In the course of some remarks on the scheme proposed for the Forth Bridge, which remarks are published in the eleventh volume of the Transactions of the Royal Scottish Society of Arts, I was led to enunciate, among other theorems, one of a somewhat unexpected character, to the effect that any symmetric structure built on a rectangular basis, having no redundant parts, and depending on longitudinal strain alone, is necessarily unstable. This theorem was established by arguments restricted to the single matter under consideration; it is one of an extensive class, and I now propose to discuss the subject from a general abstract point of view.