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 structure exhibit a scaling law of Hˆ1/4. 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. ¿American Geophysical Union 1990