"[S]uppose a uniform thin-walled hemisphere... is subjected only to its own weight, and is supported round its [base] by forces which produce compressive stresses σ. If the shell has radius a and thickness t, and the material has unit weight ρ, then [the force applied to the base is equal to the weight of the structure, where 2\pi a is the circumference and 2\pi a^2 is the surface area of the hemisphere]\sigma(2\pi at) = \rho(2\pi a^2t) or [dividing by 2\pi at] \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \sigma = \rho aThus the compressive stress necessary to support the dome has a magnitude independent of the thickness of the dome. ...Now the expression \rho a ...is typical of the order of magnitude of stresses in more general shapes of shell... [I]t may be expected that externally applied loads will at most equal, and will usually be less than the self-weight loads of shells of reasonable size. ...Thus stresses resulting from snow or wind may be expected to be of the same order as those resulting from dead load."