392 Proceedings of the Royal Society of Edinburgh. [Sess. 
considerations, we may draw the graphs with an accuracy as great as the 
numbers given. 
Taking, then, Mr Crawford’s measured deflections along a diameter in 
each of his three square plates, and reducing them all so that the central 
deflection is unity, we get the following comparison between experiment 
and Ritz’s formula : — 
Distance 
from centre. 
Experiments. 
Ritz’s 
formula. 
o-oo 
1 
1 
1 
1 
0-08 
0-95 
0-90 
0-95 
o-i 
0-96 
0-92 
0-17 
0-82 
0-79 
0-80 
0-2 
0-75 
0-73 
0-25 
0-39 
0*63 
0-60 
0 3 
0*44 
0-45 
0-33 
0-35 
0 37 
0-38 
0-4 
0*17 
0-14 
0-42 
0-12 
0*17 
0-09 
0-5 
0 
0 
0 
0 
For two of the plates Mr Crawford gives a series of deflections along 
the diagonal. Taking these values and reducing as in the other cases, 
we find the following comparison : — 
Distance from 
centre. 
Deflections. 
Experiments. 
Ritz’s formula. 
0 
1 1 
1 
0-08 x V2 
0-89 
0-892 
0-1 x V2 
0-875 
0-85 
0-167 x \/2 
0-62 
0-626 
0*2 x V2 
0-542 
0-52 
0 - 25 x \J2 
0-34 
0-366 
0'3 x x/2 
0-187 
0 22 
0-333 x V2 
012 
0-14 
0-4 x a/2 
0-083 
0-02 
0-415 x \/2 
0-02 
o-oi 
0*5 x V2 
0 
0 
The agreement throughout is, in the circumstances, quite satisfactory, 
and establishes the adequacy of Ritz’s formula. 
{Issued separately September 9, 1912.) 
