The curve obtained from this expression gives an excellent fit with the data relating shrinkage of collagen at 50°in 1.0 M KI at pH 2.0 with time (Fig. 6), using values of 1.1 for k and 360 for M. The rate constant k will vary with temperature, nature of the salt used, pH and salt concentration. The constant, M, will vary with temperature, pH, nature of the salt and applied stress.1 2 3•19 By vary-

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Variational principles for expectation values of physical quantites other than the energy are derived. The expressions implicitly require Green's-function estimations, and higher-order corrections are available. One principle involves a subsidiary minimization, and the other involves the difference between two quantities which are minimum at the stationary point; consequently, numerical computations can be made with both of these principles. As a simple example, the mean-square radius of the hydrogen atom for an incorrect wave function is corrected, with excellent results. Application is also made to the meansquare radius of a model triton.