In this paper, a recently constructed apparatus for measuring electron scattering cross sections while applying a strong axial magnetic field is utilized for determining total scattering cross sections. The first molecules studied with this setup are pyrimidine (1,3-diazine) and pyrazine (1,4-diazine), whose total cross sections are obtained for the incident electron energy range of 8-500 eV. Quite good agreement with earlier theoretical predictions is found after accounting for the angular acceptance (angular resolution for forward scattering) of the apparatus. However, no other experimental total cross sections for electron scattering from pyrimidine or pyrazine have been found in the literature for comparison.