258 Proceedings of the Royal Ii-ish Academy. 



Hence we may, witliout loss of generality, regard the pitch distri- 

 bution to be expressed in the very simple form 



p = tan B tan <^, 



for, when we have obtained this pitch distribution we can pass at once 

 to the other by merely making ;» =tan a tan fi. 



There is one feature on this surface which the analogy of the 

 cylindroid would hardly have suggested, it is the existence of a pair 

 of screws thereon forming conjugate polars, and of which the pitch is 

 indeterminate ; one of these corresponds to ^= and (^ = 90°, the other 

 to ^=90° and (^ = 0. 



Much remains to be done before the theory of this surface is com- 

 plete in its dynamical applications ; but I have thought that the points 

 referred to in this Paper are of sufficient interest to justify their com- 

 munication to the Academy, in anticipation of a more complete treat- 

 ment of the subject at a future time. 



