most desirable, we will first describe the operation of
marking off the cams which operate the respective valve levers, and then
discuss the effect of various "settings" of the valves on the running of
the engine.

[Illustration: FIG. 28.]

Assuming that we are still dealing with the Otto cycle engine, the cam
or side shaft will revolve at precisely half the speed of the crank
shaft. This 2 to 1 motion is obtained by means of toothed wheels, or a
screw gear. In the former case, where plain or bevel cog-wheels are
employed, the one fixed on the crank shaft must be exactly half the
diameter of the one on the side shaft, _i.e._, it must have one half the
number of teeth. On the other hand, if a screw gear is used, the
relative diameters of the two wheels may vary, but the pitch of the
teeth on the one must be twice that of the other. These wheels sometimes
have the teeth or thread formed in the casting, and sometimes they are
cut after a plain casting has been made. The latter kind are, needless
to say, better than the former, which often require filing up in order
to make every tooth alike, and ensure sweet running.

We know already in what positions our crank has to be at the opening and
closing of the three valves, and with the aid of the diagram, fig. 28,
we can determine the size of the cams. In fig. 29, S is the side shaft
to which the cams have to be keyed, R the roller on valve lever, the
latter being represented by the centre lines LL, as all we require to
find is the motion this lever will transmit to the valve, the spindle of
which is shown at V.

Fig. 30 shows diagrammatically the position of crank at the opening and
closing of the air valve. From this we see that the angle through which
the crank travels during the time the air valve is open is equal to the
obtuse angle ABC. Now, as the side shaft S revolves at half the speed of
crank, it is obvious that the former will travel through only half that
angle in the same space of time, _i.e._, through an angle equal to ABD.
We can now transfer this angle on to S, fig. 29, and draw two lines SE,
SF, cutting a circle GHJ, representing the back of the cam, which latter
passes in front of the roller R without causing any movement of the
lever L.

[Illustration: FIG. 29.]

[Illustration: FIG. 30.]

[Illustration: FIG. 31.]

It will be seen that by drawing a line forming a tangent to the circle
GHJ at F and another at E, and producing these, they will meet at