It has been predicted that the nonlinear particle dynamics in the magnetotail leads to a class of resonance structures in the quiet‐time ion distribution functions in the Central Plasma Sheet. These structures exhibit a scaling law of . In this letter, we report the first identification of such a scaling law in quiet‐time CPS distribution functions obtained aboard ISEE 1. We propose a method which uses the observed resonance structures to determine the quiet‐time current sheet thickness based on a measurement of the distribution function and magnetic field obtained by one satellite. Copyright 1990 by the American Geophysical Union.