62] THE REPRESENTATION OF THE CYLINDROID BY A CIRCLE. 55
but, as in § 58, we have
(pa — TT' + pß — TT’) cos 6 — daß sin 0 = 0;
whence the virtual coefficient is simply,
A N
TT'cos 0 = OG~,
(Jb
and we have the following theorem :
The virtual coefficient of any pair of screws varies as the perpendicular
distance of their chord from the pole of the axis of pitch.
We also notice that the line TF expresses the actual value of the virtual
coefficient.
The theorem of course includes, as a particular case, that property of
reciprocal screws, which states that their chord passes through the pole of the
axis of pitch (§ 58).
62. Another Investigation of the Virtual Coefficient.
It will be instructive to investigate the theorem of the last article by a
different part of the theory. We shall commence with a proposition in ele-
mentary geometry.
Let ABC (Fig. 13) be a triangle circumscribed by a circle, the lengths of
the sides being, as usual, a, b, c. Draw tangents at A, B, C, and thus form
the triangle XYZ. It can be readily shown that if masses a2, b2, c2 be placed