A numerical simulation of quenched QCD on a 24\ifmmode\times\else\texttimes\fi{}12\ifmmode\times\else\texttimes\fi{}12\ifmmode\times\else\texttimes\fi{}24 lattice at $\ensuremath{\beta}=5.9$ is used to calculate the electric and magnetic form factors of the baryon octet. General forms of the baryon interpolating fields are considered. Magnetic moments, electric radii, magnetic radii, and magnetic transition moments are extracted from the form factors. The electric properties are found to be consistent with a quark-model picture involving spin-dependent forces. The lattice results for the magnetic properties show a mass and spin dependence of the effective quark moments which is not accounted for in conventional quark models. Lattice calculations underestimate the magnitude of electric radii, magnetic radii, and magnetic moments compared to experimental measurements. The finite volume of the periodic lattice may be responsible for the discrepancies. The pattern of electromagnetic radii in the lattice results are seen to be generally reproduced in the model results that are considered. The only exception is that of ${\ensuremath{\Xi}}^{\ensuremath{-}}$ which proves to be a sensitive probe of the quark dynamics. Lattice calculations indicate a positive value for the normalized square magnetic radius in ${\ensuremath{\Xi}}^{\ensuremath{-}}$ which contrasts Skyrme model results. Ratios of the magnetic moments allow a more detailed comparison with the experimental measurements. The lattice calculations are seen to better reproduce the experimental ratios than the model calculations.