any divisions as the two half-circles are. But it is not absolutely
necessary that both half-circles be divided into the same number of
equal divisions. Thus, suppose the large half-circle were divided into
ten divisions, then instead of the first half of the pitch being divided
into eight (as from _a_ to _h_) it would require to have ten lines. But
the inner half-circle may have eight only, as in our example. It is more
convenient, however, to use the same number of divisions for both
circles, so that they may both be divided together by lines radiating
from the centre. The more the points of division, the greater number of
points to draw the curves through; hence it is desirable to have as many
as possible, which is governed by the pitch of the thread, it being
obvious that the finer the pitch the less the number of distinct and
clear divisions it is practicable to divide it into. In our example the
angles of the thread are spread out to cause these lines to be thrown
further apart than they would be in a bolt of that diameter; hence it
will be seen that in threads of but two or three inches in diameter the
lines would fall very close together, and would require to be drawn
finely and with care to keep them distinct.

[Illustration: Fig. 208 _a_.]

[Illustration: Fig. 209.]

The curves for a United States standard form of thread are obtained in
the same manner as from the $V$ thread in Figure 208, but the thread
itself is more difficult to draw. The construction of this thread is
shown in Figure 208, it having a flat place at the top and at the bottom
of the thread. A common $V$ thread has its sides at an angle of 60
degrees, one to the other, the top and bottom meeting in a point. The
United States standard is obtained from drawing a common $V$ thread and
dividing its depth into eight equal divisions, as at _x_, in Figure 208
_a_, and cutting off one of these divisions at the top and filling in
one at the bottom to form flat places, as shown in the figure. But the
thread cannot be sketched on a bolt by this means unless temporary lines
are used to get the thread from, these temporary lines being drawn to
represent a bolt one-fourth the depth of the thread too large in
diameter. Thus, in Figure 208 _a_, it is seen that cutting off
one-eighth the depth of the thread reduces the diameter of the thread.
It is necessary, then, to draw the flat place on top of the thread
first, the order of procedure being shown in Figur