It has been shown that the mean number $B\left(T\right)\mathrm{}$ of discharges during any time $T$ is given by $B\left(T\right)=\int 0^T\mathrm{}[1-p(t\left)\right]a\left(t\right)\mathrm{dt},$ where $a\left(t\right)\mathrm{}$ is the total density of radiation penetrating the tube at the time $t$ and $p\left(t\right)\mathrm{}$ is the solution of the integral equation: $p\left(t\right)=\int {t-\tau }^t\mathrm{}[1-p(x\left)\right]a\left(x\right)d\left(x\right)\mathrm{}$ for $t>\mathrm{}\tau$ and $p\left(t\right)=1-e^{-at}$ for $0<~t<~\tau . B\left(t\right)\mathrm{}$ is explicitly obtained for the case that $a\left(t\right)\mathrm{}$ is constant. In this case it is also shown that $aT=\frac{B\left(T\right)-\eta }{1-\left[B\right(T)-\eta ]\frac{\tau }{T}}, \left|\eta \right|<~\frac{{\left(a\tau \right)}^2}{1-{\left(a\tau \right)}^2} \mathrm{for} a\tau <1.\mathrm{}$

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