A detailed study has been made of the elastic scattering properties of the Thomas-Fermi atom for low-energy electrons. The scattering lengths have been determined for essentially all atoms in the periodic table within the framework of the Thomas-Fermi approximation. The scattering length is not a monotone function, but rather a periodic (roughly) function of the atomic number of the scattering atom. Both positive and negative scattering lengths are found. The effect of the sign and magnitude of the scattering length on the shape of the cross section versus energy curve is studied. It is observed that atoms with negative scattering lengths have very low cross sections for some energy of the incoming electrons; such is not the case with all atoms having positive scattering lengths.