Starting from the work of Guernsey on the system of the two first equations of the BBGYK hierarchy, we show that an approximate solution of these equations may be found in the limit of high frequency or short wave length, and we derive general expressions for the longitudinal dielectric constant ε (k, ω) of the plasma. Limiting cases are considered: zero frequency [equilibrium quantities are derived from ε (k, 0)]; and frequencies much higher than the inverse relaxation time.