366 
Proceedings of the Royal Society of Edinburgh. [Sess. 
Square and Rectangular Plates fixed at the Edges and under 
Uniform Load on their Areas. 
The experimental work that has been done on these plates seems to be 
very meagre, and there is perhaps nothing in the whole domain of 
mechanical engineering about which so little is known for certain, as the 
stress values in these common forms. 
Recognising, then, that before there could be any certainty with regard 
to the matter, many plates would have to be tested and an average taken, 
the author decided to take up the matter as fully as possible. He had the 
more confidence in the work by reason of the results obtained for the 
circular plate. 
The apparatus used for experimental work with these plates was 
exactly the same as for the circular, with the exception, of course, that the 
duplicate blocks between which the plates were held were of the required 
square or rectangular shape. The squares used were 6 in. by 6 in., 5| in. 
by 5J in., 5 in. by 5 in., 4J in. by 4J in., and 4 in. by 4 in.; the rectangles, 
8 in. by 4 in., 7 in. by 4 in., 6 in. by 4 in., 5 in. by 4 in., and 8 in. by 6 in. 
There were thus five squares increasing regularly in length of side, and five 
rectangles having 4 in. as a basis for the short side, increasing regularly in 
length. These were thought enough to obtain sufficient points to determine 
the variation in stress with size and shape. The thickness of the plates 
also varied between limits which were small absolutely, but fairly large 
relatively ; so that there were variations of size, thickness, and applied 
pressure. 
The Square Plate. 
As in the case of the circular plate, an attempt was first made to see 
how closely experimental central deflections were in agreement with 
theoretical values. The methods of detecting deflections were similar to 
those used for circular forms, and similar types of curves were obtained, 
the three main portions, the zero error, the elastic line, and the dip, being 
again conspicuous. 
Grashof’s formula for the deflection at the centre of a fixed rectangular 
plate is given by : 
_ 1 p IW 
V 32 • Ei 3 ' + 
where l is the length and b the breadth of the plate. 
And for the square plate, where l = b, this reduces to : 
_ 1 pb 4 
