(A,
Figure 153) of smaller diameter than the width across the flats of the
bolt-head, the outline of the sides will pass above the arc on the
flats, as is shown in Figure 157, in which the chamfer A meets the side
of the head at B, and does not, therefore, meet the arc C. The length of
side lying between B and D in the side view corresponds with the part
lying between E and F in the end view.

[Illustration: Fig. 157.]

If we compare this head with similar views of a square head G, both
being of equal widths, and having their chamfer circles at an equal
distance from the sides of the flats, and at the same angle, we perceive
at once that the amount of chamfer necessary to give the same distance
between the chamfer circle and the side of the bolt (that is, the
distance from J to K, being equal to that from L to M), the length of
the chamfer N for the square head so greatly exceeds the length A for
the hexagon head that the eye detects the difference at once, and is
instinctively informed that G must be square, independently of the fact
that in the case of the square head, N meets the arc O, while in the
hexagon head, A, which corresponds to N, does not meet the arc C, which
corresponds to O.

When, however, the chamfer is drawn, but just sufficient to meet the
flats, as in the case of the hexagon H, and the square I, in Figure 157,
the chamfer line passes from the chamfer circle to the side of the head,
and the distinction is greater, as will be seen by comparing head H with
head I, both being of equal width, having the same angle of chamfer, and
an amount just sufficient to meet the sides of the flats. Here it will
be seen that in the hexagon H, each side of the head, as P, meets the
chamfer circle A. Whereas, in the square head these two lines are joined
by the chamfer line Q, the figures being quite dissimilar.

[Illustration: Fig. 158.]

It is obvious that whatever the degree or angle of the chamfer may be,
the diameter of the chamfer circle will be the same in any view in
which the head may be presented. Thus, in Figure 158, the line G in the
side view is in length equal to the diameter of circle G, in the end
view, and so long as the angle of the chamfer is forty-five degrees, as
in all the views hitherto given, the width of the chamfer will be equal
at corresponding points in the different views; thus in the figure the
widths A and B in the two views are equal.

[Illustration: Fig. 159.]

If the other vi