A more intuitive and modern way to compute a small-sample confidence interval for the mean of a Poisson distribution

Small-sample confidence intervals for the mean of a Poisson distribution have been used since the 1930s. They can be computed by trial and error, or using a computation-saving link that few are aware of and that, even if they are, is neither intuitive nor easy to remember. I trace how and why this link has been used, even if the basis for it has been lost or ignored. I promote a direct and more meaningful link that can be easily used today without having to resort to tables or approximations suited to hand calculators. More importantly, this (time-based) link is instructive and intuitive, and thus more easily derived and understood.