necessary condition of multiple connectivity is carried out by vortex filaments containing rotation trailing from the ends of each blade.
There will need to be as many cyclic systems as there are blades, so that if there are n blades the region will require to be n-ply connected. In the case, for example, of a two-bladed propeller the two cyclic paths are represented in Fig. 134 by
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| Fig. 134. | Fig. 135. |
the two circuits drawn round the blades; the trailing vortices are shown diagrammatically.
It is possible that the inner end vortices are unnecessary, for the boss and shaft may be found to determine the connectivity of the region at the axis end of the blades (Fig. 135).
The vortex filaments are presumed to persist in the region of the wake till they have, metaphorically speaking, "taken root" in the fluid, so that the conditions of multiple connectivity are simulated. It would appear to be only necessary to suppose rotation to become generally distributed (through the agency of viscous stress) in the wake of the propeller to bring about the necessary condition. (Compare Chaps. III. and IV.)
In propellers giving rise to cavitation, or when air is sucked down owing to insufficient immersion, the dependent vortices
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