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The aspirations of manufacturers engaged in rolling bearing research are indicated with emphasis on the resultant need for the use of improved mathematical models. Fundamental mathematical tools are discussed covering the Hertz theory of contacting elastic bodies; rolling bearing fatigue and the Weibull distribution; and load distribution among rolling elements. Finally, some current research problems in the areas of generalized shaft-bearing situations and elastohydrodynamic lubrication are outlined.

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The problem of the behaviour of a small aerosol particle (smallgr than the mean free path of gaseous molecules) in a non-uniformly heated gas mixture is examined on the basis of the Chapman-Enskog method. The velocity at which the particle moves through such a mixture is calculated. A numerical computation is made for a CC4+He mixture.Inversion of the particle velocity was observed, i.e., the particle may be attracted to an evaporatiag drop and repelled from a growing one. By way of particular cases the velocity of motion has been found for a particle in an isothermal binary mixture and in a simple non-uniformly heated gas.* This case was also discussed by the same method in a paper 9 published later than our work.4