114 
Proceedings of the Royal Society 
importance. As the details of the investigations will soon be pub- 
lished, a very brief sketch only is given here. 
I. Twist of a wire. If a straight wire, of uniform section, have 
a side line of reference traced on its surface parallel to its axis ; 
and if a perpendicular to this line from any point of the axis be 
called a transverse^ the amount of torsion or twist of the wire, when 
bent into any form, may be determined by the following con- 
struction : — 
Parallel to the tangent to the axis of the wire, at a point moving 
along it, let a radius of an unit sphere be drawn, cutting the 
spherical surface in a curve. From points of this curve draw 
parallels to the transverses at the corresponding points of the bar. 
The excess of the change of direction from one point to the other 
in the curve, above the increase of its inclination to the transverse, 
is equal to the twist in the corresponding part of the wire. 
From this some very curious consequences follow, of which one 
is as follows : — If a wire be bent along any curve on a spherical 
surface, so that a side line of reference lies all along in contact 
with the sphere, it acquires no twist ; so that when an apple (sup- 
posed spherical) is peeled, there is no twist in the peel. 
Again, if an infinitely narrow ribband be laid on a surface along 
a geodetic line, its twist is at every point equal to the tortuosity of 
its axis. 
II. Griven any material system at rest, and subjected to an 
impulse of any given magnitude and in any specified direction, it 
will move off so as to take the greatest amount of kinetic energy 
which the specified impulse can give it. 
Cor. If a set of material points be struck independently by 
impulses, each given in amount, more kinetic energy is generated 
if the points are perfectly free to move each independently of all 
the others than if they are connected in any way. 
III. Griven any material system at rest. Let any parts of it 
be set in motion suddenly with given velocities, the other parts 
being influenced only by their connections with those which are 
set in motion, the whole system will move so as to have less 
