, in Figure
274, into the required limits.

[Illustration: Fig. 281.]

Cut-off cams of any limit are necessarily imperfect in their operations
as to uniformity of cut-off from opposite ends of the slides, not from
any defect in the rule for laying them off, but from the well-known fact
of the crank pin travelling a greater distance, while driven by the
piston from the centre of the cylinder, through its curved path from the
cylinder, over its centre, and back to the centre of the cylinder, than
in accomplishing the remaining distance of its path in making a complete
revolution; and, although the subdivisions of eighths of the stroke
line B, in Figure 274, does not truly represent a like division of the
piston stroke, owing to deviation, caused by inclination of the
connecting rod in traversing from the centres to half stroke, still it
will be found that laying off a cut-off cam by this rule is more nearly
correct than if the divisions on stroke line B were made to correspond
exactly with a subdivision of piston stroke into eighths.

[Illustration: Fig. 282.]

The cut-off in cams laid off by the rules herein described is greater in
travelling from one side of the slides than in travelling from the
opposite end, one cut-off being more than the actual cut-off of piston
stroke, and the other less; and in practical use, owing to play or lost
motion in the connections from cam to valve, the actual cut-off is less
than the theoretical; hence cut-off cams are usually laid off to
compensate for lost motion; that is, laid off with more limit; for
instance, a five-eighths cam would be laid off to cut-off at
eleven-sixteenths instead of five-eighths.

[Illustration: Fig. 283.]

Figure 283 represents the motion a crank, C, imparts to a connecting
rod, represented by the thick line R, whose end, B, is supposed to be
guided to move in a straight line. The circle H represents the path of
the crank-pin, and dots 1, 2, 3, etc., are 24 different crank-pin
positions equidistant on the circle of crank-pin revolution. Suppose the
crank-pin to have moved to position 1, and with the compasses set to the
length of the rod R, we set one point on the centre of position 1, and
mark on the line of motion _m_ the line _a_, which will be the position
rod end B will have moved to. Suppose next that the crank-pin has moved
into position 2, and with the compass point on the centre of 2 we mark
line 2, showing that while the crank-pin moved from 1