Since 1926 investigations of the Dushman reaction have relied mainly upon "constant-rate" measurements, usually by instrumental methods. Since about that time, the confusion surrounding this venerable reaction has been growing. In part, the confusion arises because the reaction involves reactive intermediate species that have not been studied directly-and may never be. Alternative detailed mechanisms have been assumed with little restraint. One of these, which is built around HzIz03, has been explored by computer with promising results.The mechanism seems capable of reducing the confusion now attending the Dushman reaction and others related to it.

An eigenvalue problem encountered in the dynamical theory of chain molecules is ∫ −11α′′(s)(|r−s|)−12ds=−λα(r),α′(±1)=0.This is solved by three methods: use of a Fourier series for α, expansion of α in associated Legendre polynomials Pm2, and by a variation method. The eight smallest eigenvalues are calculated explicitly and an approximate formula is found for the remaining ones. Formulas are found also for the eigenfunctions.

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