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In this paper it is shown that the statistical theory of the distribution of extreme values is pertinent to the study of the way in which the breakdown strengths of paper capacitors depend on capacitor size. The theory presented in this paper permits a quantitative explanation of this phenomenon and results are given which should be useful to design engineers.

The dynamic Young's moduli of various types of paper were measured by the vibrating reed method. The Young's modulus of paper increases statistically at a rate approximately proportional to the square of its density. The modulus and density of paper increase with the degree of beating. The sulfite and sulfate fibers behave differently during beating. The angular dependence of Young's modulus, tensile strength, and elongation at break was analyzed mathematically; and the results were verified by experiments. According to this theory, the mean value of Young's modulus and tensile strength of machine‐made paper should be expressed by the geometrical mean of the values of the machine and cross directions, whereas the mean value of elongation can be given by the arithmetical mean. The removal of parenchyma cells is very effective in reducing the Young's modulus of dissolving pulp. The viscoelastic properties of paper were observed within the frequency range from 20 to 180 cps. The dynamic modulus and mechanical loss factor of the sheets employed were found to be smaller than one‐tenth of those of cellulose films. The interfiber deformation influences the dynamic properties of paper.

A stress‐strain analysis of single cubic crystals is developed which utilizes the strain data supplied by the x‐ray back‐reflection divergent beam method. The principal strains and their directions are determined and from the principal strains and the known elastic constants the complete stress‐strain configuration is obtained. Thus the maximum magnitude and the direction of the shearing strain on a given set of crystallographic planes are obtained and the set of planes on which the maximum value of the shearing maxima occurs is also determined. From a knowledge of the stress‐strain configuration, the stored elastic energy of the crystal is deduced; it can be partitioned into two components, that due to shearing strains and that due to a mixture of normal and shearing strains.The conditions under which the principal stress system coincides with the principal strain system are also investigated. Furthermore, a number is constructed that measures the distortion of the crystal in terms of the energy incremen...

An infinite sum transformation is defined and applied to a system of linear difference equations discussed by Faust and Beck in their paper on single tuned amplifiers. Some transforms of the more common functions are given and points of superiority of the transform method over the classical methods of solution of difference equations are emphasized.