In consequence of the previous consideration on the properties of a partirrular five-dimensional spare ussociuted with the electron. we derive another field equation for the usual spare-time world V₄ in such a way that it involvey only the etfects of an external field. We also derive an equation which is formally identical with the SchrÖdinger equation. An interpretation of the wave-function is given us representing √E : E₀, where E and E₀ are the values of enorgy-denuity in the clectron as observed in V₄ and V₄ respertively, the latter being the world transformed so as to exelude the effects of the external field. The requiernent of flniteness and continuity of the solution of our wave-equation provides diaerete valuen of energy-density in the electron. a result quite similar with the ease of a hydnigen-like atom. Thin Pug rift the signifleance of quantization as intimately conneeted with the inner ntmeture of the eleetron

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In this paper the thermo-diseriation of atorn-nueleus is re-examined In tale light of wave meehauies Nevertheless the authors conelusions formerly obtained hold good except for minute points. Dividing the process of nuclear dissociation into three classes. it is shown that the final product at extremely high temperatures is a-particles protans and electrons. Further it is pointed out that the thermie origin ad heat-supply of a star either from the nuclear therme-recombination of elements or fntaa the annihilation rd protcaas and eleeetmras in the regenerated state is untenable. to explain the lung life of stars

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The paper ineludes goine- experiniental invertigations on the varlations of the negative thermionic enriesion power of Wehnelt filament due to an auxiliary filament of heated platinum and etc. The mutt important effect eras a considerable general deerease of the erission power

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A simple proof of Kakeya's theorem. Fume theorems analogous to Kakeyau when the coefficients of an algebraie equation are complex

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