TOOTHED-WHEEL PAIRS. 535
Forms intermediate between the general and the special also occur, such as the pair H, S, which is represented in Fig. 365, and the pair H\K y the plane-hyperboloid and cone, both of which pairs we have mentioned before (pp. 81 and 83). These forms would be indicated by the symbols (?,) and (H f ) respectively, for the screw in Fig. 365 enters the pair because it is a ruled surface, i.e. H, and not because it is a screw S.
The pair (7, C is to be distinguished from the closed cylinder- pair ; this is easily done by using the symbol (#,) for the higher pair. The pair C, P is the special case of ( (7,) when one of the cylinders is of infinite radius. The sign (C, p ) may be used for it, the comma indicating sufficiently that the pairing between C and P is higher.
144. Synthesis of Toothed-wheel Pairs.
We come now to toothed-wheels. These might also be included under the class (JEQ, but the repetitions of the same profile occur
�in them so characteristically that it appears well to treat them as a class by themselves, as it has hitherto been usual to do. It must not be forgotten here that chain-closure does not necessarily