ferent threads is as follows:

For a U. S. standard thread:

_m_ = _d_ - 1.5155_p_ + 3_w_

For a sharp V-thread:

_m_ = _d_ - 1.732_p_ + 3_w_

For a Whitworth standard thread:

_m_ = _d_ - 1.6008_p_ + 3.1657_w_

In these formulas, _d_ = standard outside diameter of screw; _m_ =
measurement over wires; _w_ = diameter of wires; _p_ = pitch of thread =
1 / number of threads per inch.

To illustrate the use of the formula for the U. S. standard thread, let
us assume that a screw having 6 threads per inch (1/6-inch pitch) is to
be cut to a diameter of 1-1/2 inch, and that wires 0.140 inch diameter
are to be used in conjunction with a micrometer for measurement. Then
the micrometer reading _m_ should be

1-1/2 - 1.5155 x 1/6 + 3 x 0.140 = 1.6674 inch

If the micrometer reading were 1.670 inch, it would indicate that the
pitch diameter of the screw was too large, the error being equal to
difference between 1.667 and the actual reading.

[Illustration: Fig. 27. Rivett-Dock Circular Threading Tool in Working
Position]

=Rivett-Dock Threading Tool.=--A special form of thread tool, which
overcomes a number of disadvantages common to an ordinary single-point
thread tool, is shown in Fig. 27. This tool has a circular-shaped cutter
_C_, having ten teeth around its circumference, which, beginning with
tooth No. 1, gradually increase in height, cutter No. 2 being higher
than No. 1, etc. This cutter is mounted on a slide _S_, that is fitted
to the frame _F_, and can be moved in or out by lever _L_. The hub of
this lever has an eccentric stud which moves slide _S_ and locks it when
in the forward or cutting position. The action of the lever in moving
the slide engages the cutter with pawl _P_, thus rotating the cutter one
tooth at a time and presenting a different tooth to the work for each
movement of the lever. When the slide is moved forward, the heel or
underside of the tooth which is in the working position rests on a stop
that takes the thrust of the cut.

When the tool is in use, it is mounted on the tool-block of the lathe as
shown in the illustration. The cutter is set for height by placing a
tooth in the working position and setting the top level with the lathe
center. The cutter is also set square with the work by using an ordinary
square, and it is tilted slightly from the vertical to correspond with
the angle of the thread to be cut, by adjusting frame _F_. At first a
light cut is taken with lever _L_ moved