242 Proceedings of the Royal Society of Edinburgh. [Sess. 
an expression which is not reconcilable with the experimental data 
regarding the loss of energy. 
§ 14. When the angle of oscillation is so small that crystalline groups of 
“ finite ” size do not break down, if the loss of energy becomes proportional 
to the second power of the distortion, it is easy to account for the expo- 
nential law of decrement first established by Kelvin. 
When the angle of oscillation is so large that integral multiples of 0 o 
are included in it, the preceding postulates regarding the action lead to a 
periodic expression for the force, the set being very large. Some experi- 
ments by Mr Stewart, Carnegie Scholar, University College, Dundee, whose 
results are not yet published, seem to indicate the existence of a periodic 
condition even when the set is negligible. It might be negligible, even 
though the shear greatly exceeded 0 O for the groups undergoing rupture, 
provided that another type of groups did not undergo rupture at all. 
If we are to take account of the presence of a continuous series of 
types of groups, we must multiply (10) by if/( S 0 )d6 0 and integrate over any 
range specified. 
Summary. 
1. The oscillations of a viscous wire exhibiting set are simple harmonic 
with regard to the position of set throughout the whole range of the in- 
motion and a considerable part of the out-motion. In the remainder of 
the out-motion the deviation from the simple harmonic condition is great. 
2. The period of in-motion to the zero is distinctly greater than that 
of the out- motion from it. 
3. A theoretical deduction of these results, and of the law of loss of 
energy per oscillation, can be founded on the assumption that that loss 
is due to the rupture of strained molecular (which may be finite crystalline) 
groups. 
4. A sudden change in the oscillation parameters when the decreas- 
ing maxima pass through a definite magnitude is explainable by the 
existence of a dominant type of groups which cease to rupture when the 
decreasing strain reaches a definite value ; and the known peculiar tempera- 
ture and stress effects are explainable as depending on well-recognised 
conditions of structural changes. 
( Issued separately June 6, 1913.) 
