--- = -------
1-3/4 1 x 1-3/4 (1 x 36) x (1-3/4 x 16) 36 x 28

The gears having 72 and 64 teeth are the _driving_ gears, and those with
36 and 28 teeth are the _driven_ gears.

=Change Gears for Metric Pitches.=--When screws are cut in accordance
with the metric system, it is the usual practice to give the lead of the
thread in millimeters, instead of the number of threads per unit of
measurement. To find the change gears for cutting metric threads, when
using a lathe having an English lead-screw, first determine the number
of threads per inch corresponding to the given lead in millimeters.
Suppose a thread of 3 millimeters lead is to be cut in a lathe having an
English lead-screw and a screw constant of 6. As there are 25.4
millimeters per inch, the number of threads per inch will equal 25.4 /
3. Place the screw constant as the numerator, and the number of threads
per inch to be cut as the denominator:

6 25.4 6 x 3
------- = 6 / ---- = -----
25.4 3 25.4
----
3

The numerator and denominator of this fractional expression of the
change-gear ratio are next multiplied by some trial number to determine
the size of the gears. The first whole number by which 25.4 can be
multiplied so as to get a whole number as the result is 5. Thus, 25.4 x
5 = 127; hence, one gear having 127 teeth is always used when cutting
metric threads with an English lead-screw. The other gear required in
this case has 90 teeth. Thus:

6 x 3 x 5 90
--------- = ---
25.4 x 5 127

Therefore, the following rule can be used to find the change gears for
cutting metric pitches with an English lead-screw:

_Rule.--Place the lathe screw constant multiplied by the lead of the
required thread in millimeters multiplied by 5, as the numerator of the
fraction, and 127 as the denominator. The product of the numbers in the
numerator equals the number of teeth for the spindle-stud gear, and 127
is the number of teeth for the lead-screw gear._

If the lathe has a metric pitch lead-screw, and a screw having a given
number of threads per inch is to be cut, first find the "metric screw
constant" of the lathe or the lead of thread in millimeters that would
be cut with change gears of equal size on the lead-screw and spindle
stud; then the method of determining the change gears is simply the
reverse of the one already explained for cutting a metric thread with an
English lead-screw.

_Rule.--To find