II. Note on the present state of the theory of thin elastic shells

In a paper read before the Royal Society in February, 1888, and published in ‘ Phil. Trans.,’ A, of that year, I advanced a theory of the mode of deformation that takes place when a thin shell is vibrating. The theory was founded on the form of the potential energy function, obtained by a method adapted from that of Kirchhoff for plates. It appears that, in case there are no surface-stresses on the faces of the shell, this function consists of two terms, of which one contains a certain function W2 and the thickness 2h as factors, and the other contains a function W1 and h3 as factors. The term W3 depends entirely on quantities σ1, σ2, w, expressing the extension of the middle surface, while the form given for W1 contained only quantities expressing the changes of curvature. Some previous theories proceeded as if W1 alone occurred, and, in fact, this was the case with a paper by Lord Rayleigh in ‘Proceedings of the London Mathematical Society,’ vol. 13, 1882, on the “Infinitesimal Bending of Surfaces.of Revolution.”