THE PRINCIPLES OF THE MARINE ENGINE. 351

A L again in N; join AH': AN will be tbe position ofthe crank at the instant of release.

Given, the angular advance of the eccentric, the half-travel of the slide, and the lap at both sides; to find thepositions of the crank at the instants of admission, cut-off, release, and cushioning. Draw the straight linesB A C and X A a; perpendicular to each other, and takeB and C to represent the dead points. Let the arrowdenote the direction of rotation. Draw F AL, makingthe angle F A X = the angular advance of the eccentric ;and make A F = A L = half-travel. On A F and A Las diameters, draw circles. About A, with a radiusequal to the lap at the induction-side, draw an arccutting the circle on A F in H and G; also, with aradius equal to the lap at the eduction-side, draw an arccutting the circle on A L in N and P. Draw thestraight lines A H E, A G D, ANI, APQ. Thesewill represent respectively the positions of the crank atthe instants of admission, cut-off, release, and cushioning.

The information alluded to in the “ Cadet Engineer ”is described and illustrated as follows :—

Now, if we wish the port to be closed before the ter-mination of the stroke, we make the face of the valvelonger, or put on lap. In this case the throw of thevalve must be increased by an amount equal to twice thelap. But if excessive lap be put on, it is evident thatthe travel will be so much increased as to permit thesteam to exhaust at an early part of tho stroke. Toobviate this, we must put lap on the exhaust side of thevalve. This has a bad effect in causing the exhaustvalve to close too soon. This will be seen clearly inthe illustration of tho geometrical action of the slidevalve, Fig. 236. Let A B equal the length of stroke ofthe engine drawn to any scale. We will give the valvean amount of lap on the steam side equal to half thebreadth of the steam port. The travel of the valve willthen be equal to three times the breadth of the steamport. On A B, as a diameter, describe a circle whichwill represent the path described by the centre of thecrank pin, while the piston is travelling twice the dis-tance A B. Divide this circle into any number ofequal parts, and draw perpendiculars to A B from everypoint of division. We shall thus determine the positionof the piston corresponding to that of the crank atVarious points. With the same centre t, as that of thecircle A r B s, describe a circle C o D p, having thetravel of the valve for its diameter. This will representthe path of the centre of the eccentric during a revolu-tion of the crank. When the crank is on the centre,

the line connecting the centre of the crank pin and thecentre of the shaft will be A t ; so that if the valve had

Fig. 236.

AMERICAN GEOMETRICAL DIAGRAM OP THE SLIDE VALVE.’

neither lap nor lead, the line connecting the centre ofthe eccentric and the centre of the shaft should take thedirection t r, perpendicular to A t. But in the presentcase, when we have both lap and lead, we make t u equalto the sum of the lap and lead, and through u draw aline parallel to t r. Connect the point o where this linecuts the circle with tho centre, and o t will be the properposition for the line connecting tho centre of tho eccen-tric and the centre of the shaft, when the crank is onone centre. When the crank is on the other centre, thisline will appear at t F. Divide the circle CoDy intothe same number of equal parts as we divided the circleAfBs, and draw perpendiculars to o p from every pointof division. The lengths of these perpendiculars showthe distances travelled by the valve at various points.Now, let A B represent the centre of the exhaust port.Then draw a b and c d to represent the width of onesteam port, and e f and g h for the other. Make a i equalto L W, the steam lead, and draw a line i k parallel toa b. This is the line to which all the measurementsmust be referred, since the valve commences to movefrom this position. Thus, when tho crank has movedthe distance A 1, the centre of the eccentric has moved

* The curve from a to P, should be more as that below, e to B.