434] THE THEORY OF SCREWS IN NON-EUCLIDIAN SPACE. 481
It seems at first sight incredible that a theorem demonstrated with such
simplicity should be of so much significance. It is not too much to say
that the theory of Rigid Dynamics in non-Euclidian space depends, to a
large extent, upon this result. This is the second of the two fundamental
theorems referred to in § 396.
These two principles open up a geometrical Theory of Screws in non-
Euclidian space. This is a subject too extensive to be here entered into any
further. It is hoped that the present chapter will at least have conducted
the reader to a point from which he can obtain a prospect of a great field of
work. The few incursions that have as yet been made into this field (see the
bibliographical notes) have shown the exceeding richness and interest of a
region that still awaits a more complete exploration.
B.
31