With the aim of using it in mass spectrometry, we have tried to find an axisymmetric electrostatic system with very particular characteristics, viz. reduced spherical and chromatic aberrations. We chose a system made up of three coaxial cylinders of radius ρ. The inner electrode is 0.90 ρ long and is separated from the outer cylinders (which are taken to be of infinite length) by two identical gaps of 0.40 ρ. This system has been studied from both the mirror and the lens point of view. The mirror is studied using two electrostatic parameters. The potentials of the three cylinders are reffered to as V1, V2, and V3. The first parameter used is Rd=100 (V1-V2)/(V1-V3) and the second is V3/V1. For six values of Rd, ranging from 100 to 74, we examine the paraxial characteristics and the coefficients of spherical and chromatic aberration as a function of V3/V1. We only deal with the area where the mirrors are convergent and where the radii of curvature do not exceed 10ρ. For the values of Rd studied, other than 100, we use a field of variation from -0.10 to -0.50 for V3/V1. When we study the lens, we deal with the area where the outer potentials V1 and V3 are identical. There is thus only one variable, the ratio V2/V1 of the potentials of the first two cylinders. We consider two cases: V2/V1≳1 and V2/V1≪1. Among the results obtained, we have chosen two groups of mirrors for which the chromatic aberration coefficient Cc is null and whose radii of curvature are greater than 6.60 ρ, a group of mirrors for which the spherical aberration coefficient Cs is null and where Cc is greatly reduced (here the radii of curvature are greater than- 4.00 ρ), and a mirror for which both Cc and Cs are null and which has a radius of curvature of 7.28 ρ.