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 necessarily 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.