rves, as F G, may be marked; from the next
centre, as at S, the curves D E may be marked, and so on for all the
faces; that is, the tooth curves lying between the outer circle X and
the pitch circle P. For the flank curves, that is, the curve from P to
Y, the compasses are set to a radius equal to the pitch; and from the
sides of the teeth the flank curves are drawn. Thus from J, as a centre
flank, K is drawn; from V, as a centre flank, H is drawn, and so on.

The proportions of the teeth for cast gears generally accepted in this
country are those given by Professor Willis, as average practice, and
are as follows:

Depth to pitch line, 3/10 of the pitch.
Working depth, 6/10 " "
Whole depth, 7/10 " "
Thickness of tooth, 5/11 " "
Breadth of space, 6/11 " "

Instead, however, of calculating the dimensions these proportions give
for any particular pitch, a diagram or scale may be made from which they
may be taken for any pitch by a direct application of the compasses. A
scale of this kind is given in Figure 235, in which the line A B is
divided into inches and parts to represent the pitches; its total length
representing the coarsest pitch within the capacity of the scale; and,
the line B C (at a right-angle to A B) the whole depth of the tooth for
the coarsest pitch, being 7/10 of the length of A B.

[Illustration: Fig. 235.]

The other diagonal lines are for the proportion of the dimensions marked
on the figure. Thus the depth of face, or distance from the pitch line
to the extremity or tooth point for a 4 inch pitch, would be measured
along the line B C, from the vertical line B to the first diagonal. The
thickness of the tooth would be for a 4 inch pitch along line B C from B
to the second diagonal, and so on. For a 3 inch pitch the measurement
would be taken along the horizontal line, starting from the 3 on the
line A B, and so on. On the left of the diagram or scale is marked the
lbs. strain each pitch will safely transmit per inch width of wheel
face, according to Professor Marks.

[Illustration: Fig. 236.]

The application of the scale as follows: The pitch circles P P and P'
P', Figure 236, for the respective wheels, are drawn, and the height of
the teeth is obtained from the scale and marked beyond the pitch
circles, when circles Q and Q' may be drawn. Similarly, the depths of
the teeth within the pitch circles are obtained from the scale or
diagram and marke