362 
Proceedings of the .Royal Society of Edinburgh. [Sess. 
it beyond all doubt by corroborative proof, if that was possible, and for 
this purpose it was necessary to fix within a few pounds at what pressure 
permanent set commenced in the plate. This was accomplished by measur- 
ing the pressure at which permanent set at the centre began. 
Note on the Value of Permanent Set at the Centre as indicative of 
the Minutest Overstrain. 
The question naturally arose as to whether, if set occurred at any point 
in the plate, it would be observed to the greatest degree by the alteration 
in the no-load deflection reading at the centre. Many experiments 
performed always gave a positive result, i.e. set was always first observed 
at the centre ; not necessarily that set commenced at the centre, but that its 
results were observed there first. To see why this should be so requires 
some consideration, and for the purpose it is useful to think of a beam 
fixed at both ends and loaded uniformly. Suppose for the sake of illustra- 
tion that the load is such that the outside fibres near the ends have passed 
the yield point and that the remainder of the beam is perfectly elastic. 
The bottom fibres are in tension and the top in compression at the end. 
Now, if the load is removed, the strained portion will not shorten to its 
original length, but will remain somewhat longer, with the result that the 
beam cannot become quite horizontal again, but will in its no-load state 
become slightly concave upwards. This concavity will be helped by the 
fact that the under side of the beam near the ends has passed its yield 
point on the compression side. The effects of concavity will be greatest at 
the centre. As more and more load is applied to the beam, the number of 
fibres that pass the yield point becomes greater and greater, and the no-load 
concavity increases proportionately. But when a certain pressure has been 
reached, the fibres at the centre begin to pass their yield points (because 
the maximum stress is not reached at the centre till later than at the ends), 
but in this case the top fibres are in tension, and the bottom in compression. 
When this point is reached there is then a kind of neutralising action, and 
the amount of concavity does not increase proportionately, and may even 
decrease a little. After a time, however, when most of the fibres have 
yielded, the concavity again increases. This reasoning is borne out by a 
consideration of the permanent set curves of circular plates. Diagram 5 
gives such a curve. It will be noted that “ set ” increases gradually and 
proportionately for a time, then increases at a faster rate, then suddenly 
remains stationary. It is suggestive that this is owing to the neutralising 
action above referred to, and it is further suggestive that the method of 
taking the differences in the no-load deflection at the centre is a most 
