Ritz’s Solution for Flat Plates. 
391 
1911-12.] 
With these values the following twelve values of £ and y were 
calculated for xfa or yja= 1/8, 1/4, 3/8, 1/2: — 
x/a = 
•125 
•25 
•375 
•5 
= y/a. 
h 
£3 
£5 
- 0-28234 
- 1-03858 
-1-50244 
- 0-86278 
- 1-38050 
+ 0-52790 
-1-36283 
+ 0-11758 
+ 0-78600 
- 1-58425 
+ 1-24600 
-1-41400 
Vi 
3 
By combining these in various ways we can readily calculate the 
values of z/l corresponding to particular values of x and y. The following 
table gives these values for sixteen points in the quadrant of the square 
plate : — 
yfa. 
Values of z/l for various points x/a , y/a. 
•5 
0-34140 
0-95259 
1-4043 
1-5915 
•375 
0-30950 
084078 
1-2335 
1 -4043 
•25 
0-21357 
0-57696 
0-84078 
0-95259 
•125 
0-07868 
0-21357 
0-30950 
0-34140 
•125 
•25 
•375 
•5 
=x/a 
For purposes of comparison with Mr Crawford’s measured results, 
these numbers were divided by T5915, so that the maximum deflection 
at the centre of the plate was unity. It will suffice to calculate to three 
significant figures. The results are as follows : — 
y/a. 
Proportionate values of deflection. 
•5 
•215 
•599 
•883 
1-000 
•375 
•195 
•528 
•776 
•883 
•25 
•134 
•363 
•528 
•599 
•125 
■050 
•134 
•195 
•215 
•125 
•25 
•375 
•5 
=x/a 
It is useful to draw the graphs corresponding to these rows or columns 
of numbers, so as to interpolate for other values of x and y. Since the 
plate is clamped along each edge, each graph must begin tangential to 
the axis ; and, since the central deflection is a maximum point, and the 
form of the bent plate is symmetrical about each diameter parallel to the 
sides, each graph must finish tangential to the axis. Guided by these 
