of Edinburgh, Session 1871-72. 
575 
Monday , 18£/i December 1871. 
Sir ROBERT CHRISTISON, Bart., President, in the Chair. 
The following Communications were read : — 
1. On the Computation of the Strengths of the Parts of 
Skeleton or Open Structures. By Edward Sang. 
The first part of the paper is devoted to the computation of the 
strengths of the parts of a structure destined to resist given 
strains, taking into account, along with those strains, the unknown 
weights of the parts. The results obtained by this process neces- 
sarily give the best possible arrangement of the strengths, since, if 
any one part were made weaker, the whole structure would be 
weakened; or, if a part were made stronger, the unnecessary 
weight thus thrown upon the other parts would also go to weaken 
the fabric. It is believed that this investigation has now been 
given for the first time. 
It was pointed out that this method enables us to determine the 
utmost limit of magnitude of a structure having a given general 
configuration. 
The second part concerned deficient or flexible structures ; the 
mode of discovering the relations among the applied pressures, 
needed to cause the structure to assume a prescribed form, was 
indicated. 
Thirdly, the case of redundant structures was gone into. It 
was observed that the absolute strains on the parts of such struc- 
tures depend, not merely on their form, but also on the manner of 
putting them together. The changes on these strains caused by 
additional loads can, however, be computed by considering the 
compressions or distensions of the parts; and it was pointed out 
that the computation of these changes has been mistaken for that 
of the absolute strains. 
Lastly, there was investigated a new general theorem, which 
may be stated as follows : — 
When we apply a pressure to some point of a flexible system, 
