The general theory of the magnetron tubes, as developed in a former paper, showed that the magnetron should sustain oscillations in an outer circuit, when the frequency was nearly √2 times the Larmor's frequency ${\omega }_H$. The present paper contains a more detailed study of the behavior of a magnetron with one cylindrical anode, when the radius $a$ of the filament and $b$ of the anode are both taken into account. It is shown that the magnetron is able to sustain oscillations on the frequency $\omega ={\omega }_H{(2+\frac{2a^4}{b^4})}^{\frac{1}{2}}$ which lies between $\sqrt{2}{\omega }_H$ and $2{\omega }_H$, according to the dimensions of the electrodes. The agreement of this theory with some interesting results obtained by Blewett and Ramo is shown, and the limiting case of the plane magnetron is briefly discussed.

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