d within the respective pitch circles, and circles R
and R' are marked in. The pitch circles are divided off into as many
points of equal division, as at _a_, _b_, _c_, _d_, _e_, etc., as the
respective wheels are to have teeth, and the thickness of tooth having
been obtained from the scale, this thickness is marked from the points
of division on the pitch circles, as at _f_ in the figure, and the tooth
curves may then be drawn in. It may be observed, however, that the tooth
thicknesses will not be strictly correct, because the scale gives the
same chord pitch for the teeth on both wheels which will give different
arc pitches to the teeth on the two wheels; whereas, it is the arc
pitches, and not the chord pitches, that should be correct. This error
obviously increases as there is a greater amount of difference between
the two wheels.

The curves given to the teeth in Figure 234 are not the proper ones to
transmit uniform motion, but are curves merely used by draughtsmen to
save the trouble of finding the true curves, which if it be required,
may be drawn with a very near approach to accuracy, as follows, which is
a construction given by Rankine:

Draw the rolling circle D, Figure 237, and draw A D, the line of
centres. From the point of contact at C, mark on D, a point distant from
C one-half the amount of the pitch, as at P, and draw the line P C of
indefinite length beyond C. Draw the line P E passing through the line
of centres at E, which is equidistant between C and A. Then increase the
length of line P F to the right of C by an amount equal to the radius A
C, and then diminish it to an amount equal to the radius E D, thus
obtaining the point F and the latter will be the location of centre for
compasses to strike the face curve.

[Illustration: Fig. 237.]

[Illustration: Fig. 238.]

Another method of finding the face curve, with compasses, is as follows:
In Figure 238 let P P represent the pitch circle of the wheel to be
marked, and B C the path of the centre of the generating or describing
circle as it rolls outside of P P. Let the point B represent the centre
of the generating circle when it is in contact with the pitch circle at
A. Then from B mark off, on B C, any number of equidistant points, as
D, E, F, G, H, and from A mark on the pitch circle, with the same
radius, an equal number of points of division, as 1, 2, 3, 4, 5. With
the compasses set to the radius of the generating circle, that is, A B,
fro