When cutting multiple threads, which, owing to their increased lead,
incline considerably with the axis of the screw, the angles for each
side of the tool can be determined independently as follows: Draw line
_a--b_ equal in length to the circumference of the thread, as before, to
obtain the required angle _f_ of the rear or following side _e_{1}_; the
angle _l_ of the opposite or leading side is found by making _a--b_
equal to the circumference at the root of the thread. The tool
illustrated is for cutting right-hand threads; if it were intended for a
left-hand thread, the end, of course, would incline in the opposite
direction. The square thread is cut so that the depth _d_ is equal to
the width. When threading a nut for a square thread screw, it is the
usual practice to use a tool having a width slightly greater than
one-half the pitch, to provide clearance for the screw, and the width of
a tool for threading square-thread taps to be used for tapping nuts is
made slightly less than one-half the pitch.

=Cutting Multiple Threads.=--When a multiple thread is to be cut, such
as a double or triple thread, the lathe is geared with reference to the
number of single threads to the inch. For example, the lead of the
double thread, shown at _B_, Fig. 12, is one-half inch, or twice the
pitch, and the number of single threads to the inch equals 1 / 1/2 = 2.
Therefore, the lathe is geared for cutting two threads per inch. The
first cut is taken just as though a single thread were being cut,
leaving the work as shown at _A_. When this cut is finished the work is
turned one-half a revolution (for a double thread) without disturbing
the position of the lead-screw or carriage, which brings the tool midway
between the grooves of the single thread as indicated by dotted lines.
The second groove is then cut, producing a double thread as shown at
_B_. In the case of a triple thread, the work would be indexed one-third
of a revolution after turning the first groove, and then another third
revolution to locate the tool for cutting the last groove. Similarly,
for a quadruple thread, it would be turned one-quarter revolution after
cutting each successive groove or thread.

There are different methods of indexing the work when cutting multiple
threads, in order to locate the tool in the proper position for cutting
another thread groove. Some machinists, when cutting a double thread,
simply remove the work from the lathe and turn it one-half