set by the fact that too much time is required for removing
a given amount of metal when the work is revolving so slowly.

Generally speaking, the speed should be such that a fair amount of work
can be done before the tool requires re-grinding. Evidently, it would
not pay to grind a tool every few minutes in order to maintain a high
cutting speed; neither would it be economical to use a very slow speed
and waste considerable time in turning, just to save the few minutes
required for grinding. For example, if a number of roughing cuts had to
be taken over a heavy rod or shaft, time might be saved by running at
such a speed that the tool would have to be sharpened (or be replaced by
a tool previously sharpened) when it had traversed half-way across the
work; that is, the time required for sharpening or changing the tool
would be short as compared with the gain effected by the higher work
speed. On the other hand, it might be more economical to run a little
slower and take a continuous cut across the work with one tool.

The experiments of Mr. Taylor led to the conclusion that, as a rule, it
is not economical to use roughing tools at a speed so slow as to cause
them to last more than 1-1/2 hour without being re-ground; hence the
speeds given in the table previously referred to are based upon this
length of time between grindings. Sometimes the work speed cannot be as
high as the tool will permit, because of the chattering that often
results when the lathe is old and not massive enough to absorb the
vibrations, or when there is unnecessary play in the working parts. The
shape of the tool used also affects the work speed, and as there are so
many things to be considered, the proper cutting speed is best
determined by experiment.

=Rules for Calculating Cutting Speeds.=--The number of revolutions
required to give any desired cutting speed can be found by multiplying
the cutting speed, in feet per minute, by 12 and dividing the product by
the circumference of the work in inches. Expressing this as a formula we
have

_C_ x 12
_R_ = --------
[pi]_d_

in which

_R_ = revolutions per minute;
_C_ = the cutting speed in feet per minute;
[pi] = 3.1416;
_d_ = the diameter in inches.

For example if a cutting speed of 60 feet per minute is wanted and the
diameter of the work is 5 inches, the required speed would be found as
follows:

60 x 12
_R_ = ---------- = 46 revolutions per mi