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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, S', S, and so correspond to the closing positions C, C', C, and C, cut-off points R, R', R, Ro, 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 H', H, , 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,

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we have the angularities both of the main rods and the eccentric rods to contend with, and whereby irregularities are entering in the problem that must be compensated for, as referred to in the general description. It is not to be considered that a uniform circular motion is the best, but an approximation to it works with less shocks or jerks, and is therefore more desirable for so high-speed an engine as a locomotive. A few advantages can be taken, however, in selecting the suspensions and various connections, so that better results can be obtained than from a true circular motion, which are principally affected by three union points, and are, first, the connecting point of eccentric rod and link; second, the locus of the lifting-link suspension point; and third, the relative height of the crosshead-connection point of the union bar to the corresponding point of the combination lever.

It is not necessary to lay out the valve diagrams except where a given cut-off per cent is wanted. This is the most convenient way to find the required lap.

Fig. 35 and 36, the diagrams on the folding plates, represent the positions of the valve with the main crank at nine different points of the revolution of the driving wheel. In Fig. 35 the valve is of the piston type, with inside admission, and in Fig. 36 an outside admission valve is shown, of the D-slide pattern. Cardboard models of each of those valves will be found in the pocket on the inside of the front cover, and these models may be placed on the horizontal lines representing the valve seats of the folder plates and a good idea can be obtained of the work done by the Walschaert gear in either of the two methods of applying it, namely, to actuate inside and outside admission valves.

Place one of the cardboard valves on its seat and imagine the main pin to be at any one of the nine numbered points of the first half of the wheel's revolution, turning forward, and then move the valve model until its index points even with the mark at the corresponding number of the scale that shows the different positions of the combination lever; this will be the correct location of the valve at that time, and the relative positions of a point on the piston rod-say the wrist pin-both pins in the union bar that connects the lower end of the combination lever with the crosshead, both ends of the radius rod, the reversing link, its point of connection with the eccentric rod, and the position of the eccentric are all shown by the same numbers.

These diagrams are--with the exception of the reduction in size-reproduced exactly from models used by the Baldwin Locomotive Works, through the courtesy of that company, and are quite interesting,

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