Page:The Kinematics of Machinery.djvu/185

 Rh of twelve teeth the flanks become radii. This occurs if O C′ = the pitch x 6/π sin 75°. A closer examination shows this construction to be identical with that given in Fig. 116, when equal constants are used. R′ C′and R″ C″ are the diameters of our auxiliary centroids, which are here dotted so that the constructions may  118. be compared; the points C′ and C″ correspond to of a′ and b′, P and Q are found as before. Willis himself recognised and mentioned this coincidence.

§ 37

Seventh Method.—The Centroids themselves as Profiles of Elements. If we suppose the auxiliary centroids of the method of § 32 to be closed figures, and to be made smaller and smaller until they Rh