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The α‐dispersion in many polymer systems is the process to be associated with the glass transition temperature where many physical properties undergo drastic changes. We have measured and analyzed the complex dielectric behavior of the α‐dispersions for five polymers [i.e., polycarbonate and polyisophthalate esters of bisphenol A, isotactic poly‐(methyl methacrylate), poly(methyl acrylate), and a copolymer of phenyl methacrylate and acrylonitrile] and have found that the usual methods of analysis cannot be used to represent the data. However, it is possible to represent the relaxation process as the sum of two dispersions but there is no evidence to support this contention. An empirical expression is proposed to represent the data. This expression which takes the form of appears to be a general representation for the three known dispersions, i.e., Debye, circular arc, and skewed semicircle. The complex dielectric constants calculated with the aid of this expression and the parameters for each polymer system which was determined graphically were found to be in excellent agreement with the experimental complex dielectric constants. This method of representation was extended to sixteen α‐dispersions reported in the literature always with excellent results.

Recent publications have suggested that the satisfaction of a principle we call kinetic balance can provide variational safety in Dirac calculations. The theoretical foundation for this proposal is examined, first in simple one-electron problems, and then (less rigorously) in SCF calculations. The conclusion is that finite basis calculations using kinetic balance are safe from catastrophic variational collapse, but that the ‘‘bounds’’ provided by these calculations can be in error by an amount of order 1/c4. The bounds are applicable to total SCF energies, but not to SCF orbital energies. The theory is illustrated by a series of one-electron calculations.

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