, or the angle AOS in advance of the dead-centre, and on OC at cut-off. Continuing, we find the valve in its

middle position when the crank is on OG which is drawn parallel to SC through the centre O. Extend this line to F, and with the exhaust lap as a radius draw the exhaust lap circle on the opposite side of the line GF and draw DE tangent to this circle, when OD is the position of the crank at the release point. From this point the exhaust remains open until the crank reaches the position OE, when it closes and compression takes place until it again reaches OS for admission and one revolution is completed.

By placing the Zeuner diagram upon this, draw HJ perpendicular to FG, and with the radius OH of the eccentric circle as a diameter, draw the admission valve circle OVHnO, and the lap circle with the steam lap as a radius and find the intersection occurs at V, both with the circles and the previously laiddown admission line OS and the cut-off point at the intersections at n. On the line OH set off the width of the steam port from L toward H equal to Lm, and with Om as radius draw the arc KmK. The shaded figure enclosed by the letters VKK'nL represents the steam port opening during the admission period, and the width of the port opening at any desired position of the crank is found by measuring the distance radially from O between the lap and valve circles on the port line, as the case may be, on the desired crank position.

The exhaust openings are determined in the same. manner, and are shown on opposite side of FG, where the crank passes through the arc DJE during the exhaust period with a positive exhaust lap of the size EF. When the exhaust edge of the valve is line and

line this arc becomes GJF, or 180 degrees, and when a negative lap (clearance) occurs, the duration of the exhaust period exceeds the half revolution of the crank. The various events are indicated around the

eccentric circle on the figure as they take place during a complete turn of the crank.

In Fig. 34 the eccentric and admission valve circles are shown at different cut-offs where each set of lines and circles is governed by the same explanation as those of Fig. 33 where the admission points S, S1, S2, and S correspond to the closing positions C, C', C2, and C3, cut-off points R, R1, R2, R3, etc. On OH we have the full-travel valve circle, and OL the lap, or radius, of the lap circle, the latter being the same for all cut-offs as well as the lead, the radii H1, H2, H3, etc., of the eccentric circles, or diameters of the corresponding valve circles, terminate on a line HI drawn perpendicular to AB and at a distance from O equal to that of lap and lead.

When the reverse lever is in its centre position the diameter of the valve circle falls on the line AB, and is equal to lap and lead. Continuing in back position we have the same method repeated, and OI would be the full-travel valve-circle diameter, or the same as the eccentric radius for the valve travel. Any desired cut-off position may be laid out in same manner as that in Fig. 33, which shows all of the valve events for a complete revolution of the axle.

In actual practice the movements are not so regular as the circles indicate, as it is impracticable to obtain the various loci in their theoretical positions; besides,