In the standard treatments of aberration coefficients of electron lenses, deviations from perfect imagery are expressed as power series of the ray coordinates in the object and aperture planes. The resulting aberration coefficients depend on the object and aperture positions, and a complete description of the aberrations of an electron lens would require a doubly infinite set of aberration coefficients for each voltage ratio of the lens. Hawkes has carried out a general treatment of the third-order aberrations of electron lenses which is independent of object and aperture positions. Six quantities are sufficient to specify the third-order aberration properties of an electron lens. We have derived equations for these six quantities in the form of integrals, involving derivatives of the axial potential no higher than the second, and using our previously calculated potentials have computed aberration coefficients for the two-tube electrostatic lens.