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Proceedings of the Royal Society „of Edinburgh. [Sess. 
decided to attack it as fully as possible, and for this he had to bear in mind, 
firstly, that the material chosen for the plates must be nearly homogeneous 
and isotropic ; secondly, that the average results of many plates, of many 
thicknesses and many sizes, must be taken ; and thirdly, that the apparatus 
used for experimental work must correctly interpret the conditions for 
edge clamping or supporting imposed by the theory. 
The author decided to experiment with fixed plates for the reasons that 
it is easier to prevent leakage with fixed plates than with supported ones, 
that fixed plates are relatively more numerous and important in engineering 
than supported ones, and that the edge conditions can be better satisfied 
with fixed plates. It is, however, to be noticed that, should the equations 
for circular fixed plates with uniform load turn out to be true, it is certain 
that the equations for circular plates with load uniform or load concentrated 
at the centre and edge supported, would also be true, as the mathematical 
analysis is similar for them all, and one is derived from the other. 
The objects of the present research may then be stated : — 
1. To find how far the analytical equations for deflection, stress and 
strain, could be verified by experiment for the circular plate. 
2. To find whether the equations given by Grashof for square and 
rectangular plates were near the truth. 
3. To give a practical analysis of curvature for square and rectangular 
plates. 
4. To throw some light on the question as to whether the elastic 
strength of the plate was determined by the maximum principal stress or 
the maximum principal strain. 
In connection with 4, Grashof assumed that the elastic strength of 
the plate was proportional to the maximum principal strain, though in 
many works which quote his results this value, Ee x (or Young’s modulus 
multiplied by the maximum strain in the direction of x), is incorrectly 
given as the maximum principal stress. 
In the following sets of experiments, close upon one hundred plates were 
used, and as these were distributed over circular, square, rectangular, and 
elliptical forms, with fixed edges only, the abundance of the results allows 
of an average being struck, and the author believes that the figures arrived 
at are as near the truth as experiments on this type of problem can be 
expected to be. In addition, the numerous results allow of many interesting 
points being noted, such as the effect of slightly loosening the clamped 
edges, the change of slope of the permanent set curves for circular plates, 
and the zero error and its causes at the origin. 
In most experiments recorded, a hydraulic pump was employed to 
