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The nature of hysteresis in products such as pneumatic tires, solid tires, and transmission belts is analyzed and the requirements of a laboratory test for evaluating the relative hysteretic characteristics of natural and synthetic rubber stocks are developed. The significance of tmrious definitions of the "hysteresis defect" in rubberlike materials is discussed. A forced resonance vibrator in which rubber samples are deformed in shear at frequencies of 20 to 300 cycles/sec., shear strains of 0.05 to 0.35, and temperatures of -20 to +120°C is described. Experimental results obtained with natural rubber and GR-S gum and tread stocks are presented. The hysteresis index w'1 is found to be nearly independent of dynamic shear strain while the dynamic modulus G decreases moderately with increasing dynamic strain. Neither w'1 nor G depends upon the height to diameter ratio of cylindrical samples. These results are at variance with those obtained by previous investigators who, employing compressive vibrations, have reported marked dependences of both modulus and friction upon dynamic strain and the "shape factor" of tread type stocks. In agreement with previously reported work, G isfound to be independent of frequency and w'1 only slightly dependent upon frequency, for tread type stocks. Results are presented for stocks based on Buna S type copolymers with varying monomer ratio and on N-type Butaprenes, Neoprene, and butyl rubbers.

Nordheim's theory for purely random alloys and Hall's extension for nonrandom alloys in terms of Cowley parameters are further developed and applied to substitutional binary systems. The theory is valid for any degree of order, excepting perfect superlattices. Purely random alloys and nonrandom alloys are shown to possess certain analogies with normal and umklapp processes, respectively. By accounting for those Fermi volume changes with concentration arising when the two atoms are different in size and valence, it is possible to explain the experimental non-parabolic curves of resistivity versus concentration. Applications are made to the cases of the Cu-Au and the Cu-Ni systems rapidly quenched from a high temperature. Results of a limited study of the data for the slowly annealed Cu-Au system are presented, but more experimental measurements of the Cowley parameters are required to test the theory. A few new relations obeyed by the Cowley parameters are given. The work reported here meets certain independent checks carried out by Christy in unpublished calculations on ordering energy.

Functional relations existing between the Fuchs en«gy e and the Madelung energy S for Wigner solids with the usual uniform background replaced by periodic arrays of either Gaussian or Yukawa charge distributions are utilized in a study of electrostatic structural transitions between the cubic lattices. The Wigner' solid (WS) model is composed of a lattice of point charges Q (of either sign) with a neutralizing uniform background. Changing the background of a WS to a displaced lattice of point charges -Q yields the classical Coulomb lattice (CCL). Here