  Eisenhart's classical unified field theory is based on a non-Riemannian
affine connection related to the covariant derivative of the electromagnetic
field tensor. The sourceless field equations of this theory arise from
vanishing of the torsion trace and the symmetrized Ricci tensor. We formulate
Eisenhart's theory from the metric-affine variational principle. In this
formulation, a Lagrange multiplier constraining the torsion becomes the source
for the Maxwell equations.
