The unrestricted problem, “To find the form assumed by an elastic system when subjected to. known strains,” is one of those mechanical problems which baffle 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:—