As measures to determine the performance of log N period meters, use can be made of (a) fluctuations due to statistical data from the detection process, (b) power overshoot due to scram delay, and (c) transient overshoot during a given period. While (a) is related to the time constants by a simple analytical expression, evaluation of (b) and (c) requires numerical calculation. This paper presents convenient formats for data sheets to be used in evaluating the performances (b) and (c) accompanying exponentially increasing power. The parameters are chosen as follows: (a) Inverse period of exponentially increasing power normalized with reference to scram level, (b) time constant of the period meter similarly normalized, and (c) initiating time constant of log N amplifier normalized with reference to period meter time constant. The following behavior has been noted: (a) When the margin of power overshoot is the preponderant factor, evaluation of the transient initiated at a high power is enough, (b) the transient overshoot represented in terms of inverse period has a maximum at a certain period meter time constant. Using these data sheets, the constants, commonly used in reactor instrumentation in Japan have been rescrutized, and proposals presented on the necessity and the possibility of revising them.