which requires the least number of measurements. As an illustration of
how errors may accumulate, let us assume that seven holes are to be
bored in the jig-plate shown in Fig. 23, so that they are the same
distance from each other and in a straight line. The buttons may be
brought into alignment by the use of a straight-edge, and to simplify
matters, it will be taken for granted that they have been ground and
lapped to the same size. If the diameter of the buttons is first
determined by measuring with a micrometer, and then this diameter is
deducted from the center distance _x_, the difference will be the
distance _y_ between adjacent buttons. Now if a temporary gage is made
to length _y_, all the buttons can be set practically the same distance
apart, the error between any two adjacent ones being very slight. If,
however, the total length _z_ over the end buttons is measured by some
accurate means, the chances are that this distance will not equal six
times dimension _x_ plus the diameter of one button, as it should,
because even a very slight error in the gage for distance _y_ would
gradually accumulate as each button was set. If a micrometer were
available that would span two of the buttons, the measurements could be
taken direct and greater accuracy would doubtless be obtained. On work
of this kind where there are a number of holes that need to have
accurate over-all dimensions, the long measurements should first be
taken when setting the buttons, providing, of course, there are proper
facilities for so doing, and then the short ones. For example, the end
buttons in this case should first be set, then the central one and
finally those for the sub-divisions.

[Illustration: Fig. 23. Example of Work illustrating Accumulation of
Errors]

=Eccentric Turning.=--When one cylindrical surface must be turned
eccentric to another, as when turning the eccentric of a steam engine,
an arbor having two sets of centers is commonly used, as shown in Fig.
24. The distance _x_ between the centers must equal one-half the total
"throw" or stroke of the eccentric. The hub of the eccentric is turned
upon the centers _a--a_, and the tongued eccentric surface, upon the
offset centers, as indicated by the illustration. Sometimes eccentrics
are turned while held upon special fixtures attached to the faceplate.

[Illustration: Fig. 24. Special Arbor for Turning Eccentrics]

When making an eccentric arbor, the offset center in each end shou