The problem of gliding discharges on high voltage equipment is faced in practice, coith inclined interface, such as cable terminations, bushings. Many researches present very important results about the relationship between the applied voltages and this partial discharge . But studies about the insulation systems that have small cross capacitor or that have air gaps are limited, considering many points, one of them: the discharge procedure looks like the partial discharge in insulators, with longitudinal interfaces. Achieving precise relationships for such systems and finding the actual discharge behavior gives high scientific efficiency and important application for design of high voltages devices, especially when high voltages, which are changing with time voltage like alternatring and lightning voltages, are applied.