4. Quaternion Investigations connected with Minding's Theorem

Abstract

Minding's Theorem deals with what may be called by analogy the “focal lines,” of the system of single resultants of a set of given forces, applied at given points to a rigid body, when these forces are turned about so as to preserve unchanged their inclinations to one another.

Having obtained an exceedingly simple proof of the theorem by quaternions, I next tried to find the locus of the foot of the perpendicular let fall on each of these resultants from the “centre of the plane of centres.” The resulting equation is very complex:— but if we extend the data so as to include every position of the central axis (whether there is a couple or no), we arrive at a very simple, and at the same time singular, result.