238 Proceedings of the Royal Society of Edinburgh. [Sess. 
some of the groups being even just at the point of rupture. This view, 
of course, is supported by all the phenomena of “ after-action ” or slow 
recovery from set. 
§ 9. Consider molecular groups or small crystalline groups, all of one 
type, which break their configuration whenever the shear to which they 
are subjected exceeds a value (p 0 : and regard those which are contained in 
unit length of a cylindrical shell, of radius r and thickness dr, of the 
material of a wire. When the wire is twisted, say to the right, groups 
which, in the initial state of internal equilibrating stresses, were already 
sheared to the limiting extent 0 O , instantly break down ; and any group, 
already sheared to the right to the extent ( 1 — m)0 o , breaks down when 
the shear m<£ 0 is attained. If 0 be the angle of twist per unit length of 
the wire, the material of the cylindrical shell is sheared to the extent 
< p = rO . So, if f"(m(p 0 )d(m(p 0 ) be the number, per unit volume, of the 
groups which break in the range d(m<p 0 ), the total number breaking in 
unit length of the cylindrical shell is 2i j^drf"(m(j> Q )d(m<p 0 ). These would 
again break and retake their original position if a negative shear (1 — m)<p 0 
were imposed. Rupture would again ensue, according to our postulate, if 
the positive shear m0 o , or the negative shear (1 — m)(p 0 (measured of course 
from the initial position of equilibrium as zero), were exceeded by any 
integral multiple of 0 O . 
After, say, positive shear to any extent less than or exceeding (p 0 , if the 
twist be again reduced, a position of positive set will be found somewhere 
between the greatest integral multiple of 0 O attained and the next greatest. 
But, if we first limit the investigation to a material constituted of only 
one type of groups, and also limit it to cases in which the set does not 
form a large fraction of the total distortion, we need only consider at most 
one integral multiple of 0 O in the shear. 
When, after a positive excursion of any magnitude, say exceeding 
Q 0 = ( p 0 /r, the twist again becomes zero, the distribution of groups is /"(m0 o ) 
due to groups which were initially distorted to the positive side, together 
with f"(l — m) (p 0 due to groups initially distorted to the negative side; 
and all of these are pulling the wire towards the positive position of set. 
The condition is now such that in any motion on the positive side of the 
initial zero, provided that the shear be not exceeded and that no negative 
displacement occur, absolutely no dissipation of energy will take place in 
so far as these groups are concerned. Farther, if a negative shear q<p 0 is 
now made (g<l), any motion involving shear between the limits (1 — q)(p 0 
and q<p 0 on the positive and negative sides respectively, will take place with- 
out dissipation of energy. The material could oscillate about the 'position 
