172 
Proceedings of the Eoycd Society 
BUSINESS. 
The following Candidates were balloted for and declared duly 
elected Fellows of the Society: — Dr P. M‘Bryde, P.R.C.P. Ed.; 
Mr G. W. W. Barclay; and Mr Thomas Andrews, E.C.S. 
Monday, lUh April 18 S3. 
Mr JOHN MUERAY in the Chair. 
The following Communications were read: — 
1. On some Properties of the Line of Simple Flexure. 
By Edward Sang, C.E. (Plates 
The unrestricted problem, “ To find the form assumed by an 
elastic system when subjected to known strains,” is one of those 
mechanical problems which haffie the powers even of the modern 
calculus. It is only when the change of form is exceedingly small 
that we can obtain approximate results. In the simplest case — that 
of a straight uniform elastic body — there is, so far as I know, no 
complete solution ; and thus I venture to suppose that the following 
remarks may not be devoid of interest : — 
If a thin flat rectangular plate — a physical line, as it were — be 
bent by means of a string attached to its two ends, it takes a parti- 
cular form, to which the name “ curve of simple flexure ” may be 
given. 
From the nature of the case, it is clear that if ABC represent the 
bent plate and AC the string, the curve must be symmetric from the 
two ends ; so that if B be the middle of the bow and BO the ordi- 
nate therefrom, the two parts AOB, COB must be alike. Farther, 
if a second spring of the sam(3 dimensions, and bent by a string of 
the same length, were placed endways to this one, as at CDE, the 
strings AC, CE being in one straight line, but the bend being on the 
other side thereof, the ends may be conceived as united at C, so as 
to form a continuous elastic plate, while the cord may be supposed 
attached to the two ende A and E. 
The same kind of extension may be continued indefinitely both 
ways ; and thus it follows that the curve of simple flexure is com- 
