200 
Proceedings of the Roycd Society 
4. Quaternion Investigations connected with Minding’s 
Theorem. By Professor Tait. 
(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 lind the locus of the foot of the per- 
pendicular 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. 
The locus has then the equation 
p = xf/znf/a, 
where a is a given vector, w a given pure strain, and if/ any rotational 
strain. This represents a volume not a surface. 
In the statical problem 
■za-a = 0 , 
and the locus is the volume included between the two sheets of the 
electric image of a Fresnel's Wave-surface, in which one of the three 
parameters is infinite. This image has the equation 
S P (^ 2 + p 2 ) p = 0, 
a surface whose treatment is easy. But when z*a does not vanish we 
have for the boundary of the locus 
S (p — '&(*.) (w 2 + p 2 ) (p — ®a) = 0 , 
which is by no means so simple. 
Monday, 5 th May 1879. 
Dr BALPOUB, General Secretary, in the Chair. 
The following Communications were read : — 
1. The Pituri Poison of Australia. By Dr Thomas B. Fraser, 
Professor of Materia Medica, University of Edinburgh. 
(Abstract) 
An opportunity for examining the Pituri of Australia was afforded 
to the author by Dr Bancroft of Brisbane, who, in 1877, gave him 
