  We adopt the continuum limit of a linear, isotropic, homogeneous,
transparent, dispersion-negligible dielectric of refractive index $n$ and
examine the consequences of the effective speed of light in a stationary
dielectric, $c/n$, for D'Alembert's principle and the Lagrange equations. The
principles of dynamics in the dielectric-filled space are then applied to the
electromagnetic Lagrangian and we derive equations of motion for the
macroscopic fields. A direct derivation of the total energy--momentum tensor
from the field strength tensor for the electromagnetic field in a dielectric is
used to demonstrate the utility of the new theory by resolving the century-old
Abraham--Minkowski electromagnetic momentum controversy in a way that preserves
the principles of conservation of energy, conservation of linear momentum, and
conservation of angular momentum.
