Measurement of reactor period at low power levels (from 10-10 to 10-5 of full power) during start-up is desirable to permit the full power level to be reached rapidly yet safely. At low flux levels, it is natural to attempt to obtain period information by differentiating the output of a logarithmic counting-rate meter. Because of the random arrival of pulses at the input of the system, however, the period indicated at the output will fluctuate about the correct value, the magnitude of the fluctuation depending upon the average counting rate and upon the system parameters. If the diode in the logarithmic circuit is replaced for incremental analysis by an appropriate linear resistor, the magnitude of the output fluctuations can be calculated by applying shot noise theory. These calculations are here carried out for the infinite-period case (constant counting rate), using the counting rate as an independent variable. Experiments were carried out, and the results agreed closely with theory. Although the present study is based on fluctuations occurring when flux is held constant, other work shows the results to be applicable also to flux transients.